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values","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"8.D1.2","language":"en","educationLevel":["08"],"lastChangeDateTime":"2020-12-24T17:27:46+00:00"},{"identifier":"29bd04c0-4608-11eb-8311-15afa0e8d82c","uri":"https://opensalt.net/uri/29bd04c0-4608-11eb-8311-15afa0e8d82c","fullStatement":"create an infographic about a data set, representing the data in appropriate ways, including in tables and scatter plots, and incorporating any other relevant information that helps to tell a story about the 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values","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"8.C1.1","language":"en","educationLevel":["08"],"lastChangeDateTime":"2020-12-24T17:01:18+00:00"},{"identifier":"29beec5e-4608-11eb-8178-f121f5b404ff","uri":"https://opensalt.net/uri/29beec5e-4608-11eb-8178-f121f5b404ff","fullStatement":"Patterns","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["08"],"lastChangeDateTime":"2020-12-24T17:00:55+00:00"},{"identifier":"29bec3f0-4608-11eb-8ae8-87651d9c38ee","uri":"https://opensalt.net/uri/29bec3f0-4608-11eb-8ae8-87651d9c38ee","fullStatement":"identify, describe, extend, create, and make predictions about a 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course.","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:48:50+00:00"},{"identifier":"3f757668-46ed-11eb-bbbe-ddf30c446efd","uri":"https://opensalt.net/uri/3f757668-46ed-11eb-bbbe-ddf30c446efd","fullStatement":"Manipulating Expressions and Solving Equations","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:48:27+00:00"},{"identifier":"3f75e512-46ed-11eb-b5bf-fbaf976bae3b","uri":"https://opensalt.net/uri/3f75e512-46ed-11eb-b5bf-fbaf976bae3b","fullStatement":"relate their understanding of inverse operations to squaring and taking the square root, and apply inverse operations to simplify expressions and solve equations","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.B2.3","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:48:58+00:00"},{"identifier":"3f763058-46ed-11eb-97c7-47cd7cfb7c68","uri":"https://opensalt.net/uri/3f763058-46ed-11eb-97c7-47cd7cfb7c68","fullStatement":"add and subtract polynomials with up to two variables [e.g., (2x \u2013 5) + (3x + 1), (3x\u00b2y + 2xy\u00b2) + (4x\u00b2y \u2013 6xy\u00b2)], using a variety of tools (e.g., algebra tiles, computer algebra systems, paper and pencil)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.B2.4","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:49:08+00:00"},{"identifier":"3f764d40-46ed-11eb-a8f4-4bae04b7db64","uri":"https://opensalt.net/uri/3f764d40-46ed-11eb-a8f4-4bae04b7db64","fullStatement":"multiply a polynomial by a monomial involving the same variable [e.g., 2x(x + 4), 2x\u00b2(3x\u00b2 \u2013 2x + 1)], using a variety of tools (e.g., algebra tiles, diagrams, computer algebra systems, paper and pencil)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.B2.5","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:49:16+00:00"},{"identifier":"3f769f8e-46ed-11eb-8a06-89862f8b420a","uri":"https://opensalt.net/uri/3f769f8e-46ed-11eb-8a06-89862f8b420a","fullStatement":"expand and simplify polynomial expressions involving one variable [e.g., 2x(4x + 1) \u2013 3x(x + 2)], using a variety of tools (e.g., algebra tiles, computer algebra systems, paper and pencil)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.B2.6","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:49:24+00:00"},{"identifier":"3f76bc26-46ed-11eb-b22b-7fd0b9a5c621","uri":"https://opensalt.net/uri/3f76bc26-46ed-11eb-b22b-7fd0b9a5c621","fullStatement":"solve first-degree equations, including equations with fractional coefficients, using a variety of tools (e.g., computer algebra systems, paper and pencil) and strategies (e.g., the balance analogy, algebraic strategies)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.B2.7","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:49:33+00:00"},{"identifier":"3f76d850-46ed-11eb-9e63-5d0b02f0e8a6","uri":"https://opensalt.net/uri/3f76d850-46ed-11eb-9e63-5d0b02f0e8a6","fullStatement":"rearrange formulas involving variables in the first degree, with and without substitution (e.g., in analytic geometry, in measurement)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.B2.8","notes":"**Sample Problem**:\r\n\r\nA circular garden has a circumference of 30 m. What is the length of a straight path that goes through the centre of this garden?","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:14:02+00:00"},{"identifier":"3f771cb6-46ed-11eb-8c5f-159e6aa6fa34","uri":"https://opensalt.net/uri/3f771cb6-46ed-11eb-8c5f-159e6aa6fa34","fullStatement":"simplify numerical expressions involving integers and rational numbers, with and without the use of technology","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.B2.1","notes":"The knowledge and skills described in this expectation are to be introduced as needed and applied and consolidated throughout the course.","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:48:40+00:00"},{"identifier":"3f75166e-46ed-11eb-a8b4-a332c6e6e56d","uri":"https://opensalt.net/uri/3f75166e-46ed-11eb-a8b4-a332c6e6e56d","fullStatement":"extend the multiplication rule to derive and understand the power of a power rule, and apply it to simplify expressions involving one and two variables with positive exponents","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.B1.4","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:48:10+00:00"},{"identifier":"3f74b782-46ed-11eb-a9e7-bddcf57eb4a7","uri":"https://opensalt.net/uri/3f74b782-46ed-11eb-a9e7-bddcf57eb4a7","fullStatement":"describe the relationship between the algebraic and geometric representations of a single-variable term up to degree three [i.e., length, which is one dimensional, can be represented by x; area, which is two dimensional, can be represented by (x)(x) or x\u00b2; volume, which is three dimensional, can be represented by (x)(x)(x), (x\u00b2)(x), or x\u00b3]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.B1.2","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:47:49+00:00"},{"identifier":"3f74d384-46ed-11eb-a58b-ab523a4aedf4","uri":"https://opensalt.net/uri/3f74d384-46ed-11eb-a58b-ab523a4aedf4","fullStatement":"derive, through the investigation and examination of patterns, the exponent rules for multiplying and dividing monomials, and apply these rules in expressions involving one and two variables with positive exponents","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.B1.3","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:47:59+00:00"},{"identifier":"3f797272-46ed-11eb-b817-41d047a6a102","uri":"https://opensalt.net/uri/3f797272-46ed-11eb-b817-41d047a6a102","fullStatement":"determine the maximum area of a rectangle with a given perimeter by constructing a variety of rectangles, using a variety of tools (e.g., geoboards, graph paper, tooth- picks, a pre-made dynamic geometry sketch), and by examining various values of the area as the side lengths change and the perimeter remains constant","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.E1.1","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:56:19+00:00"},{"identifier":"3f793c26-46ed-11eb-8ed3-bd6c9a8fb73f","uri":"https://opensalt.net/uri/3f793c26-46ed-11eb-8ed3-bd6c9a8fb73f","fullStatement":"Investigating the Optimal Values of Measurements","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T17:11:56+00:00"},{"identifier":"3f790c38-46ed-11eb-a6b8-217a40784e05","uri":"https://opensalt.net/uri/3f790c38-46ed-11eb-a6b8-217a40784e05","fullStatement":"determine, through investigation, the optimal values of various measurements","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MPM1D-E1","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T20:56:30+00:00"},{"identifier":"3f78da1a-46ed-11eb-b306-770d51690e1b","uri":"https://opensalt.net/uri/3f78da1a-46ed-11eb-b306-770d51690e1b","fullStatement":"Measurement and Geometry","CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19"},"humanCodingScheme":"MPM1D-E","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-02-13T13:40:40+00:00"},{"identifier":"3f7a0e4e-46ed-11eb-8df1-89697e80f76f","uri":"https://opensalt.net/uri/3f7a0e4e-46ed-11eb-8df1-89697e80f76f","fullStatement":"solve problems involving the measurements of two-dimensional shapes and the surface areas and volumes of three-dimensional figures","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MPM1D-E2","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T20:56:38+00:00"},{"identifier":"3f7a74d8-46ed-11eb-9a9f-970951a7a3a5","uri":"https://opensalt.net/uri/3f7a74d8-46ed-11eb-9a9f-970951a7a3a5","fullStatement":"solve problems involving the areas and perimeters of composite two-dimensional shapes (i.e., combinations of rectangles, triangles, parallelograms, trapezoids, and circles)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.E2.3","notes":"**Sample Problem**:\r\n\r\nA new park is in the shape of an isosceles trapezoid with a square attached to the shortest side. The side lengths of the trapezoidal section are 200 m, 500 m, 500 m, and 800 m, and the side length of the square section is 200 m. If the park is to be fully fenced and sodded, how much fencing and sod are required?","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:24:58+00:00"},{"identifier":"3f7a44ae-46ed-11eb-bfa1-ff60b32c665f","uri":"https://opensalt.net/uri/3f7a44ae-46ed-11eb-bfa1-ff60b32c665f","fullStatement":"Solving Problems Involving Perimeter, Area, Surface Area, and Volume","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T17:17:52+00:00"},{"identifier":"3f7a922e-46ed-11eb-8ff5-a31b7816d6f2","uri":"https://opensalt.net/uri/3f7a922e-46ed-11eb-8ff5-a31b7816d6f2","fullStatement":"develop, through investigation (e.g., using concrete materials), the formulas for the volume of a pyramid, a cone, and a sphere (e.g., use three-dimensional figures to show that the volume of a pyramid [or cone] is 1/3 the volume of a prism [or cylinder] with the same base and height, and therefore that V(pyramid) = V(prism)/3 or V(pyramid) = (area of base)(height)/3","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.E2.4","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-28T16:31:01+00:00"},{"identifier":"3f7ad6da-46ed-11eb-a5df-c960f92a8132","uri":"https://opensalt.net/uri/3f7ad6da-46ed-11eb-a5df-c960f92a8132","fullStatement":"relate the geometric representation of the Pythagorean theorem and the algebraic representation a\u00b2 + b\u00b2 = c\u00b2","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.E2.1","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:57:23+00:00"},{"identifier":"3f7b1d2a-46ed-11eb-b38e-ed4bbd9ebe55","uri":"https://opensalt.net/uri/3f7b1d2a-46ed-11eb-b38e-ed4bbd9ebe55","fullStatement":"solve problems using the Pythagorean theorem, as required in applications (e.g., calculate the height of a cone, given the radius and the slant height, in order to determine the volume of the cone)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.E2.2","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:57:32+00:00"},{"identifier":"3f79efb8-46ed-11eb-b442-7187195055ff","uri":"https://opensalt.net/uri/3f79efb8-46ed-11eb-b442-7187195055ff","fullStatement":"explain the significance of optimal area, surface area, or volume in various applications (e.g., the minimum amount of packaging material; the relationship between surface area and heat loss)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.E1.4","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:24:16+00:00"},{"identifier":"3f799036-46ed-11eb-8669-ab53f7256aaf","uri":"https://opensalt.net/uri/3f799036-46ed-11eb-8669-ab53f7256aaf","fullStatement":"determine the minimum perimeter of a rectangle with a given area by constructing a variety of rectangles, using a variety of tools (e.g., geoboards, graph paper, a pre-made dynamic geometry sketch), and by examining various values of the side lengths and the perimeter as the area stays constant","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.E1.2","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:56:28+00:00"},{"identifier":"3f79ac6a-46ed-11eb-93cd-df6e972425db","uri":"https://opensalt.net/uri/3f79ac6a-46ed-11eb-93cd-df6e972425db","fullStatement":"identify, through investigation with a variety of tools (e.g. concrete materials, computer software), the effect of varying the dimensions on the surface area [or volume] of square-based prisms and cylinders, given a fixed volume [or surface area]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.E1.3","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:56:36+00:00"},{"identifier":"3f7bd2b0-46ed-11eb-ab72-a37480ea7ca8","uri":"https://opensalt.net/uri/3f7bd2b0-46ed-11eb-ab72-a37480ea7ca8","fullStatement":"express the equation of a line in the form y = mx + b, given the form Ax + By + C = 0","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.D1.3","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:54:02+00:00"},{"identifier":"3f7b6bcc-46ed-11eb-8145-77c61d04f6c3","uri":"https://opensalt.net/uri/3f7b6bcc-46ed-11eb-8145-77c61d04f6c3","fullStatement":"determine the relationship between the form of an equation and the shape of its graph with respect to linearity and non-linearity","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MPM1D-D1","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T20:56:15+00:00"},{"identifier":"3f7b3ca6-46ed-11eb-8c27-472bf92b7d3d","uri":"https://opensalt.net/uri/3f7b3ca6-46ed-11eb-8c27-472bf92b7d3d","fullStatement":"Analytic Geometry","CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19"},"humanCodingScheme":"MPM1D-D","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T20:56:09+00:00"},{"identifier":"3f7cdf2a-46ed-11eb-b91f-934b84c38e75","uri":"https://opensalt.net/uri/3f7cdf2a-46ed-11eb-b91f-934b84c38e75","fullStatement":"determine, through investigation, the properties of the slope and y-intercept of a linear relation","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MPM1D-D2","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T20:56:19+00:00"},{"identifier":"3f7d3722-46ed-11eb-98d2-91aebc31dc08","uri":"https://opensalt.net/uri/3f7d3722-46ed-11eb-98d2-91aebc31dc08","fullStatement":"identify, through investigation with technology, the geometric significance of m and b in the equation y = mx + b","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.D2.2","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:54:31+00:00"},{"identifier":"3f7d075c-46ed-11eb-8e0f-09dcf2cfb968","uri":"https://opensalt.net/uri/3f7d075c-46ed-11eb-8e0f-09dcf2cfb968","fullStatement":"Investigating the Properties of Slope","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T16:32:31+00:00"},{"identifier":"3f7d55a4-46ed-11eb-aa2c-75738873ca1c","uri":"https://opensalt.net/uri/3f7d55a4-46ed-11eb-aa2c-75738873ca1c","fullStatement":"determine, through investigation, various formulas for the slope of a line segment or a line (e.g., m = rise/run, m = (the change in y)/(the change in x) or m = \u0394y/\u0394x, (y2-y1)/(x2-x1) ), and use the formulas to determine the slope of a line segment or a line","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.D2.1","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:54:22+00:00"},{"identifier":"3f7c5924-46ed-11eb-91c1-750d915cf445","uri":"https://opensalt.net/uri/3f7c5924-46ed-11eb-91c1-750d915cf445","fullStatement":"identify, through investigation, properties of the slopes of lines and line segments (e.g., direction, positive or negative rate of change, steepness, parallelism, perpendicularity), using graphing technology to facilitate investigations, where appropriate.","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.D2.4","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:54:46+00:00"},{"identifier":"3f7c7616-46ed-11eb-9838-3171289358d3","uri":"https://opensalt.net/uri/3f7c7616-46ed-11eb-9838-3171289358d3","fullStatement":"Investigating the Relationship Between the Equation of a Relation and the Shape of Its Graph","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T16:30:23+00:00"},{"identifier":"3f7ca500-46ed-11eb-959b-4b492849fa13","uri":"https://opensalt.net/uri/3f7ca500-46ed-11eb-959b-4b492849fa13","fullStatement":"determine, through investigation, the characteristics that distinguish the equation of a straight line from the equations of non-linear relations (e.g., use a graphing calculator or graphing software to graph a variety of linear and non-linear relations from their equations; classify the relations according to the shapes of their graphs; connect an equation of degree one to a linear relation)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.D1.1","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:20:41+00:00"},{"identifier":"3f7cc242-46ed-11eb-bdbf-bd8aebb6c141","uri":"https://opensalt.net/uri/3f7cc242-46ed-11eb-bdbf-bd8aebb6c141","fullStatement":"identify, through investigation, the equation of a line in any of the forms y = mx + b, Ax + By + C = 0, x = a, y = b","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.D1.2","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-29T14:24:02+00:00"},{"identifier":"3f7bef48-46ed-11eb-8702-9bad4f45f115","uri":"https://opensalt.net/uri/3f7bef48-46ed-11eb-8702-9bad4f45f115","fullStatement":"determine, through investigation, connections among the representations of a constant rate of change of a linear relation (e.g., the cost of producing a book of photographs is $50, plus $5 per book, so an equation is C = 50 + 5p; a table of values provides the first difference of 5; the rate of change has a value of 5, which is also the slope of the corresponding line; and 5 is the coefficient of the independent variable, p, in this equation)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.D2.3","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:54:39+00:00"},{"identifier":"3f7e22ea-46ed-11eb-9241-9b5f02230a8c","uri":"https://opensalt.net/uri/3f7e22ea-46ed-11eb-9241-9b5f02230a8c","fullStatement":"interpret the meanings of points on scatter plots or graphs that represent linear relations, including scatter plots or graphs in more than one quadrant [e.g., on a scatter plot of height versus age, interpret the point (13, 150) as representing a student who is 13 years old and 150 cm tall; identify points on the graph that represent students who are taller and younger than this student]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.C1.1","notes":"**Sample Problem**: \r\n\r\nGiven a graph that represents the relationship of the Celsius scale and the Fahrenheit scale, determine the Celsius equivalent of \u20135\u00b0F.","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:15:47+00:00"},{"identifier":"3f7de3a2-46ed-11eb-9239-2f464674af60","uri":"https://opensalt.net/uri/3f7de3a2-46ed-11eb-9239-2f464674af60","fullStatement":"Using Data Management to Investigate Relationships","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:50:47+00:00"},{"identifier":"3f7db800-46ed-11eb-80f8-993ace7a70d1","uri":"https://opensalt.net/uri/3f7db800-46ed-11eb-80f8-993ace7a70d1","fullStatement":"apply data-management techniques to investigate relationships between two variables","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MPM1D-C1","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T20:55:55+00:00"},{"identifier":"3f7d7976-46ed-11eb-b8b0-73373636937f","uri":"https://opensalt.net/uri/3f7d7976-46ed-11eb-b8b0-73373636937f","fullStatement":"Linear Relations","CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19"},"humanCodingScheme":"MPM1D-C","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T20:55:48+00:00"},{"identifier":"3f7e9f72-46ed-11eb-90c0-63183b40da0b","uri":"https://opensalt.net/uri/3f7e9f72-46ed-11eb-90c0-63183b40da0b","fullStatement":"demonstrate an understanding of the characteristics of a linear relation","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MPM1D-C2","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T20:56:00+00:00"},{"identifier":"3f7f039a-46ed-11eb-87dd-5da299dee36d","uri":"https://opensalt.net/uri/3f7f039a-46ed-11eb-87dd-5da299dee36d","fullStatement":"compare the properties of direct variation and partial variation in applications, and identify the initial value (e.g., for a relation described in words, or represented as a graph or an equation","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.C2.4","notes":"**Sample Problem**: \r\n\r\nYoga costs $20 for registration, plus $8 per class. Tai chi costs $12 per class. Which situation represents a direct variation, and which represents a partial variation? For each relation, what is the initial value? Explain your answers.","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:18:07+00:00"},{"identifier":"3f7ed122-46ed-11eb-9852-c1235f5705ec","uri":"https://opensalt.net/uri/3f7ed122-46ed-11eb-9852-c1235f5705ec","fullStatement":"Understanding Characteristics of Linear Relations","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T16:18:55+00:00"},{"identifier":"3f7f2258-46ed-11eb-9422-b7c80c21d6c3","uri":"https://opensalt.net/uri/3f7f2258-46ed-11eb-9422-b7c80c21d6c3","fullStatement":"identify, through investigation, some properties of linear relations (i.e., numerically, the first difference is a constant, which represents a constant rate of change; graphically, a straight line represents the relation), and apply these properties to determine whether a relation is linear or non-linear","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.C2.3","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:17:52+00:00"},{"identifier":"3f7f742e-46ed-11eb-9ac4-356583099bbc","uri":"https://opensalt.net/uri/3f7f742e-46ed-11eb-9ac4-356583099bbc","fullStatement":"construct tables of values, scatter plots, and lines or curves of best fit as appropriate, using a variety of tools (e.g., spreadsheets, graphing software, graphing calculators, paper and pencil), for linearly related and non-linearly related data collected from a variety of sources (e.g., experiments, electronic secondary sources, patterning with concrete materials)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.C2.2","notes":"**Sample Problem**: \r\n\r\nCollect data, using concrete materials or dynamic geometry software, and construct a table of values, a scatter plot, and a line or curve of best fit to represent the following relationships: the volume and the height for a square-based prism with a fixed base; the volume and the side length of the base for a square-based prism with a fixed height.","language":"en","educationLevel":["08"],"lastChangeDateTime":"2021-01-05T18:01:25+00:00"},{"identifier":"3f7f92f6-46ed-11eb-ba61-99adf0464089","uri":"https://opensalt.net/uri/3f7f92f6-46ed-11eb-ba61-99adf0464089","fullStatement":"construct tables of values, graphs, and equations, using a variety of tools (e.g., graphing calculators, spreadsheets, graphing software, paper and pencil), to represent linear relations derived from descriptions of realistic situations","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.C2.1","notes":"**Sample Problem**: \r\n\r\nConstruct a table of values, a graph, and an equation to represent a monthly cellphone plan that costs $25, plus $0.10 per minute of airtime.","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:17:11+00:00"},{"identifier":"3f7fb286-46ed-11eb-aa00-0d36d9e31be6","uri":"https://opensalt.net/uri/3f7fb286-46ed-11eb-aa00-0d36d9e31be6","fullStatement":"connect various representations of a linear relation","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MPM1D-C3","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T20:56:04+00:00"},{"identifier":"3f800f92-46ed-11eb-9a1d-6f5b48d33895","uri":"https://opensalt.net/uri/3f800f92-46ed-11eb-9a1d-6f5b48d33895","fullStatement":"determine values of a linear relation by using a table of values, by using the equation of the relation, and by interpolating or extrapolating from the graph of the relation","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.C3.1","notes":"**Sample Problem**:\r\n\r\nThe equation H = 300 \u2013 60t represents the height of a hot air balloon that is initially at 300 m and is descending at a constant rate of 60 m/ min. Determine algebraically and graphically how long the balloon will take to reach a height of 160 m.","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:19:03+00:00"},{"identifier":"3f7fdd06-46ed-11eb-b5dc-bf0c3b64f332","uri":"https://opensalt.net/uri/3f7fdd06-46ed-11eb-b5dc-bf0c3b64f332","fullStatement":"Connecting Various Representations of Linear Relations","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T16:23:56+00:00"},{"identifier":"3f802e5a-46ed-11eb-82c8-9fcee7ce566b","uri":"https://opensalt.net/uri/3f802e5a-46ed-11eb-82c8-9fcee7ce566b","fullStatement":"describe a situation that would explain the events illustrated by a given graph of a relationship between two variables","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.C3.2","notes":"**Sample Problem**:\r\n\r\nThe walk of an individual is illustrated in the given graph, produced by a motion detector and a graphing calculator. Describe the walk [e.g., the initial distance from the motion detector, the rate of walk].","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:19:17+00:00"},{"identifier":"3f804dd6-46ed-11eb-ab60-37b6b213cca2","uri":"https://opensalt.net/uri/3f804dd6-46ed-11eb-ab60-37b6b213cca2","fullStatement":"determine the equation of a line of best fit for a scatter plot, using an informal process (e.g., using a movable line in dynamic statistical software; using a process of trial and error on a graphing calculator; determining the equation of the line joining two carefully chosen points on the scatter plot).","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MPM1D-9.C2.5","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:52:23+00:00"},{"identifier":"3f7e4266-46ed-11eb-ae5b-d1006bc6855b","uri":"https://opensalt.net/uri/3f7e4266-46ed-11eb-ae5b-d1006bc6855b","fullStatement":"pose problems, identify variables, and formulate hypotheses associated with relationships between two variables","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.C1.2","notes":"**Sample Problem**: \r\n\r\nDoes the rebound height of a ball depend on the height from which it was dropped?);","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:16:00+00:00"},{"identifier":"3f7e612e-46ed-11eb-ac5b-b77b69b3066a","uri":"https://opensalt.net/uri/3f7e612e-46ed-11eb-ac5b-b77b69b3066a","fullStatement":"design and carry out an investigation or experiment involving relationships between two variables, including the collection and organization of data, using appropriate methods, equipment, and/ or technology (e.g., surveying; using measuring tools, scientific probes, the Internet) and techniques (e.g., making tables, drawing graphs)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.C1.3","notes":"**Sample Problem**: \r\n\r\nDesign and perform an experiment to measure and record the temperature of ice water in a plastic cup and ice water in a thermal mug over a 30 min period, for the purpose of comparison. What factors might affect the outcome of this experiment? How could you design the experiment to account for them?","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:16:18+00:00"},{"identifier":"3f7e7f38-46ed-11eb-b0bb-5f343c41fdf2","uri":"https://opensalt.net/uri/3f7e7f38-46ed-11eb-b0bb-5f343c41fdf2","fullStatement":"describe trends and relationships observed in data, make inferences from data, compare the inferences with hypotheses about the data, and explain any differences between the inferences and the hypotheses (e.g., describe the trend observed in the data. Does a relationship seem to exist? Of what sort? Is the outcome consistent with your hypothesis? Identify and explain any outlying pieces of data. Suggest a formula that relates the variables. How might you vary this experiment to examine other relationships?)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.C1.4","notes":"**Sample Problem**:\r\n\r\nHypothesize the effect of the length of a pendulum on the time required for the pendulum to make five full swings. Use data to make an inference. Compare the inference with the hypothesis. Are there other relationships you might investigate involving pendulums?","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:16:41+00:00"},{"identifier":"d1d51fd8-4709-11eb-a033-4b32f64980d1","uri":"https://opensalt.net/uri/d1d51fd8-4709-11eb-a033-4b32f64980d1","fullStatement":"solve problems that can be modelled with first-degree equations, and compare algebraic methods to other solution methods","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.B2.9","notes":"**Sample Problem**: \r\n\r\nSolve the following problem in more than one way: Jonah is involved in a walkathon. His goal is to walk 25 km. He begins at 9:00 a.m. and walks at a steady rate of 4 km / h. How many kilometres does he still have left to walk at 1:15 p.m. if he is to achieve his goal?","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:14:16+00:00"},{"identifier":"d51921d4-4796-11eb-a0f5-5d8ed65c934d","uri":"https://opensalt.net/uri/d51921d4-4796-11eb-a0f5-5d8ed65c934d","fullStatement":"determine other representations of a linear relation, given one representation (e.g., given a numeric model, determine a graphical model and an algebraic model; given a graph, determine some points on the graph and determine an algebraic model)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.C3.3","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:53:01+00:00"},{"identifier":"d769b214-4796-11eb-9159-b728a479a0cb","uri":"https://opensalt.net/uri/d769b214-4796-11eb-9159-b728a479a0cb","fullStatement":"describe the effects on a linear graph and make the corresponding changes to the linear equation when the conditions of the situation they represent are varied (e.g., given a partial variation graph and an equation representing the cost of producing a yearbook, describe how the graph changes if the cost per book is altered, describe how the graph changes if the fixed costs are altered, and make the corresponding changes to the equation).","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.C3.4","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:53:08+00:00"},{"identifier":"7f5bf504-4797-11eb-b953-81fec1ab962c","uri":"https://opensalt.net/uri/7f5bf504-4797-11eb-b953-81fec1ab962c","fullStatement":"solve problems involving linear relations","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MPM1D-D3","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T20:56:24+00:00"},{"identifier":"7f5c52c4-4797-11eb-bc42-13c68be05a3e","uri":"https://opensalt.net/uri/7f5c52c4-4797-11eb-bc42-13c68be05a3e","fullStatement":"determine the equation of a line from information about the line (e.g., the slope and y-intercept; the slope and a point; two points)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.D3.2","notes":"**Sample Problem**: \r\n\r\nCompare the equations of the lines parallel to and perpendicular to y = 2x \u2013 4, and with the same x-intercept as 3x \u2013 4y = 12. Verify using dynamic geometry software.","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:22:23+00:00"},{"identifier":"7f5c22b8-4797-11eb-bf81-498fca77bfc0","uri":"https://opensalt.net/uri/7f5c22b8-4797-11eb-bf81-498fca77bfc0","fullStatement":"Using the Properties of Linear Relations to Solve Problems","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T16:45:34+00:00"},{"identifier":"7f5c6f20-4797-11eb-9b33-85823388b025","uri":"https://opensalt.net/uri/7f5c6f20-4797-11eb-9b33-85823388b025","fullStatement":"graph lines by hand, using a variety of techniques (e.g., graph y = (2/3)x-4 using the y-intercept and slope; graph 2x + 3y = 6 using the x- and y-intercepts)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.D3.1","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:55:06+00:00"},{"identifier":"d60b218e-4799-11eb-834a-f5ae07ba2e34","uri":"https://opensalt.net/uri/d60b218e-4799-11eb-834a-f5ae07ba2e34","fullStatement":"describe the meaning of the slope and y-intercept for a linear relation arising from a realistic situation (e.g., the cost to rent the community gym is $40 per evening, plus $2 per person for equipment rental; the vertical intercept, 40, represents the $40 cost of renting the gym; the value of the rate of change, 2, represents the $2 cost per person), and describe a situation that could be modelled by a given linear equation (e.g., the linear equation M = 50 + 6d could model the mass of a shipping package, including 50 g for the packaging material, plus 6 g per flyer added to the package)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.D3.3","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:55:20+00:00"},{"identifier":"f8f95ac6-4799-11eb-9ac3-fbd0327bc48a","uri":"https://opensalt.net/uri/f8f95ac6-4799-11eb-9ac3-fbd0327bc48a","fullStatement":"identify and explain any restrictions on the variables in a linear relation arising from a realistic situation (e.g., in the relation C = 50 + 25n, C is the cost of holding a party in a hall and n is the number of guests; n is restricted to whole numbers of 100 or less, because of the size of the hall, and C is consequently restricted to $50 to $2550)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.D3.4","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:55:39+00:00"},{"identifier":"fadbd602-4799-11eb-82cd-e79efae09b0b","uri":"https://opensalt.net/uri/fadbd602-4799-11eb-82cd-e79efae09b0b","fullStatement":"determine graphically the point of intersection of two linear relations, and interpret the intersection point in the context of an application","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.D3.5","notes":"**Sample Problem**:\r\n\r\nA video rental company has two monthly plans. Plan A charges a flat fee of $30 for unlimited rentals; Plan B charges $9, plus $3 per video. Use a graphical model to determine the conditions under which you should choose Plan A or Plan B.","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:23:02+00:00"},{"identifier":"60a43c4c-479d-11eb-a51d-134a6bee355c","uri":"https://opensalt.net/uri/60a43c4c-479d-11eb-a51d-134a6bee355c","fullStatement":"verify, through investigation facilitated by dynamic geometry software, geometric properties and relationships involving two-dimensional shapes, and apply the results to solving problems","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MPM1D-E3","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:23:40+00:00"},{"identifier":"60a4ad58-479d-11eb-88f0-530bc86184a0","uri":"https://opensalt.net/uri/60a4ad58-479d-11eb-88f0-530bc86184a0","fullStatement":"determine, through investigation using a variety of tools (e.g., dynamic geometry software, concrete materials), and describe the properties and relationships of the interior and exterior angles of triangles, quadrilaterals, and other polygons, and apply the results to problems involving the angles of polygons","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.E3.1","notes":"**Sample Problem**:\r\n\r\nWith the assistance of dynamic geometry software, determine the relationship between the sum of the interior angles of a polygon and the number of sides. Use your conclusion to determine the sum of the interior angles of a 20-sided polygon.","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:29:05+00:00"},{"identifier":"60a47450-479d-11eb-b2a1-4d6fad4511e3","uri":"https://opensalt.net/uri/60a47450-479d-11eb-b2a1-4d6fad4511e3","fullStatement":"Investigating and Applying Geometric Relationships","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T17:31:32+00:00"},{"identifier":"60a4c9dc-479d-11eb-8692-53cf74c3ab57","uri":"https://opensalt.net/uri/60a4c9dc-479d-11eb-8692-53cf74c3ab57","fullStatement":"determine, through investigation using a variety of tools (e.g., dynamic geometry software, paper folding), and describe some properties of polygons (e.g., the figure that results from joining the midpoints of the sides of a quadrilateral is a parallelogram; the diagonals of a rectangle bisect each other; the line segment joining the midpoints of two sides of a triangle is half the length of the third side), and apply the results in problem solving (e.g., given the width of the base of an A-frame tree house, determine the length of a horizontal support beam that is attached half way up the sloping sides)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.E3.2","language":"en","educationLevel":["09"],"lastChangeDateTime":"2020-12-26T19:58:32+00:00"},{"identifier":"60a4e642-479d-11eb-b41c-a15c98a7007c","uri":"https://opensalt.net/uri/60a4e642-479d-11eb-b41c-a15c98a7007c","fullStatement":"pose questions about geometric relationships, investigate them, and present their findings, using a variety of mathematical forms (e.g., written explanations, diagrams, dynamic sketches, formulas, tables)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.E3.3","notes":"**Sample Problem**: \r\n\r\nHow many diagonals can be drawn from one vertex of a 20-sided polygon? How can I find out without counting them?","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-29T16:11:04+00:00"},{"identifier":"60a52a8a-479d-11eb-8cef-6b4cd47851ea","uri":"https://opensalt.net/uri/60a52a8a-479d-11eb-8cef-6b4cd47851ea","fullStatement":"illustrate a statement about a geometric property by demonstrating the statement with multiple examples, or deny the statement on the basis of a counter-example, with or without the use of dynamic geometry software","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.E3.4","notes":"**Sample Problem**: \r\n\r\nConfirm or deny the following statement: If a quadrilateral has perpendicular diagonals, then it is a square.","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:27:18+00:00"},{"identifier":"8f2da5f8-479d-11eb-95ba-8950c8e639e5","uri":"https://opensalt.net/uri/8f2da5f8-479d-11eb-95ba-8950c8e639e5","fullStatement":"pose and solve problems involving maximization and minimization of measurements of geometric shapes and figures (e.g., determine the dimensions of the rectangular field with the maximum area that can be enclosed by a fixed amount of fencing, if the fencing is required on only three sides)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.E1.5","notes":"**Sample Problem**: \r\n\r\nDetermine the dimensions of a square-based, open- topped prism with a volume of 24 cm\u00b3 and with the minimum surface area.).","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:27:50+00:00"},{"identifier":"625d3f38-479e-11eb-9846-d1bd6d9510bd","uri":"https://opensalt.net/uri/625d3f38-479e-11eb-9846-d1bd6d9510bd","fullStatement":"determine, through investigation, the relationship for calculating the surface area of a pyramid (e.g., use the net of a square-based pyramid to determine that the surface area is the area of the square base plus the areas of the four congruent triangles)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.E2.5","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:25:43+00:00"},{"identifier":"645e21d0-479e-11eb-84b3-a1f64934fd9c","uri":"https://opensalt.net/uri/645e21d0-479e-11eb-84b3-a1f64934fd9c","fullStatement":"solve problems involving the surface areas and volumes of prisms, pyramids, cylinders, cones, and spheres, including composite figures","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM1D-9.E2.6","notes":"**Sample Problem**: \r\n\r\nBreak-bit Cereal is sold in a single-serving size, in a box in the shape of a rectangular prism of dimensions 5 cm by 4 cm by 10 cm. The manufacturer also sells the cereal in a larger size, in a box with dimensions double those of the smaller box. Compare the surface areas and the volumes of the two boxes, and explain the implications of your answers.","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-05T17:26:07+00:00"},{"identifier":"30e060e8-492e-11eb-9dc9-9bb4ec223dfd","uri":"https://opensalt.net/uri/30e060e8-492e-11eb-9dc9-9bb4ec223dfd","fullStatement":"Grade 10","CFItemType":"Grade Level","CFItemTypeURI":{"title":"Grade Level","identifier":"8047d85d-6c8e-5231-bd6d-050731684413","uri":"https://api.acmt-prod.learningmate.com/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/8047d85d-6c8e-5231-bd6d-050731684413"},"language":"en","educationLevel":["10"],"lastChangeDateTime":"2021-01-08T20:17:17+00:00"},{"identifier":"30e18a04-492e-11eb-a5b9-b3abe122f0df","uri":"https://opensalt.net/uri/30e18a04-492e-11eb-a5b9-b3abe122f0df","fullStatement":"collect data that can be represented as a quadratic relation, from experiments using appropriate equipment and technology (e.g., concrete materials, scientific probes, graphing calculators), or from secondary sources (e.g., the Internet, Statistics Canada); graph the data and draw a curve of best fit, if appropriate, with or without the use of technology","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.B1.1","notes":"**Sample Problem**:\r\n\r\nMake a 1 m ramp that makes a 15\u00b0 angle with the floor. Place a can 30 cm up the ramp. Record the time it takes for the can to roll to the bottom. Repeat by placing the can 40 cm, 50 cm, and 60 cm up the ramp, and so on. Graph the data and draw the curve of best fit.","language":"en","educationLevel":["09"],"lastChangeDateTime":"2021-01-06T16:57:31+00:00"},{"identifier":"30e14620-492e-11eb-8534-fd34d790e6e7","uri":"https://opensalt.net/uri/30e14620-492e-11eb-8534-fd34d790e6e7","fullStatement":"Investigating the Basic Properties of Quadratic Relations","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:08:57+00:00"},{"identifier":"30e1161e-492e-11eb-86c1-3bb5764a370a","uri":"https://opensalt.net/uri/30e1161e-492e-11eb-86c1-3bb5764a370a","fullStatement":"determine the basic properties of quadratic relations","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MPM2D-B1","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:07:54+00:00"},{"identifier":"30e0dee2-492e-11eb-8086-8f984a4a24ee","uri":"https://opensalt.net/uri/30e0dee2-492e-11eb-8086-8f984a4a24ee","fullStatement":"Quadratic Relations of the Form y = ax\u00b2 + bx + c","CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19"},"humanCodingScheme":"MPM2D-B","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:02:41+00:00"},{"identifier":"30e09b08-492e-11eb-b73a-2f0402244f06","uri":"https://opensalt.net/uri/30e09b08-492e-11eb-b73a-2f0402244f06","fullStatement":"Principles of Mathematics, Grade 10, Academic","CFItemType":"Grade Level","CFItemTypeURI":{"title":"Grade Level","identifier":"8047d85d-6c8e-5231-bd6d-050731684413","uri":"https://api.acmt-prod.learningmate.com/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/8047d85d-6c8e-5231-bd6d-050731684413"},"humanCodingScheme":"MPM2D","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:01:28+00:00"},{"identifier":"30e4ef00-492e-11eb-a3ab-35be08448ba1","uri":"https://opensalt.net/uri/30e4ef00-492e-11eb-a3ab-35be08448ba1","fullStatement":"expand and simplify second-degree polynomial expressions [e.g., (2x + 5)\u00b2, (2x \u2013 y)(x + 3y)], using a variety of tools (e.g., algebra tiles, diagrams, computer algebra systems, paper and pencil) and strategies (e.g., patterning)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.B3.1","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:26:02+00:00"},{"identifier":"30e4a5c2-492e-11eb-8f47-53eba30d71d2","uri":"https://opensalt.net/uri/30e4a5c2-492e-11eb-8f47-53eba30d71d2","fullStatement":"Solving Quadratic Equations","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:20:03+00:00"},{"identifier":"30e474ee-492e-11eb-b4ba-4d0c14bdbb9f","uri":"https://opensalt.net/uri/30e474ee-492e-11eb-b4ba-4d0c14bdbb9f","fullStatement":"solve quadratic equations and interpret the solutions with respect to the corresponding relations","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MPM2D-B3","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:08:20+00:00"},{"identifier":"30e519d0-492e-11eb-a1ab-75d891f183b6","uri":"https://opensalt.net/uri/30e519d0-492e-11eb-a1ab-75d891f183b6","fullStatement":"factor polynomial expressions involving common factors, trinomials, and differences of squares [e.g., 2x\u00b2 + 4x, 2x \u2013 2y + ax \u2013 ay, x\u00b2 \u2013 x \u2013 6, 2a\u00b2 + 11a + 5, 4x\u00b2 \u2013 25], using a variety of tools (e.g., concrete materials, computer algebra systems, paper and pencil) and strategies (e.g., patterning);","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.B3.2","language":"en","educationLevel":["10"],"lastChangeDateTime":"2021-01-06T17:01:55+00:00"},{"identifier":"30e542b6-492e-11eb-afdb-2503a95a531f","uri":"https://opensalt.net/uri/30e542b6-492e-11eb-afdb-2503a95a531f","fullStatement":"determine, through investigation, and describe the connection between the factors of a quadratic expression and the x-intercepts (i.e., the zeros) of the graph of the corresponding quadratic relation, expressed in the form y = a(x \u2013 r)(x \u2013 s)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.B3.3","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:26:02+00:00"},{"identifier":"30e56c82-492e-11eb-9a49-87160158de5d","uri":"https://opensalt.net/uri/30e56c82-492e-11eb-9a49-87160158de5d","fullStatement":"interpret real and non-real roots of quadratic equations, through investigation using graphing technology, and relate the roots to the x-intercepts of the corresponding relations","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.B3.4","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:26:02+00:00"},{"identifier":"30e588f2-492e-11eb-a117-f5f1b667fdd4","uri":"https://opensalt.net/uri/30e588f2-492e-11eb-a117-f5f1b667fdd4","fullStatement":"express y = ax\u00b2 + bx + c in the form y = a(x \u2013 h)\u00b2 + k by completing the square in situations involving no fractions, using a variety of tools (e.g. concrete materials, diagrams, paper and pencil)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.B3.5","notes":"**Sample problem**: \r\n\r\nDetermine the dimensions of a square-based, open- topped prism with a volume of 24 cm\u00b3 and with the minimum surface area.).","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:26:02+00:00"},{"identifier":"30e5d97e-492e-11eb-b04c-cbcb17eb9736","uri":"https://opensalt.net/uri/30e5d97e-492e-11eb-b04c-cbcb17eb9736","fullStatement":"Solving Problems Involving Quadratic Relations","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:28:53+00:00"},{"identifier":"30e5a972-492e-11eb-a7a2-cb1124f0359d","uri":"https://opensalt.net/uri/30e5a972-492e-11eb-a7a2-cb1124f0359d","fullStatement":"solve problems involving quadratic relations","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MPM2D-B4","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:08:42+00:00"},{"identifier":"30e67da2-492e-11eb-92e3-2f1d7df92d7e","uri":"https://opensalt.net/uri/30e67da2-492e-11eb-92e3-2f1d7df92d7e","fullStatement":"determine the zeros and the maximum or minimum value of a quadratic relation from its graph (i.e., using graphing calculators or graphing software) or from its defining equation (i.e., by applying algebraic techniques)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.B4.1","language":"en","educationLevel":["10"],"lastChangeDateTime":"2021-01-06T17:03:32+00:00"},{"identifier":"30e6a73c-492e-11eb-ae9f-d33a539a7fe8","uri":"https://opensalt.net/uri/30e6a73c-492e-11eb-ae9f-d33a539a7fe8","fullStatement":"solve problems arising from a realistic situation represented by a graph or an equation of a quadratic relation, with and without the use of technology (e.g., given the graph or the equation of a quadratic relation representing the height of a ball over elapsed time, answer questions such as the following: What is the maximum height of the ball? After what length of time will the ball hit the ground? Over what time interval is the height of the ball greater than 3 m?)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.B4.2","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:30:12+00:00"},{"identifier":"30e81e00-492e-11eb-a033-cd024a665b41","uri":"https://opensalt.net/uri/30e81e00-492e-11eb-a033-cd024a665b41","fullStatement":"Trigonometry","CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19"},"humanCodingScheme":"MPM2D-D","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:03:38+00:00"},{"identifier":"30e8b392-492e-11eb-b781-25076bd68977","uri":"https://opensalt.net/uri/30e8b392-492e-11eb-b781-25076bd68977","fullStatement":"verify, through investigation (e.g., using dynamic geometry software, concrete materials), the properties of similar triangles (e.g., given similar triangles, verify the equality of corresponding angles and the proportionality of corresponding sides)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.D1.1","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:43:34+00:00"},{"identifier":"30e87daa-492e-11eb-8e00-633ddd1e904f","uri":"https://opensalt.net/uri/30e87daa-492e-11eb-8e00-633ddd1e904f","fullStatement":"Investigating Similarity and Solving Problems Involving Similar Triangles","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:43:05+00:00"},{"identifier":"30e854b0-492e-11eb-81b3-eb4121cf2f39","uri":"https://opensalt.net/uri/30e854b0-492e-11eb-81b3-eb4121cf2f39","fullStatement":"use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MPM2D-D1","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:42:00+00:00"},{"identifier":"30e8d0fc-492e-11eb-8f52-81ba7104d482","uri":"https://opensalt.net/uri/30e8d0fc-492e-11eb-8f52-81ba7104d482","fullStatement":"describe and compare the concepts of similarity and congruence","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.D1.2","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:43:54+00:00"},{"identifier":"30e8ed6c-492e-11eb-8f7e-37c491242164","uri":"https://opensalt.net/uri/30e8ed6c-492e-11eb-8f7e-37c491242164","fullStatement":"solve problems involving similar triangles in realistic situations (e.g., shadows, reflections, scale models, surveying)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.D1.3","notes":"**Sample problem**: \r\n\r\nUse a metre stick to determine the height of a tree, by means of the similar triangles formed by the tree, the metre stick, and their shadows.","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:44:46+00:00"},{"identifier":"30e96e7c-492e-11eb-a2b5-cfef2511a6bc","uri":"https://opensalt.net/uri/30e96e7c-492e-11eb-a2b5-cfef2511a6bc","fullStatement":"determine the measures of the sides and angles in right triangles, using the primary trigonometric ratios and the Pythagorean theorem","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.D2.2","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:46:19+00:00"},{"identifier":"30e93254-492e-11eb-b591-ddd17a95a5f8","uri":"https://opensalt.net/uri/30e93254-492e-11eb-b591-ddd17a95a5f8","fullStatement":"Solving Problems Involving the Trigonometry of Right Triangles","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:45:05+00:00"},{"identifier":"30e909d2-492e-11eb-8fed-7943af7d8b4a","uri":"https://opensalt.net/uri/30e909d2-492e-11eb-8fed-7943af7d8b4a","fullStatement":"solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MPM2D-D2","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:42:18+00:00"},{"identifier":"30e98c22-492e-11eb-9632-f14795817504","uri":"https://opensalt.net/uri/30e98c22-492e-11eb-9632-f14795817504","fullStatement":"determine, through investigation (e.g., using dynamic geometry software, concrete materials), the relationship between the ratio of two sides in a right triangle and the ratio of the two corresponding sides in a similar right triangle, and define the sine, cosine, and tangent ratios (e.g., sin A = opposite/hypotenuse)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.D2.1","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:45:57+00:00"},{"identifier":"30e9a838-492e-11eb-adfd-6309a247098c","uri":"https://opensalt.net/uri/30e9a838-492e-11eb-adfd-6309a247098c","fullStatement":"solve problems involving the measures of sides and angles in right triangles in real-life applications (e.g., in surveying, in navigating, in determining the height of an inaccessible object around the school), using the primary trigonometric ratios and the Pythagorean theorem","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.D2.3","language":"en","educationLevel":["10"],"lastChangeDateTime":"2021-01-30T13:25:06+00:00"},{"identifier":"30ea4e96-492e-11eb-a4a3-a1ea9fb36595","uri":"https://opensalt.net/uri/30ea4e96-492e-11eb-a4a3-a1ea9fb36595","fullStatement":"explore the development of the cosine law within acute triangles (e.g., use dynamic geometry software to verify the cosine law; follow the algebraic development of the cosine law and identify its relationship to the Pythagorean theorem and the cosine ratio [student reproduction of the development of the formula is not required])","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.D3.2","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:48:18+00:00"},{"identifier":"30ea092c-492e-11eb-96d9-35cd894cbc59","uri":"https://opensalt.net/uri/30ea092c-492e-11eb-96d9-35cd894cbc59","fullStatement":"Solving Problems Involving the Trigonometry of Acute Triangles","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:47:17+00:00"},{"identifier":"30e9e050-492e-11eb-865e-ff001bf3c90e","uri":"https://opensalt.net/uri/30e9e050-492e-11eb-865e-ff001bf3c90e","fullStatement":"solve problems involving acute triangles, using the sine law and the cosine law","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MPM2D-D3","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:42:41+00:00"},{"identifier":"30ea6c32-492e-11eb-b164-c54c835a706b","uri":"https://opensalt.net/uri/30ea6c32-492e-11eb-b164-c54c835a706b","fullStatement":"explore the development of the sine law within acute triangles (e.g., use dynamic geometry software to determine that the ratio of the side lengths equals the ratio of the sines of the opposite angles; follow the algebraic development of the sine law and identify the application of solving systems of equations [student reproduction of the development of the formula is not required])","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.D3.1","language":"en","educationLevel":["10"],"lastChangeDateTime":"2021-01-06T17:07:43+00:00"},{"identifier":"30ea8780-492e-11eb-8ddd-1999f2a6f656","uri":"https://opensalt.net/uri/30ea8780-492e-11eb-8ddd-1999f2a6f656","fullStatement":"determine the measures of sides and angles in acute triangles, using the sine law and the cosine law","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.D3.3","notes":"Sample problem: In triangle ABC, angle A = 35\u00b0, angle B = 65\u00b0, and AC = 18 cm. Determine BC. Check your result using dynamic geometry software.)","language":"en","educationLevel":["10"],"lastChangeDateTime":"2021-01-06T17:08:11+00:00"},{"identifier":"30eaa332-492e-11eb-b9e0-87c6eb77f330","uri":"https://opensalt.net/uri/30eaa332-492e-11eb-b9e0-87c6eb77f330","fullStatement":"solve problems involving the measures of sides and angles in acute triangles","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.D3.4","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:51:10+00:00"},{"identifier":"30eaddac-492e-11eb-a365-23c0e2da3159","uri":"https://opensalt.net/uri/30eaddac-492e-11eb-a365-23c0e2da3159","fullStatement":"Analytic Geometry","CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19"},"humanCodingScheme":"MPM2D-C","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:03:13+00:00"},{"identifier":"30eb9062-492e-11eb-bd69-5508d701befa","uri":"https://opensalt.net/uri/30eb9062-492e-11eb-bd69-5508d701befa","fullStatement":"solve systems of two linear equations involving two variables, using the algebraic method of substitution or elimination","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.C1.1","notes":"**Sample Problem**: \r\n\r\nSolve y = (1/2) x \u2013 5, 3x + 2y = \u20132 for x and y algebraically, and verify algebraically and graphically.","language":"en","educationLevel":["10"],"lastChangeDateTime":"2021-01-06T17:04:58+00:00"},{"identifier":"30eb4c88-492e-11eb-8ff7-1d4561464440","uri":"https://opensalt.net/uri/30eb4c88-492e-11eb-8ff7-1d4561464440","fullStatement":"Using Linear Systems to Solve Problems","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:33:35+00:00"},{"identifier":"30eb1c0e-492e-11eb-b448-6f8826ee7fbc","uri":"https://opensalt.net/uri/30eb1c0e-492e-11eb-b448-6f8826ee7fbc","fullStatement":"model and solve problems involving the intersection of two straight lines","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MPM2D-C1","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:32:38+00:00"},{"identifier":"30ebbaec-492e-11eb-bd56-2bce51dceb07","uri":"https://opensalt.net/uri/30ebbaec-492e-11eb-bd56-2bce51dceb07","fullStatement":"solve problems that arise from realistic situations described in words or represented by linear systems of two equations involving two variables, by choosing an appropriate algebraic or graphical method","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.C1.2","notes":"**Sample problem**: \r\n\r\nThe Robotics Club raised $5000 to build a robot for a future competition. The club invested part of the money in an account that paid 4% annual interest, and the rest in a government bond that paid 3.5% simple interest per year. After one year, the club earned a total of $190 in interest. How much was invested at each rate?Verify your result.","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:35:41+00:00"},{"identifier":"30ecb730-492e-11eb-9995-bb2607cd0b54","uri":"https://opensalt.net/uri/30ecb730-492e-11eb-9995-bb2607cd0b54","fullStatement":"determine the radius of a circle with centre (0, 0), given its equation; write the equation of a circle with centre (0, 0), given the radius; and sketch the circle, given the equation in the form x\u00b2 + y\u00b2 = r\u00b2","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.C2.4","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:38:44+00:00"},{"identifier":"30ec6d0c-492e-11eb-ba99-9530e3903699","uri":"https://opensalt.net/uri/30ec6d0c-492e-11eb-ba99-9530e3903699","fullStatement":"Solving Problems Involving Properties of Line Segments","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:36:25+00:00"},{"identifier":"30ec3d1e-492e-11eb-b94f-11480f212cff","uri":"https://opensalt.net/uri/30ec3d1e-492e-11eb-b94f-11480f212cff","fullStatement":"solve problems using analytic geometry involving properties of lines and line segments","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MPM2D-C2","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:32:59+00:00"},{"identifier":"30ecd468-492e-11eb-8654-1fa998a72403","uri":"https://opensalt.net/uri/30ecd468-492e-11eb-8654-1fa998a72403","fullStatement":"develop the equation for a circle with centre (0, 0) and radius r, by applying the formula for the length of a line segment","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.C2.3","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:37:55+00:00"},{"identifier":"30ecfe84-492e-11eb-b8c5-45e7b7f49368","uri":"https://opensalt.net/uri/30ecfe84-492e-11eb-b8c5-45e7b7f49368","fullStatement":"develop the formula for the midpoint of a line segment, and use this formula to solve problems (e.g., determine the coordinates of the midpoints of the sides of a triangle, given the coordinates of the vertices, and verify concretely or by using dynamic geometry software)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.C2.1","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:36:57+00:00"},{"identifier":"30ed2878-492e-11eb-a3a0-655464e0eddc","uri":"https://opensalt.net/uri/30ed2878-492e-11eb-a3a0-655464e0eddc","fullStatement":"develop the formula for the length of a line segment, and use this formula to solve problems (e.g., determine the lengths of the line segments joining the midpoints of the sides of a triangle, given the coordi- nates of the vertices of the triangle, and verify using dynamic geometry software)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.C2.2","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:37:24+00:00"},{"identifier":"30ed52da-492e-11eb-a207-e1f3e98cf7ee","uri":"https://opensalt.net/uri/30ed52da-492e-11eb-a207-e1f3e98cf7ee","fullStatement":"solve problems involving the slope, length, and midpoint of a line segment (e.g., determine the equation of the right bisector of a line segment, given the coordinates of the endpoints; determine the distance from a given point to a line whose equation is given, and verify using dynamic geometry software)","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MPM2D-10.C2.5","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:39:14+00:00"},{"identifier":"30ede38a-492e-11eb-9615-8d5af8ef9cf4","uri":"https://opensalt.net/uri/30ede38a-492e-11eb-9615-8d5af8ef9cf4","fullStatement":"determine, through investigation (e.g., using dynamic geometry software, by paper folding), some characteristics and properties of geometric figures (e.g., medians in a triangle, similar figures constructed on the sides of a right triangle)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.C3.1","language":"en","educationLevel":["10"],"lastChangeDateTime":"2021-01-06T17:05:51+00:00"},{"identifier":"30eda10e-492e-11eb-b3c8-b58e718df825","uri":"https://opensalt.net/uri/30eda10e-492e-11eb-b3c8-b58e718df825","fullStatement":"Using Analytic Geometry to Verify Geometric Properties","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:39:36+00:00"},{"identifier":"30ed713e-492e-11eb-9283-ddc3b866bb64","uri":"https://opensalt.net/uri/30ed713e-492e-11eb-9283-ddc3b866bb64","fullStatement":"verify geometric properties of triangles and quadrilaterals, using analytic geometry","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MPM2D-C3","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:33:21+00:00"},{"identifier":"30ee0ee6-492e-11eb-be9b-239d167a8da3","uri":"https://opensalt.net/uri/30ee0ee6-492e-11eb-be9b-239d167a8da3","fullStatement":"verify, using algebraic techniques and analytic geometry, some characteristics of geometric figures (e.g., verify that two lines are perpendicular, given the coordinates of two points on each line; verify, by determining side length, that a triangle is equilateral, given the coordinates of the vertices)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.C3.2","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:41:01+00:00"},{"identifier":"30ee38e4-492e-11eb-a173-6fe56d75ba17","uri":"https://opensalt.net/uri/30ee38e4-492e-11eb-a173-6fe56d75ba17","fullStatement":"plan and implement a multi-step strategy that uses analytic geometry and algebraic techniques to verify a geometric property (e.g., given the coordinates of the vertices of a triangle, verify that the line segment joining the midpoints of two sides of the triangle is parallel to the third side and half its length, and check using dynamic geometry software; given the coordinates of the vertices of a rectangle, verify that the diagonals of the rectangle bisect each other)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.C3.3","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:41:28+00:00"},{"identifier":"30e232ce-492e-11eb-8679-9757b29a4b25","uri":"https://opensalt.net/uri/30e232ce-492e-11eb-8679-9757b29a4b25","fullStatement":"relate transformations of the graph of y = x\u00b2 to the algebraic representation y = a(x \u2013 h)\u00b2 + k","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MPM2D-B2","language":"en","educationLevel":["10"],"lastChangeDateTime":"2021-01-06T16:56:51+00:00"},{"identifier":"30e2c414-492e-11eb-b160-adc1c53ffa73","uri":"https://opensalt.net/uri/30e2c414-492e-11eb-b160-adc1c53ffa73","fullStatement":"identify, through investigation using technology, the effect on the graph of y = x\u00b2 of transformations (i.e., translations, reflections in the x-axis, vertical stretches or compressions) by considering separately each parameter a, h, and k [i.e., investigate the effect on the graph of y = x\u00b2 of a, h, and k in y = x\u00b2 + k, y = (x \u2013 h)\u00b2, and y = ax\u00b2]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.B2.1","language":"en","educationLevel":["10"],"lastChangeDateTime":"2021-01-06T17:00:38+00:00"},{"identifier":"30e2617c-492e-11eb-bc93-19b410d2b855","uri":"https://opensalt.net/uri/30e2617c-492e-11eb-bc93-19b410d2b855","fullStatement":"Relating the Graph of y = x\u00b2 and Its Transformations","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:12:49+00:00"},{"identifier":"30e2ee08-492e-11eb-ae8e-e73b2eea0e9f","uri":"https://opensalt.net/uri/30e2ee08-492e-11eb-ae8e-e73b2eea0e9f","fullStatement":"explain the roles of a, h, and k in y = a(x \u2013 h)\u00b2 + k, using the appropriate terminology to describe the transformations, and identify the vertex and the equation of the axis of symmetry","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.B2.2","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:15:45+00:00"},{"identifier":"30e31856-492e-11eb-9f98-c9e673596310","uri":"https://opensalt.net/uri/30e31856-492e-11eb-9f98-c9e673596310","fullStatement":"sketch, by hand, the graph of y = a(x \u2013 h)\u00b2 + k by applying transformations to the graph of y = x\u00b2","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.B2.3","notes":"**Sample Problem**: \r\n\r\nSketch the graph of y = \u20131/2 (x \u2013 3)\u00b2 + 4, and verify using technology.","language":"en","educationLevel":["10"],"lastChangeDateTime":"2021-01-06T17:01:25+00:00"},{"identifier":"30e34240-492e-11eb-af25-436861731e01","uri":"https://opensalt.net/uri/30e34240-492e-11eb-af25-436861731e01","fullStatement":"determine the equation, in the form y = a(x \u2013 h)\u00b2 + k, of a given graph of a parabola","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.B2.4","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:19:12+00:00"},{"identifier":"30e1b4d4-492e-11eb-8251-1960d6aab1e7","uri":"https://opensalt.net/uri/30e1b4d4-492e-11eb-8251-1960d6aab1e7","fullStatement":"determine, through investigation with and without the use of technology, that a quadratic relation of the form y = ax\u00b2 + bx + c (a \u2260 0) can be graphically represented as a parabola, and that the table of values yields a constant second difference","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.B1.2","notes":"**Sample Problem**: \r\n\r\nGraph the relation y = x\u00b2 \u2013 4x by developing a table of values and plotting points. Observe the shape of the graph. Calculate first and second differences. Repeat for different quadratic relations. Describe your observations and make conclusions, using the appropriate terminology.","language":"en","educationLevel":["10"],"lastChangeDateTime":"2021-01-06T16:59:22+00:00"},{"identifier":"30e1de32-492e-11eb-9e84-d362cd370769","uri":"https://opensalt.net/uri/30e1de32-492e-11eb-9e84-d362cd370769","fullStatement":"identify the key features of a graph of a parabola (i.e., the equation of the axis of symmetry, the coordinates of the vertex, the y-intercept, the zeros, and the maxi- mum or minimum value), and use the appropriate terminology to describe them","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.B1.3","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:11:02+00:00"},{"identifier":"30e20772-492e-11eb-b62e-aba5a89954dd","uri":"https://opensalt.net/uri/30e20772-492e-11eb-b62e-aba5a89954dd","fullStatement":"compare, through investigation using technology, the features of the graph of y = x\u00b2 and the graph of y = 2x, and determine the meaning of a negative exponent and of zero as an exponent (e.g., by examining patterns in a table of values for y = 2x; by applying the exponent rules for multiplication and division)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.B1.4","language":"en","educationLevel":["10"],"lastChangeDateTime":"2021-01-30T12:50:48+00:00"},{"identifier":"bb9e7384-4931-11eb-ac52-932def2d2828","uri":"https://opensalt.net/uri/bb9e7384-4931-11eb-ac52-932def2d2828","fullStatement":"sketch or graph a quadratic relation whose equation is given in the form y = ax\u00b2 + bx + c, using a variety of methods (e.g., sketching y = x\u00b2 \u2013 2x \u2013 8 using intercepts and symmetry; sketching y = 3x\u00b2 \u2013 12x + 1 by completing the square and applying transformations; graphing h = \u20134.9t\u00b2 + 50t + 1.5 using technology)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.B3.6","language":"en","educationLevel":["10"],"lastChangeDateTime":"2021-01-06T17:03:00+00:00"},{"identifier":"bf7df164-4931-11eb-a509-2d8006b64ba4","uri":"https://opensalt.net/uri/bf7df164-4931-11eb-a509-2d8006b64ba4","fullStatement":"explore the algebraic development of the quadratic formula (e.g., given the algebraic development, connect the steps to a numerical example; follow a demonstration of the algebraic development [student reproduction of the development of the general case is not required]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.B3.7","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:27:28+00:00"},{"identifier":"c2493a20-4931-11eb-90b8-2359c3c4bbd9","uri":"https://opensalt.net/uri/c2493a20-4931-11eb-90b8-2359c3c4bbd9","fullStatement":"solve quadratic equations that have real roots, using a variety of methods (i.e., factoring, using the quadratic formula, graphing)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-10.B3.8","notes":"**Sample problem**: \r\n\r\nSolve x\u00b2 + 10x + 16 = 0 by factoring, and verify algebraically. Solve x\u00b2 + x \u2013 4 = 0 using the quadratic formula, and verify graphically using technology. Solve \u20134.9t\u00b2 + 50t + 1.5 = 0 by graphing h = \u20134.9t\u00b2 + 50t + 1.5 using technology.).","language":"en","educationLevel":["10"],"lastChangeDateTime":"2020-12-28T17:28:37+00:00"},{"identifier":"79a48748-49e5-11eb-846b-eb6980413d62","uri":"https://opensalt.net/uri/79a48748-49e5-11eb-846b-eb6980413d62","fullStatement":"Grade 11","CFItemType":"Grade Level","CFItemTypeURI":{"title":"Grade Level","identifier":"8047d85d-6c8e-5231-bd6d-050731684413","uri":"https://api.acmt-prod.learningmate.com/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/8047d85d-6c8e-5231-bd6d-050731684413"},"language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-08T20:17:17+00:00"},{"identifier":"838bc0a0-49e5-11eb-82c0-a3851d3ee367","uri":"https://opensalt.net/uri/838bc0a0-49e5-11eb-82c0-a3851d3ee367","fullStatement":"Functions, Grade 11","CFItemType":"Grade Level","CFItemTypeURI":{"title":"Grade Level","identifier":"8047d85d-6c8e-5231-bd6d-050731684413","uri":"https://api.acmt-prod.learningmate.com/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/8047d85d-6c8e-5231-bd6d-050731684413"},"humanCodingScheme":"MCR3U","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-30T21:06:46+00:00"},{"identifier":"838cc8ce-49e5-11eb-ab14-7b5c6f7b2f1c","uri":"https://opensalt.net/uri/838cc8ce-49e5-11eb-ab14-7b5c6f7b2f1c","fullStatement":"explain the meaning of the term function, and distinguish a function from a relation that is not a function, through investigation of linear and quadratic relations using a variety of representations (i.e., tables of values, mapping diagrams, graphs, function machines, equations) and strategies (e.g., identifying a one-to-one or many-to-one mapping; using the vertical- line test)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.A1.1","notes":"**Sample Problem**:\r\n\r\nInvestigate, using numeric and graphical representations, whether the relation x = y\u00b2 is a function, and justify your reasoning.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:37:39+00:00"},{"identifier":"838c872e-49e5-11eb-828b-cf5301f86a5c","uri":"https://opensalt.net/uri/838c872e-49e5-11eb-828b-cf5301f86a5c","fullStatement":"Representing Functions","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T14:56:46+00:00"},{"identifier":"838c57ae-49e5-11eb-abf1-e1e81315583b","uri":"https://opensalt.net/uri/838c57ae-49e5-11eb-abf1-e1e81315583b","fullStatement":"demonstrate an understanding of functions, their representations, and their inverses, and make connections between the algebraic and graphical representations of functions using transformations","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MCR3U-A1","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T14:55:48+00:00"},{"identifier":"838c1050-49e5-11eb-a2ca-f77905cf7113","uri":"https://opensalt.net/uri/838c1050-49e5-11eb-a2ca-f77905cf7113","fullStatement":"Characteristics of Functions","CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19"},"humanCodingScheme":"MCR3U-A","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T14:54:29+00:00"},{"identifier":"838d71fc-49e5-11eb-82d5-57d35619043f","uri":"https://opensalt.net/uri/838d71fc-49e5-11eb-82d5-57d35619043f","fullStatement":"determine the zeros and the maximum or minimum of a quadratic function, and solve problems involving quadratic functions, including problems arising from real-world applications","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MCR3U-A2","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T14:56:07+00:00"},{"identifier":"838de2fe-49e5-11eb-89e1-f76c9998d1dd","uri":"https://opensalt.net/uri/838de2fe-49e5-11eb-89e1-f76c9998d1dd","fullStatement":"determine the number of zeros (i.e., x-intercepts) of a quadratic function, using a variety of strategies (e.g., inspecting graphs; factoring; calculating the discriminant)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.A2.1","notes":"**Sample Problem**: \r\n\r\nInvestigate, using graphing technology and algebraic techniques, the transformations that affect the number of zeros for a given quadratic function.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:41:14+00:00"},{"identifier":"838da08c-49e5-11eb-a4fa-5ba5eead8edd","uri":"https://opensalt.net/uri/838da08c-49e5-11eb-a4fa-5ba5eead8edd","fullStatement":"Solving Problems Involving Quadratic Functions","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T16:17:01+00:00"},{"identifier":"838e0e5a-49e5-11eb-aae3-354a2031f073","uri":"https://opensalt.net/uri/838e0e5a-49e5-11eb-aae3-354a2031f073","fullStatement":"determine the maximum or minimum value of a quadratic function whose equation is given in the form f(x) = ax\u00b2 + bx + c, using an algebraic method (e.g., completing the square; factoring to determine the zeros and averaging the zeros)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.A2.2","notes":"**Sample Problem**: \r\n\r\nExplain how partially factoring f(x) = 3x\u00b2 \u2013 6x + 5 into the form f(x) = 3x(x \u2013 2) + 5 helps you determine the minimum of the function.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:41:40+00:00"},{"identifier":"838e37e0-49e5-11eb-a9a4-45c23dbd6385","uri":"https://opensalt.net/uri/838e37e0-49e5-11eb-a9a4-45c23dbd6385","fullStatement":"solve problems involving quadratic functions arising from real-world applications and represented using function notation","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.A2.3","notes":"**Sample Problem**: \r\n\r\nThe profit, P(x), of a video company, in thousands of dollars, is given by P(x) = \u2013 5x\u00b2 + 550x \u2013 5000, where x is the amount spent on advertising, in thousands of dollars. Determine the maximum profit that the company can make, and the amounts spent on advertising that will result in a profit and that will result in a profit of at least $4 000 000.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:41:56+00:00"},{"identifier":"838e606c-49e5-11eb-a287-f735d2b9ddb3","uri":"https://opensalt.net/uri/838e606c-49e5-11eb-a287-f735d2b9ddb3","fullStatement":"determine, through investigation, the transformational relationship among the family of quadratic functions that have the same zeros, and determine the algebraic representation of a quadratic function, given the real roots of the corresponding quadratic equation and a point on the function","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.A2.4","notes":"**Sample Problem**: \r\n\r\nDetermine the equation of the quadratic function that passes through (2, 5) if the roots of the corresponding quadratic equation are 1 + \u221a5 and 1 \u2013 \u221a5.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:42:28+00:00"},{"identifier":"838e8b5a-49e5-11eb-bee7-01fa4c2a0e61","uri":"https://opensalt.net/uri/838e8b5a-49e5-11eb-bee7-01fa4c2a0e61","fullStatement":"demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MCR3U-A3","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:37:09+00:00"},{"identifier":"838f14da-49e5-11eb-a3b5-f152d5dd71ab","uri":"https://opensalt.net/uri/838f14da-49e5-11eb-a3b5-f152d5dd71ab","fullStatement":"simplify polynomial expressions by adding, subtracting, and multiplying","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.A3.1","notes":"**Sample Problem**: \r\n\r\nWrite and simplify an expression for the volume of a cube with edge length 2x + 1.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T20:01:56+00:00"},{"identifier":"838eba9e-49e5-11eb-81e7-8dadd7dc2f69","uri":"https://opensalt.net/uri/838eba9e-49e5-11eb-81e7-8dadd7dc2f69","fullStatement":"Determining Equivalent Algebraic Expressions","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"notes":"The knowledge and skills described in the expectations in this section are to be introduced as needed, and applied and consolidated, as appropriate, in solving problems throughout the course.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T16:21:48+00:00"},{"identifier":"838f40c2-49e5-11eb-9de9-3946ebb2f017","uri":"https://opensalt.net/uri/838f40c2-49e5-11eb-9de9-3946ebb2f017","fullStatement":"verify, through investigation with and without technology, that \u221aab = \u221aa x \u221ab, a \u2265 0, b \u2265 0, and use this relationship to simplify radicals (e.g., \u221a24) and radical expressions obtained by adding, subtracting, and multiplying [e.g., (2 + \u221a6)( 3 \u2013 \u221a12)]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.A3.2","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T16:23:26+00:00"},{"identifier":"838f6b38-49e5-11eb-ad3c-f10196862635","uri":"https://opensalt.net/uri/838f6b38-49e5-11eb-ad3c-f10196862635","fullStatement":"simplify rational expressions by adding, subtracting, multiplying, and dividing, and state the restrictions on the variable values","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.A3.3","notes":"**Sample Problem**:\r\n\r\nSimplify 2x/(4x\u00b2 + 6x) - 3/(2x + 3), and state the restrictions on the variable.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T16:24:56+00:00"},{"identifier":"838f8776-49e5-11eb-8529-f3cdd8fc5af8","uri":"https://opensalt.net/uri/838f8776-49e5-11eb-8529-f3cdd8fc5af8","fullStatement":"determine if two given algebraic expressions are equivalent (i.e., by simplifying; by substituting values)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.A3.4","notes":"**Sample Problem**:\r\n\r\nDetermine if the expressions (2x\u00b2 - 4x -6)/(x + 1) and 8x\u00b2 - 2x(4x-1) - 6 are equivalent.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T20:02:09+00:00"},{"identifier":"838cf3f8-49e5-11eb-86c3-b1e7bd0fb518","uri":"https://opensalt.net/uri/838cf3f8-49e5-11eb-86c3-b1e7bd0fb518","fullStatement":"represent linear and quadratic functions using function notation, given their equations, tables of values, or graphs, and substitute into and evaluate functions [e.g., evaluate f(1/2), given f(x) = 2x\u00b2 + 3x - 1]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.A1.2","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T16:08:02+00:00"},{"identifier":"838d1d88-49e5-11eb-8a43-272d981a6ccc","uri":"https://opensalt.net/uri/838d1d88-49e5-11eb-8a43-272d981a6ccc","fullStatement":"explain the meanings of the terms domain and range, through investigation using numeric, graphical, and algebraic representations of the functions f(x) = x, f(x) = x\u00b2, f(x) = \u221ax, and f(x) = 1/x,; describe the domain and range of a function appropriately (e.g., for y = x + 1, the domain is the set of real numbers, and the range is y \u2265 1); and explain any restrictions on the domain and range in contexts arising from real-world applications","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.A1.3","notes":"**Sample Problem**: \r\n\r\nA quadratic function represents the relationship between the height of a ball and the time elapsed since the ball was thrown. What physical factors will restrict the domain and range of the quadratic function?","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:38:06+00:00"},{"identifier":"838d46fa-49e5-11eb-bb76-8b70adc535b5","uri":"https://opensalt.net/uri/838d46fa-49e5-11eb-bb76-8b70adc535b5","fullStatement":"relate the process of determining the inverse of a function to their understanding of reverse processes (e.g., applying inverse operations)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.A1.4","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T16:08:02+00:00"},{"identifier":"83916a0a-49e5-11eb-960e-35402bc7ea30","uri":"https://opensalt.net/uri/83916a0a-49e5-11eb-960e-35402bc7ea30","fullStatement":"make connections between sequences and discrete functions, represent sequences using function notation, and distinguish between a discrete function and a continuous function [e.g., f(x) = 2x, where the domain is the set of natural numbers, is a discrete linear function and its graph is a set of equally spaced points; f(x) = 2x, where the domain is the set of real numbers, is a continuous linear function and its graph is a straight line]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.C1.1","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T17:46:19+00:00"},{"identifier":"83912b76-49e5-11eb-a282-c170953c6541","uri":"https://opensalt.net/uri/83912b76-49e5-11eb-a282-c170953c6541","fullStatement":"Representing Sequences","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T17:43:48+00:00"},{"identifier":"8390fb38-49e5-11eb-ae21-519ee03f0513","uri":"https://opensalt.net/uri/8390fb38-49e5-11eb-ae21-519ee03f0513","fullStatement":"demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make connections to Pascal\u2019s triangle","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MCR3U-C1","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T17:43:00+00:00"},{"identifier":"8390bf74-49e5-11eb-8cc1-45e678dce16a","uri":"https://opensalt.net/uri/8390bf74-49e5-11eb-8cc1-45e678dce16a","fullStatement":"Discrete Functions","CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19"},"humanCodingScheme":"MCR3U-C","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T14:54:29+00:00"},{"identifier":"8391e8c2-49e5-11eb-96aa-cd1790b25467","uri":"https://opensalt.net/uri/8391e8c2-49e5-11eb-96aa-cd1790b25467","fullStatement":"demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series, and solve related problems","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MCR3U-C2","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T17:42:53+00:00"},{"identifier":"839254e2-49e5-11eb-a0fb-813eafa20b90","uri":"https://opensalt.net/uri/839254e2-49e5-11eb-a0fb-813eafa20b90","fullStatement":"determine the formula for the general term of an arithmetic sequence [i.e., tn = a + (n \u2013 1) d ] or geometric sequence (i.e., tn = arn \u2013 1), through investigation using a variety of tools (e.g., linking cubes, algebra tiles, diagrams, calculators) and strategies (e.g., patterning; connecting the steps in a numerical example to the steps in the algebraic development), and apply the formula to calculate any term in a sequence","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.C2.2","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T17:59:19+00:00"},{"identifier":"839217f2-49e5-11eb-9493-9d004b59311f","uri":"https://opensalt.net/uri/839217f2-49e5-11eb-9493-9d004b59311f","fullStatement":"Investigating Arithmetic and Geometric Sequences and Series","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T17:54:42+00:00"},{"identifier":"83927e2c-49e5-11eb-9d18-0b3933049873","uri":"https://opensalt.net/uri/83927e2c-49e5-11eb-9d18-0b3933049873","fullStatement":"identify sequences as arithmetic, geometric, or neither, given a numeric or algebraic representation","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.C2.1","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T17:59:19+00:00"},{"identifier":"8392a7d0-49e5-11eb-a581-b3fc69f25e3a","uri":"https://opensalt.net/uri/8392a7d0-49e5-11eb-a581-b3fc69f25e3a","fullStatement":"determine the formula for the sum of an arithmetic or geometric series, through investigation using a variety of tools (e.g., linking cubes, algebra tiles, diagrams, calculators) and strategies (e.g., patterning; connecting the steps in a numerical example to the steps in the algebraic development), and apply the formula to calculate the sum of a given number of consecutive terms","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-11.C2.3","notes":"**Sample Problem**: \r\n\r\nGiven the following array built with grey and white connecting cubes, investigate how different ways of determining the total number of grey cubes can be used to evaluate the sum of the arithmetic series 1 + 2 + 3 + 4 + 5. Extend the series, use patterning to make generalizations for finding the sum, and test the generalizations for other arithmetic series.\r\n\r\n[Figure]","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:51:49+00:00"},{"identifier":"8392d2fa-49e5-11eb-be7a-0fe9208f64f2","uri":"https://opensalt.net/uri/8392d2fa-49e5-11eb-be7a-0fe9208f64f2","fullStatement":"make connections between sequences, series, and financial applications, and solve problems involving compound interest and ordinary annuities","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MCR3U-C3","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:49:20+00:00"},{"identifier":"839347d0-49e5-11eb-8ee5-8b7bc02f400f","uri":"https://opensalt.net/uri/839347d0-49e5-11eb-8ee5-8b7bc02f400f","fullStatement":"make and describe connections between compound interest, geometric sequences, and exponential growth, through investigation with technology (e.g., use a spreadsheet to make compound interest calculations, determine finite differences in the amounts over time, and graph amount versus time)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.C3.2","notes":"**Sample Problem**: \r\n\r\nDescribe an investment that could be represented by the function f(x) = 500(1.05)x.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T20:03:26+00:00"},{"identifier":"839304aa-49e5-11eb-8da6-0fe3b01782e4","uri":"https://opensalt.net/uri/839304aa-49e5-11eb-8da6-0fe3b01782e4","fullStatement":"Solving Problems Involving Financial Applications","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T18:52:50+00:00"},{"identifier":"83937228-49e5-11eb-8978-1163fa91e128","uri":"https://opensalt.net/uri/83937228-49e5-11eb-8978-1163fa91e128","fullStatement":"make and describe connections between simple interest, arithmetic sequences, and linear growth, through investigation with technology (e.g., use a spreadsheet or graphing calculator to make simple interest calculations, determine first differences in the amounts over time, and graph amount versus time)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.C3.1","notes":"**Sample Problem**: \r\n\r\nDescribe an investment that could be represented by the function f(x) = 500(1 + 0.05x).","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:27:04+00:00"},{"identifier":"83939bcc-49e5-11eb-8f57-3d58271b6515","uri":"https://opensalt.net/uri/83939bcc-49e5-11eb-8f57-3d58271b6515","fullStatement":"solve problems, using a scientific calculator, that involve the calculation of the amount, A (also referred to as future value, FV ), the principal, P (also referred to as present value, PV ), or the interest rate per compounding period, i, using the compound interest formula in the form A = P(1 + i)n [or FV = PV(1 + i)n]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.C3.3","notes":"**Sample Problem**: \r\n\r\nTwo investments are available, one at 6% compounded annually and the other at 6% compounded monthly. Investigate graphically the growth of each investment, and determine the interest earned from depositing $1000 in each investment for 10 years.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:27:04+00:00"},{"identifier":"8393c548-49e5-11eb-a7e1-7b69f2e5ff05","uri":"https://opensalt.net/uri/8393c548-49e5-11eb-a7e1-7b69f2e5ff05","fullStatement":"determine, through investigation using technology (e.g., scientific calculator, the TVM Solver on a graphing calculator, online tools), the number of compounding periods, n, using the compound interest formula in the form A = P(1 + i )n [or FV = PV(1 + i )n]; describe strategies (e.g., guessing and checking; using the power of a power rule for exponents; using graphs) for calculating this number; and solve related problems","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.C3.4","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:54:58+00:00"},{"identifier":"839193a4-49e5-11eb-9688-d51e3e2f1650","uri":"https://opensalt.net/uri/839193a4-49e5-11eb-9688-d51e3e2f1650","fullStatement":"determine and describe (e.g., in words; using flow charts) a recursive procedure for generating a sequence, given the initial terms (e.g., 1, 3, 6, 10, 15, 21, \u2026), and represent sequences as discrete functions in a variety of ways (e.g., tables of values, graphs)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.C1.2","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T17:46:19+00:00"},{"identifier":"8391bd52-49e5-11eb-af5d-8163bfd90f2b","uri":"https://opensalt.net/uri/8391bd52-49e5-11eb-af5d-8163bfd90f2b","fullStatement":"connect the formula for the nth term of a sequence to the representation in function notation, and write terms of a sequence given one of these representations or a recursion formula","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.C1.3","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T17:46:19+00:00"},{"identifier":"839493ce-49e5-11eb-81e1-53fdb08edea8","uri":"https://opensalt.net/uri/839493ce-49e5-11eb-81e1-53fdb08edea8","fullStatement":"graph, with and without technology, an exponential relation, given its equation in the form y = ax (a > 0, a \u2260 1), define this relation as the function f(x) = ax, and explain why it is a function","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.B1.1","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:45:08+00:00"},{"identifier":"83945d32-49e5-11eb-8bff-e34e9efdf8b5","uri":"https://opensalt.net/uri/83945d32-49e5-11eb-8bff-e34e9efdf8b5","fullStatement":"Representing Exponential Functions","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T16:34:54+00:00"},{"identifier":"83942c9a-49e5-11eb-9a8f-891955071b99","uri":"https://opensalt.net/uri/83942c9a-49e5-11eb-9a8f-891955071b99","fullStatement":"evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential functions represented in a variety of ways","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MCR3U-B1","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:44:22+00:00"},{"identifier":"8393f0f4-49e5-11eb-83ac-4da155093ac6","uri":"https://opensalt.net/uri/8393f0f4-49e5-11eb-83ac-4da155093ac6","fullStatement":"Exponential Functions","CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19"},"humanCodingScheme":"MCR3U-B","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T14:54:29+00:00"},{"identifier":"8394e93c-49e5-11eb-962a-8300299f481e","uri":"https://opensalt.net/uri/8394e93c-49e5-11eb-962a-8300299f481e","fullStatement":"make connections between the numeric, graphical, and algebraic representations of exponential\r\nfunctions","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MCR3U-B2","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T16:28:10+00:00"},{"identifier":"839561c8-49e5-11eb-b97c-0ba9daa1736c","uri":"https://opensalt.net/uri/839561c8-49e5-11eb-b97c-0ba9daa1736c","fullStatement":"determine, through investigation using technology, that the equation of a given exponential function can be expressed using different bases [e.g., f(x) = 9x can be expressed as f(x) = 32x ], and explain the connections between the equivalent forms in a variety of ways (e.g., comparing graphs; using transformations; using the exponent laws)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.B2.4","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T16:49:10+00:00"},{"identifier":"839518a8-49e5-11eb-81ac-61055cd48306","uri":"https://opensalt.net/uri/839518a8-49e5-11eb-81ac-61055cd48306","fullStatement":"Connecting Graphs and Equations of Exponential Functions","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T16:42:47+00:00"},{"identifier":"83958b12-49e5-11eb-b4a2-4993948f0fd8","uri":"https://opensalt.net/uri/83958b12-49e5-11eb-b4a2-4993948f0fd8","fullStatement":"sketch graphs of y = af (k(x \u2013 d )) + c by applying one or more transformations to the graph of f(x) = ax (a > 0, a \u2260 1), and state the domain and range of the transformed functions","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.B2.3","notes":"**Sample Problem**: \r\n\r\nTransform the graph of f(x) = 3x to sketch g(x) = 3 \u2013 (x + 1) \u2013 2, and state the domain and range of each function.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T20:02:53+00:00"},{"identifier":"8395b434-49e5-11eb-9d71-17a145603fe7","uri":"https://opensalt.net/uri/8395b434-49e5-11eb-9d71-17a145603fe7","fullStatement":"distinguish exponential functions from linear and quadratic functions by making comparisons in a variety of ways (e.g., comparing rates of change using finite differences in tables of values; identifying a constant ratio in a table of values; inspecting graphs; comparing equations)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.B2.1","notes":"**Sample Problem**: \r\n\r\nExplain in a variety of ways how you can distinguish the exponential function f(x) = 2x from the quadratic function f(x) = x\u00b2 and the linear function f(x) = 2x.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T20:02:43+00:00"},{"identifier":"8395dd92-49e5-11eb-b319-f5cc98bd645c","uri":"https://opensalt.net/uri/8395dd92-49e5-11eb-b319-f5cc98bd645c","fullStatement":"determine, through investigation using technology, the roles of the parameters a, k, d, and c in functions of the form y = af (k(x \u2013 d )) + c, and describe these roles in terms of transformations on the graph of f(x) = ax (a > 0, a \u2260 1) (i.e., translations; reflections in the axes; vertical and horizontal stretches and compressions to and from the x- and y-axes)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.B2.2","notes":"**Sample Problem**: \r\n\r\nInvestigate the graph of f(x) = 3x \u2013 d \u2013 5 for various values of d, using technology, and describe the effects of changing d in terms of a transformation.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:46:57+00:00"},{"identifier":"839606dc-49e5-11eb-8365-d9dbd10f13c1","uri":"https://opensalt.net/uri/839606dc-49e5-11eb-8365-d9dbd10f13c1","fullStatement":"represent an exponential function with an equation, given its graph or its properties","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MCR3U-11.B2.5","notes":"**Sample Problem**:\r\n\r\nWrite two equations to represent the same exponential function with a y-intercept of 5 and an asymptote at y = 3. Investigate whether other exponential functions have the same properties. Use transformations to explain your observations.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T16:50:44+00:00"},{"identifier":"839631b6-49e5-11eb-9222-8b8d4facd3bc","uri":"https://opensalt.net/uri/839631b6-49e5-11eb-9222-8b8d4facd3bc","fullStatement":"identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from real-world applications","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MCR3U-B3","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T16:28:35+00:00"},{"identifier":"83969c82-49e5-11eb-90f3-f94fc549f250","uri":"https://opensalt.net/uri/83969c82-49e5-11eb-90f3-f94fc549f250","fullStatement":"collect data that can be modelled as an exponential function, through investigation with and without technology, from primary sources, using a variety of tools (e.g., concrete materials such as number cubes, coins; measurement tools such as electronic probes), or from secondary sources (e.g., websites such as Statistics Canada, E-STAT), and graph the data","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.B3.1","notes":"**Sample Problem**: \r\n\r\nCollect data and graph the cooling curve representing the relationship between temperature and time for hot water cooling in a porcelain mug. Predict the shape of the cooling curve when hot water cools in an insulated mug. Test your prediction.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:47:50+00:00"},{"identifier":"839660be-49e5-11eb-b527-cde7e26a2a20","uri":"https://opensalt.net/uri/839660be-49e5-11eb-b527-cde7e26a2a20","fullStatement":"Solving Problems Involving Exponential Functions","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T16:51:03+00:00"},{"identifier":"8396c748-49e5-11eb-9685-0fc4cb03ab30","uri":"https://opensalt.net/uri/8396c748-49e5-11eb-9685-0fc4cb03ab30","fullStatement":"identify exponential functions, including those that arise from real-world applications involving growth and decay (e.g., radioactive decay, population growth, cooling rates, pressure in a leaking tire), given various representations (i.e., tables of values, graphs, equations), and explain any restrictions that the context places on the domain and range (e.g., ambient temperature limits the range for a cooling curve)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.B3.2","notes":"**Sample Problem**: \r\n\r\nUsing data from Statistics Canada, investigate to determine if there was a period of time over which the increase in Canada\u2019s national debt could be modelled using an exponential function.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T16:53:08+00:00"},{"identifier":"8396f09c-49e5-11eb-9847-8d98c5f8f05d","uri":"https://opensalt.net/uri/8396f09c-49e5-11eb-9847-8d98c5f8f05d","fullStatement":"solve problems using given graphs or equations of exponential functions arising from a variety of real-world applications (e.g., radioactive decay, population growth, height of a bouncing ball, compound interest) by interpreting the graphs or by substituting values for the exponent into the equations","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.B3.3","notes":"**Sample Problem**:\r\n\r\nThe temperature of a cooling liquid over time can be modelled by the exponential function T(x) = 60(1/2)x/30 + 20, where T(x) is the temperature, in degrees Celsius, and x is the elapsed time, in minutes. Graph the function and determine how long it takes for the temperature to reach 28\u00baC.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T16:55:04+00:00"},{"identifier":"8394bdfe-49e5-11eb-a2bb-8359fd122cfa","uri":"https://opensalt.net/uri/8394bdfe-49e5-11eb-a2bb-8359fd122cfa","fullStatement":"determine, through investigation using a variety of tools (e.g., calculator, paper and pencil, graphing technology) and strategies (e.g., patterning; finding values from a graph; interpreting the exponent laws), the value of m a power with a rational exponent (i.e., xm/n , where x > 0 and m and n are integers)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.B1.2","notes":"**Sample Problem**: \r\n\r\nThe exponent laws suggest that 41/2 x 41/2 = 41. What value would you assign to 41/2 ? What value would you assign to 271/3? Explain your reasoning. Extend your reasoning to make a generalization about the meaning of x1/n, where x > 0 and n is a natural number.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T20:02:19+00:00"},{"identifier":"c0ca6002-49e5-11eb-b952-9b99b3a9ac59","uri":"https://opensalt.net/uri/c0ca6002-49e5-11eb-b952-9b99b3a9ac59","fullStatement":"Trigonometric Functions","CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19"},"humanCodingScheme":"MCR3U-D","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T14:54:48+00:00"},{"identifier":"c0cb29c4-49e5-11eb-8eed-55a24eb6b229","uri":"https://opensalt.net/uri/c0cb29c4-49e5-11eb-8eed-55a24eb6b229","fullStatement":"determine the exact values of the sine, cosine, and tangent of the special angles: 0\u00ba, 30\u00ba, 45\u00ba, 60\u00ba, and 90\u00ba","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.D1.1","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:34:08+00:00"},{"identifier":"c0cae392-49e5-11eb-ab52-859a499aab6e","uri":"https://opensalt.net/uri/c0cae392-49e5-11eb-ab52-859a499aab6e","fullStatement":"Determining and Applying Trigonometric Ratios","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:30:39+00:00"},{"identifier":"c0caad64-49e5-11eb-bf31-3f453dfcc8fe","uri":"https://opensalt.net/uri/c0caad64-49e5-11eb-bf31-3f453dfcc8fe","fullStatement":"determine the values of the trigonometric ratios for angles less than 360\u00ba; prove simple trigonometric identities; and solve problems using the primary trigonometric ratios, the sine law, and the cosine law","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MCR3U-D1","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:29:48+00:00"},{"identifier":"c0cb5b42-49e5-11eb-9516-d7164078b12c","uri":"https://opensalt.net/uri/c0cb5b42-49e5-11eb-9516-d7164078b12c","fullStatement":"determine the values of the sine, cosine, and tangent of angles from 0\u00ba to 360\u00ba, through investigation using a variety of tools (e.g., dynamic geometry software, graphing tools) and strategies (e.g., applying the unit circle; examining angles related to special angles)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.D1.2","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:34:08+00:00"},{"identifier":"c0cb8aae-49e5-11eb-b941-fb9752df99a4","uri":"https://opensalt.net/uri/c0cb8aae-49e5-11eb-b941-fb9752df99a4","fullStatement":"determine the measures of two angles from 0\u00ba to 360\u00ba for which the value of a given trigonometric ratio is the same","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.D1.3","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:34:08+00:00"},{"identifier":"c0cbbaf6-49e5-11eb-b1de-37d8a1d92ff8","uri":"https://opensalt.net/uri/c0cbbaf6-49e5-11eb-b1de-37d8a1d92ff8","fullStatement":"define the secant, cosecant, and cotangent ratios for angles in a right triangle in terms of the sides of the triangle (e.g., sec A = hypoteneuse/adjacent) and relate these ratios to the cosine, sine, and tangent ratios (e.g., sec A = a/cos A)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.D1.4","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:34:08+00:00"},{"identifier":"c0cc6834-49e5-11eb-8a99-3b55b4a861c8","uri":"https://opensalt.net/uri/c0cc6834-49e5-11eb-8a99-3b55b4a861c8","fullStatement":"describe key properties (e.g., cycle, amplitude, period) of periodic functions arising from real-world applications (e.g., natural gas consumption in Ontario, tides in the Bay of Fundy), given a numeric or graphical representation","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.D2.1","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:42:22+00:00"},{"identifier":"c0cc22b6-49e5-11eb-8e2c-9da5b6c13c14","uri":"https://opensalt.net/uri/c0cc22b6-49e5-11eb-8e2c-9da5b6c13c14","fullStatement":"Connecting Graphs and Equations of Sinusoidal Functions","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:38:30+00:00"},{"identifier":"c0cbec74-49e5-11eb-ae5a-1732761776bb","uri":"https://opensalt.net/uri/c0cbec74-49e5-11eb-ae5a-1732761776bb","fullStatement":"demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MCR3U-D2","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:29:37+00:00"},{"identifier":"c0cc98c2-49e5-11eb-9e13-9903be5050e4","uri":"https://opensalt.net/uri/c0cc98c2-49e5-11eb-9e13-9903be5050e4","fullStatement":"predict, by extrapolating, the future behaviour of a relationship modelled using a numeric or graphical representation of a periodic function (e.g., predicting hours of daylight on a particular date from previous measurements; predicting natural gas consumption in Ontario from previous consumption)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.D2.2","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:42:22+00:00"},{"identifier":"c0ccc82e-49e5-11eb-8718-0b0837586306","uri":"https://opensalt.net/uri/c0ccc82e-49e5-11eb-8718-0b0837586306","fullStatement":"make connections between the sine ratio and the sine function and between the cosine ratio and the cosine function by graphing the relationship between angles from 0\u00ba to 360\u00ba and the corresponding sine ratios or cosine ratios, with or without technology (e.g., by generating a table of values using a calculator; by unwrapping the unit circle), defining this relationship as the function f(x) = sin x or f(x) = cos x, and explaining why the relationship is a function","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.D2.3","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:42:22+00:00"},{"identifier":"c0ccf79a-49e5-11eb-ba18-5b5be284753b","uri":"https://opensalt.net/uri/c0ccf79a-49e5-11eb-ba18-5b5be284753b","fullStatement":"sketch the graphs of f(x) = sin x and f(x) = cos x for angle measures expressed in degrees, and determine and describe their key properties (i.e., cycle, domain, range, intercepts, amplitude, period, maximum and minimum values, increasing/decreasing intervals)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.D2.4","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:57:40+00:00"},{"identifier":"c0cd28d2-49e5-11eb-9bb4-433c17c164ae","uri":"https://opensalt.net/uri/c0cd28d2-49e5-11eb-9bb4-433c17c164ae","fullStatement":"identify and represent sinusoidal functions, and solve problems involving sinusoidal functions, including problems arising from real-world applications","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MCR3U-D3","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:30:15+00:00"},{"identifier":"ff7da354-49ef-11eb-8b76-cd174620a995","uri":"https://opensalt.net/uri/ff7da354-49ef-11eb-8b76-cd174620a995","fullStatement":"determine the numeric or graphical representation of the inverse of a linear or quadratic function, given the numeric, graphical, or algebraic representation of the function, and make connections, through investigation using a variety of tools (e.g., graphing technology, Mira, tracing paper), between the graph of a function and the graph of its inverse (e.g., the graph of the inverse is the reflection of the graph of the function in the line y = x)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.A1.5","notes":"**Sample Problem**:\r\n\r\nGiven a graph and a table of values representing population over time, produce a table of values for the inverse and graph the inverse on a new set of axes.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:38:30+00:00"},{"identifier":"01067a98-49f0-11eb-a5b3-5be5906917c9","uri":"https://opensalt.net/uri/01067a98-49f0-11eb-a5b3-5be5906917c9","fullStatement":"determine, through investigation, the relationship between the domain and range of a function and the domain and range of the inverse relation, and determine whether or not the inverse relation is a function","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.A1.6","notes":"**Sample Problem**:\r\n\r\nGiven the graph of f(x) = x\u00b2, graph the inverse relation. Compare the domain and range of the function with the domain and range of the inverse relation, and investigate connections to the domain and range of the functions g(x) = \u221ax and h(x) = \u2013 \u221ax.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:38:55+00:00"},{"identifier":"02f30ef2-49f0-11eb-bd4d-3d398e370d95","uri":"https://opensalt.net/uri/02f30ef2-49f0-11eb-bd4d-3d398e370d95","fullStatement":"determine, using function notation when appropriate, the algebraic representation of the inverse of a linear or quadratic function, given the algebraic representation of the function [e.g., f(x) = (x \u2013 2)\u00b2 \u2013 5], and make connections, through investigation using a variety of tools (e.g., graphing technology, Mira, tracing paper), between the algebraic representations of a function and its inverse (e.g., the inverse of a linear function involves applying the inverse operations in the reverse order)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.A1.7","notes":"**Sample Problem**:\r\n\r\nGiven the equations of several linear functions, graph the functions and their inverses, determine the equations of the inverses, and look for patterns that connect the equation of each linear function with the equation of the inverse.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:39:22+00:00"},{"identifier":"055e03c2-49f0-11eb-af16-f9edc35d3775","uri":"https://opensalt.net/uri/055e03c2-49f0-11eb-af16-f9edc35d3775","fullStatement":"determine, through investigation using technology, the roles of the parameters a, k, d, and c in functions of the form y = af (k(x \u2013 d )) + c, and describe these roles in terms of transformations on the graphs of f(x) = x, f(x) = x\u00b2, f(x) = \u221ax, and f(x) = 1/x (i.e., translations; reflections in the axes; vertical and horizontal stretches and compressions to and from the x- and y-axes)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.A1.8","notes":"**Sample Problem**:\r\n\r\nInvestigate the graph f(x) = 3(x \u2013 d)\u00b2 + 5 for various values of d, using technology, and describe the effects of changing d in terms of a transformation.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:40:04+00:00"},{"identifier":"073c4924-49f0-11eb-8647-8d6a6364b64f","uri":"https://opensalt.net/uri/073c4924-49f0-11eb-8647-8d6a6364b64f","fullStatement":"sketch graphs of y = af(k(x \u2013 d)) + c by applying one or more transformations to the graphs of f(x) = x, f(x) = x\u00b2 , f(x) = \u221ax, and f(x) = 1/x, and state the domain and range of the transformed functions.","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.A1.9","notes":"**Sample Problem**:\r\n\r\nTransform the graph of f(x) to sketch g(x), and state the domain and range of each function, for the following: f(x) = \u221ax, g(x) = \u221ax-4; f(x) = 1/x, g(x) = -1/(x+1).","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:40:52+00:00"},{"identifier":"cd3b5632-49f1-11eb-8483-f9f2aed1bed3","uri":"https://opensalt.net/uri/cd3b5632-49f1-11eb-8483-f9f2aed1bed3","fullStatement":"solve problems involving the intersection of a linear function and a quadratic function graphically and algebraically (e.g., determine the time when two identical cylindrical water tanks contain equal volumes of water, if one tank is being filled at a constant rate and the other is being emptied through a hole in the bottom)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.A2.5","notes":"**Sample Problem**: \r\n\r\nDetermine, through investigation, the equations of the lines that have a slope of 2 and that intersect the quadratic function f(x) = x(6 \u2013 x) once; twice; never.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:42:46+00:00"},{"identifier":"c83656a8-49f3-11eb-9ef2-0935a330fe9b","uri":"https://opensalt.net/uri/c83656a8-49f3-11eb-9ef2-0935a330fe9b","fullStatement":"simplify algebraic expressions containing integer and rational exponents [e.g., (x3) \u00f7 x1/2, (x6y3)1/3], and evaluate numeric expressions containing integer and rational exponents and rational bases [e.g., 2-3, (-6)-3, 41/2, 1.01120]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.B1.3","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T20:02:28+00:00"},{"identifier":"ce5712ca-49f3-11eb-b87f-7b0cbcd22191","uri":"https://opensalt.net/uri/ce5712ca-49f3-11eb-b87f-7b0cbcd22191","fullStatement":"determine, through investigation, and describe key properties relating to domain and range, intercepts, increasing/decreasing intervals, and asymptotes (e.g., the domain is the set of real numbers; the range is the set of positive real numbers; the function either increases or decreases throughout its domain) for exponential functions represented in a variety of ways [e.g., tables of values, mapping diagrams, graphs, equations of the form f(x) = ax (a > 0, a \u2260 1), function machines]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.B1.4","notes":"**Sample Problem**:\r\n\r\nGraph f(x) = 2x, g(x) = 3x, and h(x) = 0.5x on the same set of axes. Make comparisons between the graphs, and explain the relationship between the y-intercepts.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:46:19+00:00"},{"identifier":"bf2cb124-49fd-11eb-9d79-07dc6c324e77","uri":"https://opensalt.net/uri/bf2cb124-49fd-11eb-9d79-07dc6c324e77","fullStatement":"represent a sequence algebraically using a recursion formula, function notation, or the formula for the nth term [e.g., represent 2, 4, 8, 16, 32, 64, \u2026 as t1 = 2; tn = 2tn \u2013 1, as f(n) = 2n, or as tn = 2n, or represent 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, ... as t1 = 1/2; tn = tn-1 + 1/n(n+1), as f(n) = n/(n+1), or as tn = n/(n+1), where n is a natural number], and describe the information that can be obtained by inspecting each representation (e.g., function notation or the formula for the nth term may show the type of function; a recursion formula shows the relationship between terms)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.C1.4","notes":"**Sample Problem**: \r\n\r\nRepresent the sequence 0, 3, 8, 15, 24, 35, \u2026 using a recursion formula, function notation, and the formula for the nth term. Explain why this sequence can be described as a discrete quadratic function. Explore how to identify a sequence as a discrete quadratic function by inspecting the recursion formula.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T17:52:35+00:00"},{"identifier":"c0a90854-49fd-11eb-aeda-97315f241ba6","uri":"https://opensalt.net/uri/c0a90854-49fd-11eb-aeda-97315f241ba6","fullStatement":"determine, through investigation, recursive patterns in the Fibonacci sequence, in related sequences, and in Pascal\u2019s triangle, and represent the patterns in a variety of ways (e.g., tables of values, algebraic notation)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.C1.5","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T17:53:09+00:00"},{"identifier":"c2122144-49fd-11eb-9dca-4799dd142497","uri":"https://opensalt.net/uri/c2122144-49fd-11eb-9dca-4799dd142497","fullStatement":"determine, through investigation, and describe the relationship between Pascal\u2019s triangle and the expansion of binomials, and apply the relationship to expand bino- mials raised to whole-number exponents [e.g., (1 + x)4, (2x \u2013 1)5, (2x \u2013 y)6, (x2 + 1)5]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.C1.6","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T17:54:14+00:00"},{"identifier":"92ff69fa-49ff-11eb-8913-a9b611b70239","uri":"https://opensalt.net/uri/92ff69fa-49ff-11eb-8913-a9b611b70239","fullStatement":"solve problems involving arithmetic and geometric sequences and series, including those arising from real-world applications","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MPM2D-11.C2.4","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T17:59:41+00:00"},{"identifier":"d1f2a580-4a0b-11eb-af33-410c2e0df0a3","uri":"https://opensalt.net/uri/d1f2a580-4a0b-11eb-af33-410c2e0df0a3","fullStatement":"explain the meaning of the term annuity, and determine the relationships between ordinary simple annuities (i.e., annuities in which payments are made at the end of each period, and compounding and payment periods are the same), geometric series, and exponential growth, through investigation with technology (e.g., use a spreadsheet to determine and graph the future value of an ordinary simple annuity for varying numbers of compounding periods; investigate how the contributions of each payment to the future value of an ordinary simple annuity are related to the terms of a geometric series)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.C3.5","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:27:36+00:00"},{"identifier":"d388e38c-4a0b-11eb-8632-751ee09b7097","uri":"https://opensalt.net/uri/d388e38c-4a0b-11eb-8632-751ee09b7097","fullStatement":"determine, through investigation using technology (e.g., the TVM Solver on a graphing calculator, online tools), the effects of changing the conditions (i.e., the payments, the frequency of the payments, the interest rate, the compounding period) of ordinary simple annuities (e.g., long-term savings plans, loans)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.C3.6","notes":"**Sample Problem**: \r\n\r\nCompare the amounts at age 65 that would result from making an annual deposit of $1000 starting at age 20, or from making an annual deposit of $3000 starting at age 50, to an RRSP that earns 6% interest per annum, compounded annually. What is the total of the deposits in each situation?","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:28:10+00:00"},{"identifier":"d4fea7a6-4a0b-11eb-9382-5ba90a46739b","uri":"https://opensalt.net/uri/d4fea7a6-4a0b-11eb-9382-5ba90a46739b","fullStatement":"solve problems, using technology (e.g., scientific calculator, spreadsheet, graphing calculator), that involve the amount, the present value, and the regular payment of an ordinary simple annuity (e.g., calculate the total interest paid over the life of a loan, using a spreadsheet, and compare the total interest with the original principal of the loan)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.C3.7","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:48:55+00:00"},{"identifier":"ce6e1344-4a0c-11eb-9498-c3161bb89652","uri":"https://opensalt.net/uri/ce6e1344-4a0c-11eb-9498-c3161bb89652","fullStatement":"prove simple trigonometric identities, using the Pythagorean identity sin\u00b2x + cos\u00b2x = 1; the quotient identity tan x = sin x/cos x; and the reciprocal identities of sec x = 1/cos x, csc x = 1/sin x, and cot x - 1/tan x","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.D1.5","notes":"**Sample Problem**: \r\n\r\nProve that 1 \u2013 cos\u00b2 x = sin x cos x tan x.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:36:32+00:00"},{"identifier":"d01bd5e6-4a0c-11eb-98e9-c9dbd1a2909e","uri":"https://opensalt.net/uri/d01bd5e6-4a0c-11eb-98e9-c9dbd1a2909e","fullStatement":"pose problems involving right triangles and oblique triangles in two-dimensional settings, and solve these and other such problems using the primary trigonometric ratios, the cosine law, and the sine law (including the ambiguous case)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.D1.6","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:37:03+00:00"},{"identifier":"d19567a2-4a0c-11eb-959c-d563f3e4f7a2","uri":"https://opensalt.net/uri/d19567a2-4a0c-11eb-959c-d563f3e4f7a2","fullStatement":"pose problems involving right triangles and oblique triangles in three-dimensional set- tings, and solve these and other such problems using the primary trigonometric ratios, the cosine law, and the sine law","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.D1.7","notes":"**Sample Problem**: \r\n\r\nExplain how a surveyor could find the height of a vertical cliff that is on the other side of a raging river, using a measuring tape, a theodolite, and some trigonometry. Determine what the surveyor might measure, and use hypothetical values for these data to calculate the height of the cliff.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:38:12+00:00"},{"identifier":"f2e142fe-4a0d-11eb-8926-e741469d3d3a","uri":"https://opensalt.net/uri/f2e142fe-4a0d-11eb-8926-e741469d3d3a","fullStatement":"determine, through investigation using technology, the roles of the parameters a, k, d, and c in functions of the form y = af (k (x \u2013 d )) + c, where f(x) = sin x or f(x) = cos x with angles expressed in degrees, and describe these roles in terms of transformations on the graphs of f(x) = sin x and f(x) = cos x (i.e., translations; reflections in the axes; vertical and horizontal stretches and compressions to and from the x- and y-axes)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.D2.5","notes":"**Sample Problem**:\r\n\r\nInvestigate the graph f(x) = 2 sin(x \u2013 d ) + 10 for various values of d, using technology, and describe the effects of changing d in terms of a transformation.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:43:26+00:00"},{"identifier":"f4ff09f4-4a0d-11eb-b6e4-ad71bd638428","uri":"https://opensalt.net/uri/f4ff09f4-4a0d-11eb-b6e4-ad71bd638428","fullStatement":"determine the amplitude, period, phase shift, domain, and range of sinusoidal functions whose equations are given in the form f(x) = asin(k(x \u2013 d )) + c or f(x) = acos(k(x \u2013 d )) + c","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.D2.6","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:58:15+00:00"},{"identifier":"f6720502-4a0d-11eb-a19d-77891b4bc714","uri":"https://opensalt.net/uri/f6720502-4a0d-11eb-a19d-77891b4bc714","fullStatement":"sketch graphs of y = af (k(x \u2013 d )) + c by applying one or more transformations to the graphs of f(x) = sin x and f(x) = cos x, and state the domain and range of the transformed functions","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.D2.7","notes":"**Sample Problem**:\r\n\r\nTransform the graph of f(x) = cos x to sketch g(x) = 3cos2x \u2013 1, and state the domain and range of each function.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:44:52+00:00"},{"identifier":"f86af77e-4a0d-11eb-8c15-bd94524acef0","uri":"https://opensalt.net/uri/f86af77e-4a0d-11eb-8c15-bd94524acef0","fullStatement":"represent a sinusoidal function with an equation, given its graph or its properties","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.D2.8","notes":"**Sample Problem**: \r\n\r\nA sinusoidal function has an amplitude of 2 units, a period of 180\u00ba, and a maximum at (0, 3). Represent the function with an equation in two different ways.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2021-01-07T19:59:18+00:00"},{"identifier":"6ae00da8-4a0e-11eb-8699-91fb7d861ab4","uri":"https://opensalt.net/uri/6ae00da8-4a0e-11eb-8699-91fb7d861ab4","fullStatement":"Solving Problems Involving Sinusoidal Functions","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:45:52+00:00"},{"identifier":"6ae1026c-4a0e-11eb-897a-bf741408593e","uri":"https://opensalt.net/uri/6ae1026c-4a0e-11eb-897a-bf741408593e","fullStatement":"pose problems based on applications involving a sinusoidal function, and solve these and other such problems by using a given graph or a graph generated with technology from a table of values or from its equation","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.D3.5","notes":"**Sample Problem**:\r\n\r\nThe height above the ground of a rider on a Ferris wheel can be modelled by the sinusoidal function h(t) = 25 sin(3(t \u2013 30)) + 27, where h(t) is the height, in metres, and t is the time, in seconds. Graph the function, using graphing technology in degree mode, and determine the maximum and minimum heights of the rider, the height after 30 s, and the time required to complete one revolution.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:49:31+00:00"},{"identifier":"6ae0782e-4a0e-11eb-a9b4-718cfaec727f","uri":"https://opensalt.net/uri/6ae0782e-4a0e-11eb-a9b4-718cfaec727f","fullStatement":"collect data that can be modelled as a sinusoidal function (e.g., voltage in an AC circuit, sound waves), through investigation with and without technology, from primary sources, using a variety of tools (e.g., concrete materials, measurement tools such as motion sensors), or from secondary sources (e.g., websites such as Statistics Canada, E-STAT), and graph the data","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.D3.1","notes":"**Sample Problem**: \r\n\r\nMeasure and record distance\u2212time data for a swinging pendulum, using a motion sensor or other measurement tools, and graph the data.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:46:36+00:00"},{"identifier":"6ae0b014-4a0e-11eb-acac-2f061e627074","uri":"https://opensalt.net/uri/6ae0b014-4a0e-11eb-acac-2f061e627074","fullStatement":"identify periodic and sinusoidal functions, including those that arise from real-world applications involving periodic phenomena, given various representations (i.e., tables of values, graphs, equations), and explain any restrictions that the context places on the domain and range","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.D3.2","notes":"**Sample Problem**: \r\n\r\nUsing data from Statistics Canada, investigate to determine if there was a period of time over which changes in the population of Canadians aged 20 \u201324 could be modelled using a sinusoidal function.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:47:13+00:00"},{"identifier":"6ae0ccc0-4a0e-11eb-8b3f-3bf38983d727","uri":"https://opensalt.net/uri/6ae0ccc0-4a0e-11eb-8b3f-3bf38983d727","fullStatement":"determine, through investigation, how sinusoidal functions can be used to model periodic phenomena that do not involve angles","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.D3.3","notes":"**Sample Problem**: \r\n\r\nInvestigate, using graphing technology in degree mode, and explain how the function h(t) = 5 sin(30(t + 3)) approximately models the relationship between the height and the time of day for a tide with an amplitude of 5 m, if high tide is at midnight.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:48:00+00:00"},{"identifier":"6ae0e82c-4a0e-11eb-9f83-655a98adc9dd","uri":"https://opensalt.net/uri/6ae0e82c-4a0e-11eb-9f83-655a98adc9dd","fullStatement":"predict the effects on a mathematical model (i.e., graph, equation) of an application involving periodic phenomena when the conditions in the application are varied (e.g., varying the conditions, such as speed and direction, when walking in a circle in front of a motion sensor)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MCR3U-11.D3.4","notes":"**Sample Problem**: \r\n\r\nThe relationship between the height above the ground of a person riding a Ferris wheel and time can be modelled using a sinusoidal function. Describe the effect on this function if the platform from which the person enters the ride is raised by 1 m and if the Ferris wheel turns twice as fast.","language":"en","educationLevel":["11"],"lastChangeDateTime":"2020-12-29T19:48:53+00:00"},{"identifier":"e34bba10-4b78-11eb-af5e-999a0d264f6c","uri":"https://opensalt.net/uri/e34bba10-4b78-11eb-af5e-999a0d264f6c","fullStatement":"Grade 12","CFItemType":"Grade Level","CFItemTypeURI":{"title":"Grade Level","identifier":"8047d85d-6c8e-5231-bd6d-050731684413","uri":"https://api.acmt-prod.learningmate.com/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/8047d85d-6c8e-5231-bd6d-050731684413"},"language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T20:17:17+00:00"},{"identifier":"f0e0abae-4b78-11eb-a008-e1a4e3beb79a","uri":"https://opensalt.net/uri/f0e0abae-4b78-11eb-a008-e1a4e3beb79a","fullStatement":"Advanced Functions, Grade 12","CFItemType":"Grade Level","CFItemTypeURI":{"title":"Grade Level","identifier":"8047d85d-6c8e-5231-bd6d-050731684413","uri":"https://api.acmt-prod.learningmate.com/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/8047d85d-6c8e-5231-bd6d-050731684413"},"humanCodingScheme":"MHF4U","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-03T13:47:14+00:00"},{"identifier":"f0e1c124-4b78-11eb-8988-93016047d865","uri":"https://opensalt.net/uri/f0e1c124-4b78-11eb-8988-93016047d865","fullStatement":"recognize the logarithm of a number to a given base as the exponent to which the base must be raised to get the number, recognize the operation of finding the logarithm to be the inverse operation (i.e., the undoing or reversing) of exponentiation, and evaluate simple logarithmic expressions","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.A1.1","notes":"**Sample Problem**:\r\n\r\nWhy is it not possible to determine log10(\u2013 3) or log20? Explain your reasoning.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T18:01:51+00:00"},{"identifier":"f0e1644a-4b78-11eb-a8c7-0dd8c41229e8","uri":"https://opensalt.net/uri/f0e1644a-4b78-11eb-a8c7-0dd8c41229e8","fullStatement":"Evaluating Logarithmic Expressions","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T15:05:49+00:00"},{"identifier":"f0e13af6-4b78-11eb-931b-3379b25dbb9b","uri":"https://opensalt.net/uri/f0e13af6-4b78-11eb-931b-3379b25dbb9b","fullStatement":"demonstrate an understanding of the relationship between exponential expressions and logarithmic expressions, evaluate logarithms, and apply the laws of logarithms to simplify numeric expressions","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MHF4U-A1","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T15:04:51+00:00"},{"identifier":"f0e103b0-4b78-11eb-8dfe-7b3c78e3677c","uri":"https://opensalt.net/uri/f0e103b0-4b78-11eb-8dfe-7b3c78e3677c","fullStatement":"Exponential and Logarithmic Functions","CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19"},"humanCodingScheme":"MHF4U-A","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T15:01:22+00:00"},{"identifier":"f0e2c344-4b78-11eb-9da6-f3ffefd580f7","uri":"https://opensalt.net/uri/f0e2c344-4b78-11eb-9da6-f3ffefd580f7","fullStatement":"identify and describe some key features of the graphs of logarithmic functions, make connections among the numeric, graphical, and algebraic representations of logarithmic functions, and solve related problems graphically","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MHF4U-A2","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T15:05:15+00:00"},{"identifier":"f0e32dc0-4b78-11eb-8dc5-a382c014d29f","uri":"https://opensalt.net/uri/f0e32dc0-4b78-11eb-8dc5-a382c014d29f","fullStatement":"determine, through investigation with technology (e.g., graphing calculator, spreadsheet) and without technology, key features (i.e., vertical and horizontal asymptotes, domain and range, intercepts, increasing/decreasing behaviour) of the graphs of logarithmic functions of the form f(x) = logbx, and make connections between the algebraic and graphical representations of these logarithmic functions","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.A2.1","notes":"**Sample problem**: \r\n\r\nCompare the key features of the graphs of f(x) = log2x, g(x) = log4x, and h(x) = log5x using graphing technology.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:10:29+00:00"},{"identifier":"f0e2eb6c-4b78-11eb-8938-41e6b559f540","uri":"https://opensalt.net/uri/f0e2eb6c-4b78-11eb-8938-41e6b559f540","fullStatement":"Connecting Graphs and Equations of Logarithmic Functions","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T15:16:58+00:00"},{"identifier":"f0e349b8-4b78-11eb-9bac-37c6dde55af0","uri":"https://opensalt.net/uri/f0e349b8-4b78-11eb-9bac-37c6dde55af0","fullStatement":"recognize the relationship between an exponential function and the corresponding logarithmic function to be that of a function and its inverse, deduce that the graph of a logarithmic function is the reflection of the graph of the corresponding exponential function in the line y = x, and verify the deduction using technology","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.A2.2","notes":"**Sample problem**: \r\n\r\nGive examples to show that the inverse of a function is not necessarily a function. Use the key features of the graphs of logarithmic and exponential functions to give reasons why the inverse of an exponential function is a function.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:10:34+00:00"},{"identifier":"f0e3652e-4b78-11eb-b287-2d521ef25c6e","uri":"https://opensalt.net/uri/f0e3652e-4b78-11eb-b287-2d521ef25c6e","fullStatement":"determine, through investigation using technology, the roles of the parameters d and c in functions of the form y = log10(x \u2013 d) + c and the roles of the parameters a and k in functions of the form y = alog10(kx), and describe these roles in terms of transformations on the graph of f(x) = log10x (i.e., vertical and horizontal translations; reflections in the axes; vertical and horizontal stretches and compressions to and from the x- and y-axes)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.A2.3","notes":"**Sample problem**: \r\n\r\nInvestigate the graphs of f(x) = log10(x) + c, f(x) = log10(x \u2013 d), f(x) = alog10x, and f(x) = log10(kx) for various values of c, d, a, and k, using technology, describe the effects of changing these parameters in terms of transformations, and make connections to the transformations of other functions such as polynomial functions, exponential functions, and trigonometric functions.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:10:41+00:00"},{"identifier":"f0e383c4-4b78-11eb-a855-19809aa33c97","uri":"https://opensalt.net/uri/f0e383c4-4b78-11eb-a855-19809aa33c97","fullStatement":"pose problems based on real-world applications of exponential and logarithmic functions (e.g., exponential growth and decay, the Richter scale, the pH scale, the decibel scale), and solve these and other such problems by using a given graph or a graph generated with technology from a table of values or from its equation","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.A2.4","notes":"**Sample Problem**: \r\n\r\nThe pH or acidity of a solution is given by the equation pH = \u2013 logC, where C is the concentration of [H+] ions in multiples of M = 1 mol/L. Use graphing software to graph this function. What is the change in pH if the solution is diluted from a concentration of 0.1M to a concentration of 0.01M? From 0.001M to 0.0001M? Describe the change in pH when the concentration of any acidic solution is reduced to 1/10 of its original concentration. Rearrange the given equation to determine concentration as a function of pH.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T18:04:20+00:00"},{"identifier":"f0e3bc9a-4b78-11eb-8f47-cf5e21571631","uri":"https://opensalt.net/uri/f0e3bc9a-4b78-11eb-8f47-cf5e21571631","fullStatement":"solve exponential and simple logarithmic equations in one variable algebraically, including those in problems arising from real-world applications","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MHF4U-A3","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T15:05:34+00:00"},{"identifier":"f0e4216c-4b78-11eb-864e-5d1158f75f8f","uri":"https://opensalt.net/uri/f0e4216c-4b78-11eb-864e-5d1158f75f8f","fullStatement":"recognize equivalent algebraic expressions involving logarithms and exponents, and simplify expressions of these types","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.A3.1","notes":"**Sample problem**: \r\n\r\nSketch the graphs of f(x) = log10(100x) and g(x) = 2 + log10x, compare the graphs, and explain your findings algebraically.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:11:01+00:00"},{"identifier":"f0e3e486-4b78-11eb-9c3e-439418296777","uri":"https://opensalt.net/uri/f0e3e486-4b78-11eb-9c3e-439418296777","fullStatement":"Solving Exponential and Logarithmic Equations","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T15:33:36+00:00"},{"identifier":"f0e43e40-4b78-11eb-90ec-7175ee50a954","uri":"https://opensalt.net/uri/f0e43e40-4b78-11eb-90ec-7175ee50a954","fullStatement":"solve exponential equations in one variable by determining a common base (e.g., solve 4x = 8x+ 3 by expressing each side as a power of 2) and by using logarithms (e.g., solve 4x = 8x+ 3 by taking the logarithm base 2 of both sides), recognizing that logarithms base 10 are commonly used (e.g., solving 3x = 7 by taking the logarithm base 10 of both sides)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.A3.2","notes":"Sample Problem: \r\n\r\nSolve 300(1.05)n = 600 and 2x+ 2 \u2013 2x = 12 either by finding a common base or by taking logarithms, and explain your choice of method in each case.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T18:05:23+00:00"},{"identifier":"f0e459ac-4b78-11eb-9856-fd6f786b72f7","uri":"https://opensalt.net/uri/f0e459ac-4b78-11eb-9856-fd6f786b72f7","fullStatement":"solve simple logarithmic equations in one variable algebraically [e.g., log3(5x + 6) = 2, log10(x + 1) = 1]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.A3.3","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:11:19+00:00"},{"identifier":"f0e47572-4b78-11eb-bb64-a9e87acaccd4","uri":"https://opensalt.net/uri/f0e47572-4b78-11eb-bb64-a9e87acaccd4","fullStatement":"solve problems involving exponential and logarithmic equations algebraically, including problems arising from real-world applications","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.A3.4","notes":"**Sample Problem**:\r\n\r\nThe pH or acidity of a soluion is given by the equation pH = \u2013 logC, where C is the concentration of [H+] ions in multiples of M = 1 mol/L. You are given a solution of hydrochloric acid with a pH of 1.7 and asked to increase the pH of the solution by 1.4. Determine how much you must dilute the solution. Does your answer differ if you start with a pH of 2.2?","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:11:30+00:00"},{"identifier":"f0e1deac-4b78-11eb-8c1a-e376a62c1e26","uri":"https://opensalt.net/uri/f0e1deac-4b78-11eb-8c1a-e376a62c1e26","fullStatement":"determine, with technology, the approximate logarithm of a number to any base, including base 10 (e.g., by reasoning that log329 is between 3 and 4 and using systematic trial to determine that log329 is approximately 3.07)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.A1.2","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:09:37+00:00"},{"identifier":"f0e1f95a-4b78-11eb-a6fd-0fa1f851a14b","uri":"https://opensalt.net/uri/f0e1f95a-4b78-11eb-a6fd-0fa1f851a14b","fullStatement":"make connections between related logarithmic and exponential equations (e.g., log5125 = 3 can also be expressed as 53 = 125), and solve simple exponential equations by rewriting them in logarithmic form (e.g., solving 3x = 10 by rewriting the equation as log310 = x)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.A1.3","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:09:45+00:00"},{"identifier":"f0e214d0-4b78-11eb-959a-bd630c8d650b","uri":"https://opensalt.net/uri/f0e214d0-4b78-11eb-959a-bd630c8d650b","fullStatement":"make connections between the laws of exponents and the laws of logarithms [e.g., use the statement 10a+b = 10a10b to deduce that log10x + log10y = log10(xy)], verify the laws of logarithms with or without technology (e.g., use patterning to verify the quotient law for logarithms by evaluating expressions such as log101000 \u2013 log10100 and then rewriting the answer as a logarithmic term to the same base), and use the laws of logarithms to simplify and evaluate numerical expressions","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.A1.4","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:09:51+00:00"},{"identifier":"f0e53afc-4b78-11eb-bb15-557757af4aa9","uri":"https://opensalt.net/uri/f0e53afc-4b78-11eb-bb15-557757af4aa9","fullStatement":"recognize a polynomial expression (i.e., a series of terms where each term is the product of a constant and a power of x with a non-negative integral exponent, such as x\u00b3 \u2013 5x\u00b2 + 2x \u2013 1); recognize the equation of a polynomial function, give reasons why it is a function, and identify linear and quadratic functions as examples of polynomial functions","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.C1.1","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T19:14:22+00:00"},{"identifier":"f0e4f042-4b78-11eb-a06e-6b57f18d5cd5","uri":"https://opensalt.net/uri/f0e4f042-4b78-11eb-a06e-6b57f18d5cd5","fullStatement":"Connecting Graphs and Equations of Polynomial Functions","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T16:29:51+00:00"},{"identifier":"f0e4c838-4b78-11eb-b6c2-f537ece44d66","uri":"https://opensalt.net/uri/f0e4c838-4b78-11eb-b6c2-f537ece44d66","fullStatement":"identify and describe some key features of polynomial functions, and make connections between the numeric, graphical, and algebraic representations of polynomial functions","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MHF4U-C1","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T16:29:19+00:00"},{"identifier":"f0e49228-4b78-11eb-898a-9565dabc95cb","uri":"https://opensalt.net/uri/f0e49228-4b78-11eb-898a-9565dabc95cb","fullStatement":"Polynomial and Rational Functions","CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19"},"humanCodingScheme":"MHF4U-C","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T15:02:09+00:00"},{"identifier":"f0e5e1c8-4b78-11eb-ab6c-d306457da5ce","uri":"https://opensalt.net/uri/f0e5e1c8-4b78-11eb-ab6c-d306457da5ce","fullStatement":"identify and describe some key features of the graphs of rational functions, and represent rational functions graphically","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MHF4U-C2","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T16:29:19+00:00"},{"identifier":"f0e646b8-4b78-11eb-9e7e-577629f96f7b","uri":"https://opensalt.net/uri/f0e646b8-4b78-11eb-9e7e-577629f96f7b","fullStatement":"determine, through investigation with and without technology, key features (i.e., vertical and horizontal asymptotes, domain and range, intercepts, positive/negative intervals, increasing/decreasing intervals) of the graphs of rational functions that have linear expressions in the numerator and denominator [e.g., f(x) = 2x/(x - 3), h(x) = (x - 2)/(3x + 4)], and make connections between the algebraic and graphical representations of these rational functions","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.C2.2","notes":"**Sample Problem**: \r\n\r\nInvestigate, using graphing technology, key features of the graphs of the family of rational functions of the form f(x) = 8x/(nx + 1) for n = 1, 2, 4, and 8, and make connections between the equations and the asymptotes.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:15:17+00:00"},{"identifier":"f0e6096e-4b78-11eb-a094-cbb5f9cfc252","uri":"https://opensalt.net/uri/f0e6096e-4b78-11eb-a094-cbb5f9cfc252","fullStatement":"Connecting Graphs and Equations of Rational Functions","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T16:41:12+00:00"},{"identifier":"f0e6630a-4b78-11eb-b5eb-6b7aa4ad1e24","uri":"https://opensalt.net/uri/f0e6630a-4b78-11eb-b5eb-6b7aa4ad1e24","fullStatement":"determine, through investigation with and without technology, key features (i.e., vertical and horizontal asymptotes, domain and range, intercepts, positive/negative intervals, increasing/decreasing intervals) of the graphs of rational functions that are the reciprocals of linear and quadratic functions, and make connections between the algebraic and graphical representations of these rational functions [e.g., make connections between f(x) = 1/(x\u00b2 -4) and its graph by using graphing technology and by reasoning that there are vertical asymptotes at x = 2 and x = \u20132 and a hori- zontal asymptote at y = 0 and that the func- tion maintains the same sign as f(x) = x\u00b2 \u2013 4]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.C2.1","notes":"**Sample Problem**: \r\n\r\nInvestigate, with technology, the key features of the graphs of families of rational functions of the form 1/(x + n) and f(x) = 2/(x\u00b2 + n) where n is an integer, and make connections between the equations and key features of the graphs.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:15:10+00:00"},{"identifier":"f0e67e30-4b78-11eb-b78a-0dcc13290738","uri":"https://opensalt.net/uri/f0e67e30-4b78-11eb-b78a-0dcc13290738","fullStatement":"sketch the graph of a simple rational function using its key features, given the algebraic rep- resentation of the function","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.C2.3","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:15:24+00:00"},{"identifier":"f0e6b6ca-4b78-11eb-9832-157a62d9dc15","uri":"https://opensalt.net/uri/f0e6b6ca-4b78-11eb-9832-157a62d9dc15","fullStatement":"solve problems involving polynomial and simple rational equations graphically and algebraically","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MHF4U-C3","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T16:29:19+00:00"},{"identifier":"f0e72cae-4b78-11eb-bc51-79a63f491c19","uri":"https://opensalt.net/uri/f0e72cae-4b78-11eb-bc51-79a63f491c19","fullStatement":"factor polynomial expressions in one variable, of degree no higher than four, by selecting and applying strategies (i.e., common factoring, difference of squares, trinomial factoring, factoring by grouping, remainder theorem, factor theorem)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.C3.2","notes":"**Sample Problem**: \r\n\r\nFactor: x\u00b3 + 2x\u00b2 \u2013 x \u2013 2; x4 \u2013 6x\u00b3 + 4x\u00b2 + 6x \u2013 5.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:15:47+00:00"},{"identifier":"f0e6de34-4b78-11eb-a3e6-4f5dd363ee2a","uri":"https://opensalt.net/uri/f0e6de34-4b78-11eb-a3e6-4f5dd363ee2a","fullStatement":"Solving Polynomial and Rational Equations","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T16:48:19+00:00"},{"identifier":"f0e74950-4b78-11eb-b034-6d719bc15d18","uri":"https://opensalt.net/uri/f0e74950-4b78-11eb-b034-6d719bc15d18","fullStatement":"make connections, through investigation using technology (e.g., computer algebra systems), between the polynomial function f(x), the divisor x \u2013 a, the remainder from the division f(x)/(x - a') and f(a) to verify the remainder theorem and the factor theorem","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.C3.1","notes":"**Sample Problem**: \r\n\r\nDivide f(x) = x4 + 4x\u00b3 \u2013 x\u00b2 \u2013 16x \u2013 14 by x \u2013 a for various integral values of a using a computer algebra system. Compare the remainder from each division with f(a).","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:15:38+00:00"},{"identifier":"f0e7652a-4b78-11eb-af6b-add7c839d554","uri":"https://opensalt.net/uri/f0e7652a-4b78-11eb-af6b-add7c839d554","fullStatement":"determine, through investigation using technology (e.g., graphing calculator, computer algebra systems), the connection between the real roots of a polynomial equation and the x-intercepts of the graph of the corresponding polynomial function, and describe this con- nection [e.g., the real roots of the equation x4 \u2013 13x\u00b2 + 36 = 0 are the x-intercepts of the graph of f(x) = x4 \u2013 13x\u00b2 + 36]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.C3.3","notes":"**Sample Problem**: \r\n\r\nDescribe the relationship between the x-intercepts of the graphs of linear and quadratic functions and the real roots of the corresponding equations. Investigate, using technology, whether this relationship exists for polynomial functions of higher degree.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:15:54+00:00"},{"identifier":"f0e781ae-4b78-11eb-b581-81f605d5b488","uri":"https://opensalt.net/uri/f0e781ae-4b78-11eb-b581-81f605d5b488","fullStatement":"solve polynomial equations in one variable, of degree no higher than four (e.g., 2x\u00b3 \u2013 3x\u00b2 + 8x \u2013 12 = 0), by selecting and applying strategies (i.e., common factoring, difference of squares, trinomial factoring, factoring by grouping, remainder theorem, factor theorem), and verify solutions using technology (e.g., using computer algebra systems to determine the roots; using graphing technology to determine the x-intercepts of the graph of the corresponding polynomial function)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.C3.4","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:16:01+00:00"},{"identifier":"f0e7a008-4b78-11eb-ad9a-afe7ff5efc38","uri":"https://opensalt.net/uri/f0e7a008-4b78-11eb-ad9a-afe7ff5efc38","fullStatement":"determine, through investigation using technology (e.g., graphing calculator, computer algebra systems), the connection between the real roots of a rational equation and the x-intercepts of the graph of the corresponding rational function, and describe this connection [e.g., the real root of the equation = (x - 2)/(x - 3) = 0 is 2, which is the x-intercept of the function f(x) = (x - 2)/(x - 3; the equation 1/(x - 3)= 0 has no real roots, and the function f(x) = 1/(x - 3) does not intersect the x-axis]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.C3.5","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:16:08+00:00"},{"identifier":"f0e7bc00-4b78-11eb-a91b-8f4dc2c6a3b2","uri":"https://opensalt.net/uri/f0e7bc00-4b78-11eb-a91b-8f4dc2c6a3b2","fullStatement":"solve simple rational equations in one variable algebraically, and verify solutions using technology (e.g., using computer algebra systems to determine the roots; using graphing technology to determine the x-intercepts of the graph of the corresponding rational function)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.C3.6","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:16:15+00:00"},{"identifier":"f0e7d7d0-4b78-11eb-9111-2948a84d01ec","uri":"https://opensalt.net/uri/f0e7d7d0-4b78-11eb-9111-2948a84d01ec","fullStatement":"solve problems involving applications of polynomial and simple rational functions and equations [e.g., problems involving the factor theorem or remainder theorem, such as deter- mining the values of k for which the function f(x) = x\u00b3 + 6x\u00b2 + kx \u2013 4 gives the same remainder when divided by x \u2013 1 and x + 2]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.C3.7","notes":"**Sample Problem**: \r\n\r\nUse long division to express the given function f(x) = (x\u00b2 + 3x -5)/(x - 1) as the sum of a polynomial function and a rational function of the form A/(x - 1) (where A is a constant), make a conjecture about the relationship between the given function and the polynomial function for very large positive and negative x-values, and verify your conjecture using graphing technology.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T19:20:27+00:00"},{"identifier":"f0e5579e-4b78-11eb-ad5e-efd3f41594fc","uri":"https://opensalt.net/uri/f0e5579e-4b78-11eb-ad5e-efd3f41594fc","fullStatement":"compare, through investigation using graphing technology, the numeric, graphical, and algebraic representations of polynomial (i.e., linear, quadratic, cubic, quartic) functions (e.g., compare finite differences in tables of values; investigate the effect of the degree of a polynomial function on the shape of its graph and the maximum number of x-intercepts; investigate the effect of varying the sign of the leading coefficient on the end behaviour of the function for very large positive or negative x-values)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.C1.2","notes":"**Sample Problem**: \r\n\r\nInvestigate the maximum number of x-intercepts for linear, quadratic, cubic, and quartic functions using graphing technology.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:14:00+00:00"},{"identifier":"f0e573c8-4b78-11eb-8b6d-4f738486d4ba","uri":"https://opensalt.net/uri/f0e573c8-4b78-11eb-8b6d-4f738486d4ba","fullStatement":"describe key features of the graphs of polynomial functions (e.g., the domain and range, the shape of the graphs, the end behaviour of the functions for very large positive or negative x-values)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-11.C1.3","notes":"**Sample Problem**: \r\n\r\nDescribe and compare the key features of the graphs of the functions f(x) = x, f(x) = x\u00b2, f(x) = x\u00b3, f(x) = x\u00b3 + x\u00b2, and f(x) = x\u00b3 + x.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T19:13:02+00:00"},{"identifier":"f0e58f8e-4b78-11eb-a005-e564a28f1661","uri":"https://opensalt.net/uri/f0e58f8e-4b78-11eb-a005-e564a28f1661","fullStatement":"distinguish polynomial functions from sinusoidal and exponential functions [e.g., f(x) = sin x, g(x) = 2x], and compare and contrast the graphs of various polynomial functions with the graphs of other types of functions","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-11.C1.4","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T19:13:15+00:00"},{"identifier":"f0e5ab04-4b78-11eb-abdf-977889117fca","uri":"https://opensalt.net/uri/f0e5ab04-4b78-11eb-abdf-977889117fca","fullStatement":"make connections, through investigation using graphing technology (e.g., dynamic geometry software), between a polynomial function given in factored form [e.g., f(x) = 2(x \u2013 3)(x + 2)(x \u2013 1)] and the x-intercepts of its graph, and sketch the graph of a polynomial function given in factored form using its key features (e.g., by determining intercepts and end behaviour; by locating positive and negative regions using test values between and on either side of the x-intercepts)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-11.C1.5","notes":"**Sample Problem**: \r\n\r\nInvestigate, using graphing technology, the x-intercepts and the shapes of the graphs of polynomial functions with one or more repeated factors, for example, f(x) = (x \u2013 2)(x \u2013 3), f(x) = (x \u2013 2)(x \u2013 2)(x \u2013 3), f(x) = (x \u2013 2)(x \u2013 2)(x \u2013 2)(x \u2013 3), and f(x) = (x + 2)(x + 2)(x \u2013 2)(x \u2013 2)(x \u2013 3), by considering whether the factor is repeated an even or an odd number of times. Use your conclusions to sketch f(x) = (x + 1)(x + 1)(x \u2013 3)(x \u2013 3), and verify\r\nusing technology.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T19:13:23+00:00"},{"identifier":"f0e5c5c6-4b78-11eb-92ba-ada7a43b3bc1","uri":"https://opensalt.net/uri/f0e5c5c6-4b78-11eb-92ba-ada7a43b3bc1","fullStatement":"determine, through investigation using technology, the roles of the parameters a, k, d, and c in functions of the form y = af (k(x \u2013 d )) + c, and describe these roles in terms of transformations on the graphs of f(x) = x\u00b3 and f(x) = x4 (i.e., vertical and horizontal translations; reflections in the axes; vertical and horizontal stretches and compressions to and from the x- and y-axes)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.C1.6","notes":"**Sample Problem**: \r\n\r\nInvestigate, using technology, the graph of f(x) = 2(x \u2013 d )\u00b3 + c for various values of d and c, and describe the effects of changing d and c in terms of transformations.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T19:16:13+00:00"},{"identifier":"f0e88fb8-4b78-11eb-9630-07697068f66e","uri":"https://opensalt.net/uri/f0e88fb8-4b78-11eb-9630-07697068f66e","fullStatement":"recognize the radian as an alternative unit to the degree for angle measurement, define the radian measure of an angle as the length of the arc that subtends this angle at the centre of a unit circle, and develop and apply the relationship between radian and degree measure","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.B1.1","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:11:40+00:00"},{"identifier":"f0e852f0-4b78-11eb-a688-07444941f32a","uri":"https://opensalt.net/uri/f0e852f0-4b78-11eb-a688-07444941f32a","fullStatement":"Understanding and Applying Radian Measure","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T15:42:06+00:00"},{"identifier":"f0e82a0a-4b78-11eb-baba-39c569b5d7d2","uri":"https://opensalt.net/uri/f0e82a0a-4b78-11eb-baba-39c569b5d7d2","fullStatement":"demonstrate an understanding of the meaning and application of radian measure","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MHF4U-B1","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T15:41:14+00:00"},{"identifier":"f0e7f4cc-4b78-11eb-9e3e-b18e219ea091","uri":"https://opensalt.net/uri/f0e7f4cc-4b78-11eb-9e3e-b18e219ea091","fullStatement":"Trigonometric Functions","CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19"},"humanCodingScheme":"MHF4U-B","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T15:01:47+00:00"},{"identifier":"f0e900ba-4b78-11eb-aa65-c7a9052f3c9c","uri":"https://opensalt.net/uri/f0e900ba-4b78-11eb-aa65-c7a9052f3c9c","fullStatement":"make connections between trigonometric ratios and the graphical and algebraic representations of the corresponding trigonometric functions and between trigonometric functions and their reciprocals, and use these connections to solve problems","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MHF4U-B2","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T15:41:33+00:00"},{"identifier":"f0e96a50-4b78-11eb-a494-d176d82692a6","uri":"https://opensalt.net/uri/f0e96a50-4b78-11eb-a494-d176d82692a6","fullStatement":"determine the amplitude, period, and phase shift of sinusoidal functions whose equations are given in the form f(x) = a sin (k (x \u2013 d)) + c or f(x) = a cos (k (x \u2013 d)) + c, with angles expressed in radians","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.B2.4","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:12:42+00:00"},{"identifier":"f0e928b0-4b78-11eb-8915-bf347f991c91","uri":"https://opensalt.net/uri/f0e928b0-4b78-11eb-8915-bf347f991c91","fullStatement":"Connecting Graphs and Equations of Trigonometric Functions","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T15:46:03+00:00"},{"identifier":"f0e987e2-4b78-11eb-af46-372cb2f6f87c","uri":"https://opensalt.net/uri/f0e987e2-4b78-11eb-af46-372cb2f6f87c","fullStatement":"graph, with technology and using the primary trigonometric functions, the reciprocal trigonometric functions (i.e., cosecant, secant, cotangent) for angle measures expressed in radians, determine and describe key proper- ties of the reciprocal functions (e.g., state the domain, range, and period, and identify and explain the occurrence of asymptotes), and recognize notations used to represent the reciprocal functions [e.g., the reciprocal of f(x) = sin x can be represented using csc x, 1/f(x), or 1/sinX, but not using f-1(x) or sin-2, which represents the inverse function]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.B2.3","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T19:07:13+00:00"},{"identifier":"f0e9a402-4b78-11eb-a53d-f98c76e2d71d","uri":"https://opensalt.net/uri/f0e9a402-4b78-11eb-a53d-f98c76e2d71d","fullStatement":"sketch the graphs of f(x) = sin x and f(x) = cos x for angle measures expressed in radians, and determine and describe some key properties (e.g., period of 2\u03c0, amplitude of 1) in terms of radians","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.B2.1","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:12:17+00:00"},{"identifier":"f0e9bf0a-4b78-11eb-8daa-d3e1a617740c","uri":"https://opensalt.net/uri/f0e9bf0a-4b78-11eb-8daa-d3e1a617740c","fullStatement":"make connections between the tangent ratio and the tangent function by using technology to graph the relationship between angles in radians and their tangent ratios and defining this relationship as the function f(x) = tan x, and describe key properties of the tangent function","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.B2.2","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:12:26+00:00"},{"identifier":"f0e9da9e-4b78-11eb-8666-dd3a0f6c1184","uri":"https://opensalt.net/uri/f0e9da9e-4b78-11eb-8666-dd3a0f6c1184","fullStatement":"sketch graphs of y = a sin (k(x \u2013 d)) + c and y = a cos(k(x \u2013 d)) + c by applying transformations to the graphs of f(x) = sin x and f(x) = cos x with angles expressed in radians, and state the period, amplitude, and phase shift of the transformed functions","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MHF4U-12.B2.5","notes":"**Sample Problem**:\r\n\r\nTransform the graph of f(x) = cos x to sketch g(x) = 3 cos (2x) \u2013 1, and state the period, amplitude, and phase shift of each function.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:12:49+00:00"},{"identifier":"f0e9f79a-4b78-11eb-8e88-6b807f7367d2","uri":"https://opensalt.net/uri/f0e9f79a-4b78-11eb-8e88-6b807f7367d2","fullStatement":"solve problems involving trigonometric equations and prove trigonometric identities","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MHF4U-B3","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T15:41:53+00:00"},{"identifier":"f0ea549c-4b78-11eb-9fe8-a335174c1e5d","uri":"https://opensalt.net/uri/f0ea549c-4b78-11eb-9fe8-a335174c1e5d","fullStatement":"recognize equivalent trigonometric expressions [e.g., by using the angles in a right triangle to recognize that sin x and cos (\u03c0/2 \u2013 x) are equivalent; by using transformations to recognize that cos (x + \u03c0/2) and \u2013sin x are equivalent], and verify equivalence using graphing technology","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.B3.1","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:13:13+00:00"},{"identifier":"f0ea1edc-4b78-11eb-ae5e-67dd3a4d2265","uri":"https://opensalt.net/uri/f0ea1edc-4b78-11eb-ae5e-67dd3a4d2265","fullStatement":"Solving Trigonometric Equations","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T15:55:24+00:00"},{"identifier":"f0ea71b6-4b78-11eb-9320-773524c9ac17","uri":"https://opensalt.net/uri/f0ea71b6-4b78-11eb-9320-773524c9ac17","fullStatement":"explore the algebraic development of the compound angle formulas (e.g., verify the formulas in numerical examples, using technology; follow a demonstration of the algebraic development [student reproduction of the development of the general case is not required]), and use the formulas to determine exact values of trigonometric ratios [e.g., determining the exact value of sin (\u03c0/12) by first rewriting it in terms of special angles as sin (\u03c0/4 \u2013 \u03c0/6)]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.B3.2","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:13:21+00:00"},{"identifier":"f0ea8d90-4b78-11eb-8ba9-9d5c14a9d88b","uri":"https://opensalt.net/uri/f0ea8d90-4b78-11eb-8ba9-9d5c14a9d88b","fullStatement":"recognize that trigonometric identities are equations that are true for every value in the domain (i.e., a counter-example can be used to show that an equation is not an identity), prove trigonometric identities through the application of reasoning skills, using a variety of relationships (e.g., tan x = sin x/cos x; sin\u00b2 x + cos\u00b2 x = 1; the reciprocal identities; the compound angle formulas), and verify identities using technology","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.B3.3","notes":"**Sample Problem**:\r\n\r\nUse the compound angle formulas to prove the double angle formulas.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:13:32+00:00"},{"identifier":"f0e8ac3c-4b78-11eb-ada9-ab86bf73f583","uri":"https://opensalt.net/uri/f0e8ac3c-4b78-11eb-ada9-ab86bf73f583","fullStatement":"represent radian measure in terms of \u03c0 (e.g., \u03c0/3 radians, 2 \u03c0 radians) and as a rational number (e.g., 1.05 radians, 6.28 radians)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.B1.2","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:11:49+00:00"},{"identifier":"f0e8c78a-4b78-11eb-9954-6312469aa3a5","uri":"https://opensalt.net/uri/f0e8c78a-4b78-11eb-9954-6312469aa3a5","fullStatement":"determine, with technology, the primary trigonometric ratios (i.e., sine, cosine, tangent) and the reciprocal trigonometric ratios (i.e., cosecant, secant, cotangent) of angles expressed in radian measure","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.B1.3","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:11:59+00:00"},{"identifier":"f0e8e364-4b78-11eb-8d73-3ba9b9c231aa","uri":"https://opensalt.net/uri/f0e8e364-4b78-11eb-8d73-3ba9b9c231aa","fullStatement":"determine, without technology, the exact values of the primary trigonometric ratios and the reciprocal trigonometric ratios for the special angles 0, \u03c0/6 , \u03c0/4 , \u03c0/3 , \u03c0/2 , and their multiples less than or equal to 2\u03c0","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.B1.4","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:12:08+00:00"},{"identifier":"f0eb5766-4b78-11eb-9e57-e99fc1c32650","uri":"https://opensalt.net/uri/f0eb5766-4b78-11eb-9e57-e99fc1c32650","fullStatement":"gather, interpret, and describe information about real-world applications of rates of change, and recognize different ways of representing rates of change (e.g., in words, numerically, graphically, algebraically)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.D1.1","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:22:37+00:00"},{"identifier":"f0eb0892-4b78-11eb-ae72-b5a021f70080","uri":"https://opensalt.net/uri/f0eb0892-4b78-11eb-ae72-b5a021f70080","fullStatement":"Understanding Rates of Change","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:08:44+00:00"},{"identifier":"f0eae0a6-4b78-11eb-ae21-2d57e7685670","uri":"https://opensalt.net/uri/f0eae0a6-4b78-11eb-ae21-2d57e7685670","fullStatement":"demonstrate an understanding of average and instantaneous rate of change, and determine, numerically and graphically, and interpret the average rate of change of a function over a given interval and the instantaneous rate of change of a function at a given point","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MHF4U-D1","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:07:55+00:00"},{"identifier":"f0eaaab4-4b78-11eb-a4ee-51eff2d431aa","uri":"https://opensalt.net/uri/f0eaaab4-4b78-11eb-a4ee-51eff2d431aa","fullStatement":"Characteristics of Functions","CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19"},"humanCodingScheme":"MHF4U-D","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T15:03:28+00:00"},{"identifier":"f0ec1b60-4b78-11eb-9aa9-cd1f774ada99","uri":"https://opensalt.net/uri/f0ec1b60-4b78-11eb-9aa9-cd1f774ada99","fullStatement":"determine functions that result from the addition, subtraction, multiplication, and division of two functions and from the composition of two functions, describe some properties of the resulting functions, and solve related problems","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MHF4U-D2","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:08:13+00:00"},{"identifier":"f0ec9996-4b78-11eb-a3e7-d9d3484b5bb8","uri":"https://opensalt.net/uri/f0ec9996-4b78-11eb-a3e7-d9d3484b5bb8","fullStatement":"determine, through investigation using graphing technology, key features (e.g., domain, range, maximum/minimum points, number of zeros) of the graphs of functions created by adding, subtracting, multiplying, or dividing functions [e.g., f(x) = 2\u2013x sin 4x, g(x) = x\u00b2 + 2x h(x) = sin x/cos x], and describe factors that affect these properties","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.D2.1","notes":"Sample problem: Investigate the effect of the behaviours of f(x) = sin x, f(x) = sin 2x, and f(x) = sin 4x on the shape of f(x) = sin x + sin 2x + sin 4x.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:27:31+00:00"},{"identifier":"f0ec43d8-4b78-11eb-b215-b540103c9442","uri":"https://opensalt.net/uri/f0ec43d8-4b78-11eb-b215-b540103c9442","fullStatement":"Combining Functions","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:24:18+00:00"},{"identifier":"f0ecb728-4b78-11eb-a7fe-d50283682f96","uri":"https://opensalt.net/uri/f0ecb728-4b78-11eb-a7fe-d50283682f96","fullStatement":"recognize real-world applications of combinations of functions (e.g., the motion of a damped pendulum can be represented by a function that is the product of a trigonometric function and an exponential function; the frequencies of tones associated with the numbers on a telephone involve the addition of two trigonometric functions), and solve related problems graphically","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.D2.2","notes":"**Sample Problem**: \r\n\r\nThe rate at which a contaminant leaves a storm sewer and enters a lake depends on two factors: the concentration of the contaminant in the water from the sewer and the rate at which the water leaves the sewer. Both of these factors vary with time. The concentration of the contaminant, in kilograms per cubic metre of water, is given by c(t) = t2, where t is in seconds. The rate at which water leaves the sewer, in cubic metres per second, is given by w(t) = 1/(t4 + 10). Determine the time at which the contaminant leaves the sewer and enters the lake at the maximum rate.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T19:28:58+00:00"},{"identifier":"f0ecd2b2-4b78-11eb-9313-07b29e4ee72d","uri":"https://opensalt.net/uri/f0ecd2b2-4b78-11eb-9313-07b29e4ee72d","fullStatement":"determine, through investigation, and explain some properties (i.e., odd, even, or neither; increasing/decreasing behaviours) of functions formed by adding, subtracting, multiplying, and dividing general functions [e.g., f(x) + g(x), f(x)g(x)]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.D2.3","notes":"**Sample Problem**: \r\n\r\nInvestigate algebraically, and verify numerically and graphically, whether the product of two functions is even or odd if the two functions are both even or both odd, or if one function is even and the other is odd.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T19:29:08+00:00"},{"identifier":"f0eceee6-4b78-11eb-8dad-a9b3f5121375","uri":"https://opensalt.net/uri/f0eceee6-4b78-11eb-8dad-a9b3f5121375","fullStatement":"determine the composition of two functions [i.e., f( g(x))] numerically (i.e., by using a table of values) and graphically, with technology, for functions represented in a variety of ways (e.g., function machines, graphs, equations), and interpret the composition of two functions in real-world applications","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.D2.4","notes":"**Sample Problem**:\r\n\r\nFor a car travelling at a constant speed, the distance driven, d kilometres, is represented by d(t) = 80t, where t is the time in hours. The cost of gasoline, in dollars, for the drive is represented by C(d) = 0.09d. Determine numerically and interpret C(d(5)), and describe the relationship represented by C(d(t)).","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:31:36+00:00"},{"identifier":"f0ed0ad4-4b78-11eb-b1df-25be9e9147d9","uri":"https://opensalt.net/uri/f0ed0ad4-4b78-11eb-b1df-25be9e9147d9","fullStatement":"determine algebraically the composition of two functions [i.e., f( g(x))], verify that f( g(x)) is not always equal to g( f(x)) [e.g., by determining f( g(x)) and g( f(x)), given f(x) = x + 1 and g(x) = 2x], and state the domain [i.e., by defining f( g(x)) for those x-values for which g(x) is defined and for which it is included in the domain of f(x)] and the range of the com- position of two functions","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.D2.5","notes":"**Sample Problem**:\r\n\r\nDetermine f( g(x)) and g( f(x)) given f(x) = cos x and g(x) = 2x + 1, state the domain and range of f( g(x)) and g( f(x)), compare f( g(x)) with g( f(x)) algebraically, and verify numerically and graphically with technology.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T19:25:21+00:00"},{"identifier":"f0ed2672-4b78-11eb-a3e5-b7fd73a4005d","uri":"https://opensalt.net/uri/f0ed2672-4b78-11eb-a3e5-b7fd73a4005d","fullStatement":"solve problems involving the composition of two functions, including problems arising from real-world applications","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.D2.6","notes":"**Sample Problem**: \r\n\r\nThe speed of a car, v kilometres per hour, at a time of t hours is represented by v(t) = 40 + 3t + t2. The rate of gasoline consumption of the car, c litres per kilometre, at a speed of v kilometres per hour is represented by c(v) = (v/500 - 0.1)\u00b2 + 0.15. Determine algebraically c( v(t)), the rate of gasoline consumption as a function of time. Determine, using technology, the time when the car is running most economically during a four-hour trip.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T19:25:51+00:00"},{"identifier":"f0ed412a-4b78-11eb-9455-69693ff4c5ed","uri":"https://opensalt.net/uri/f0ed412a-4b78-11eb-9455-69693ff4c5ed","fullStatement":"demonstrate, by giving examples for functions represented in a variety of ways (e.g., function machines, graphs, equations), the property that the composition of a function and its inverse function maps a number onto itself [i.e., f\u20131( f(x)) = x and f( f\u20131(x)) = x demonstrate that the inverse function is the reverse process of the original function and that it undoes what the function does]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.D2.7","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T19:29:19+00:00"},{"identifier":"f0ed5c14-4b78-11eb-9421-0b149d866da1","uri":"https://opensalt.net/uri/f0ed5c14-4b78-11eb-9421-0b149d866da1","fullStatement":"make connections, through investigation using technology, between transformations (i.e., vertical and horizontal translations; reflections in the axes; vertical and horizontal stretches and compressions to and from the x- and y-axes) of simple functions f(x) [e.g., f(x) = x\u00b3 + 20, f(x) = sin x, f(x) = log x] and the composition of these functions with a linear function of the form g(x) = A(x + B)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.D2.8","notes":"**Sample Problem**: \r\n\r\nCompare the graph of f(x) = x\u00b2 with the graphs of f( g(x)) and g( f(x)), where g(x) = 2(x \u2013 d), for various values of d. Describe the effects of d in terms of transformations of f(x).","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:36:02+00:00"},{"identifier":"f0ed7924-4b78-11eb-b897-55a24ed191cf","uri":"https://opensalt.net/uri/f0ed7924-4b78-11eb-b897-55a24ed191cf","fullStatement":"compare the characteristics of functions, and solve problems by modelling and reasoning with functions, including problems with solutions that are not accessible by standard algebraic techniques","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MHF4U-D3","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:08:32+00:00"},{"identifier":"f0eda232-4b78-11eb-af26-695d797562ee","uri":"https://opensalt.net/uri/f0eda232-4b78-11eb-af26-695d797562ee","fullStatement":"Using Function Models to Solve Problems","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:36:18+00:00"},{"identifier":"f0ee03a8-4b78-11eb-9244-2b946945e9c7","uri":"https://opensalt.net/uri/f0ee03a8-4b78-11eb-9244-2b946945e9c7","fullStatement":"compare, through investigation using a variety of tools and strategies (e.g., graphing with technology; comparing algebraic representations; comparing finite differences in tables of values) the characteristics (e.g., key features of the graphs, forms of the equations) of various functions (i.e., polynomial, rational, trigonometric, exponential, logarithmic)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.D3.1","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:37:08+00:00"},{"identifier":"f0ee1f1e-4b78-11eb-b351-31c00354efb4","uri":"https://opensalt.net/uri/f0ee1f1e-4b78-11eb-b351-31c00354efb4","fullStatement":"solve graphically and numerically equations and inequalities whose solutions are not accessible by standard algebraic techniques","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.D3.2","notes":"**Sample Problem**: \r\n\r\nSolve: 2x\u00b2 < 2x; cos x = x, with x in radians.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:38:01+00:00"},{"identifier":"f0ee3ae4-4b78-11eb-ab3d-23c9e501b11b","uri":"https://opensalt.net/uri/f0ee3ae4-4b78-11eb-ab3d-23c9e501b11b","fullStatement":"solve problems, using a variety of tools and strategies, including problems arising from real-world applications, by reasoning with functions and by applying concepts and procedures involving functions (e.g., by constructing a function model from data, using the model to determine mathematical results, and interpreting and communicating the results within the context of the problem)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.D3.3","notes":"**Sample Problem**: \r\n\r\nThe pressure of a car tire with a slow leak is given in the following table of values:\r\n\r\n| Time, t (min) | Pressure, P (kPa) | \r\n| -------- | -------- |\r\n| 0 | 400 |\r\n| 5 | 335 |\r\n| 10 | 295 |\r\n| 15 | 255 |\r\n| 20 | 225 |\r\n| 25 | 195 |\r\n| 30 | 170 |\r\n\r\nUse technology to investigate linear, quadratic, and exponential models for the relation- ship of the tire pressure and time, and describe how well each model fits the data. Use each model to predict the pressure after 60 min. Which model gives the most realistic answer?","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:41:00+00:00"},{"identifier":"f0eb7516-4b78-11eb-bd77-85417a887901","uri":"https://opensalt.net/uri/f0eb7516-4b78-11eb-bd77-85417a887901","fullStatement":"recognize that the rate of change for a function is a comparison of changes in the dependent variable to changes in the independent variable, and distinguish situations in which the rate of change is zero, constant, or changing by examining applications, including those arising from real-world situations (e.g., rate of change of the area of a circle as the radius increases, inflation rates, the rising trend in graduation rates among Aboriginal youth, speed of a cruising aircraft, speed of a cyclist climbing a hill, infection rates)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.D1.2","notes":"**Sample Problem**: \r\n\r\nThe population of bacteria in a sample is 250 000 at 1:00 p.m., 500 000 at 3:00 p.m., and 1 000 000 at 5:00 p.m. Compare methods used to calculate the change in the population and the rate of change in the population between 1:00 p.m. to 5:00 p.m. Is the rate of change constant? Explain your reasoning.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:22:37+00:00"},{"identifier":"f0eb9078-4b78-11eb-934e-213b35d943c2","uri":"https://opensalt.net/uri/f0eb9078-4b78-11eb-934e-213b35d943c2","fullStatement":"sketch a graph that represents a relationship involving rate of change, as described in words, and verify with technology (e.g., motion sensor) when possible","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.D1.3","notes":"**Sample Problem**: \r\n\r\nJohn rides his bicycle at a constant cruising speed along a flat road. He then decelerates (i.e., decreases speed) as he climbs a hill. At the top, he accelerates (i.e., increases speed) on a flat road back to his constant cruising speed, and he then accelerates down a hill. Finally, he comes to another hill and glides to a stop as he starts to climb. Sketch a graph of John\u2019s speed versus time and a graph of his distance travelled versus time.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:22:37+00:00"},{"identifier":"f0ebac48-4b78-11eb-a972-e182f14c0b05","uri":"https://opensalt.net/uri/f0ebac48-4b78-11eb-a972-e182f14c0b05","fullStatement":"calculate and interpret average rates of change of functions (e.g., linear, quadratic, exponential, sinusoidal) arising from real-world applications (e.g., in the natural, physical, and social sciences), given various representations of the functions (e.g., tables of values, graphs, equations)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.D1.4","notes":"**Sample Problem**: \r\n\r\nFluorine-20 is a radioactive substance that decays over time. At time 0, the mass of a sample of the substance is 20 g. The mass decreases to 10 g after 11 s, to 5 g after 22 s, and to 2.5 g after 33 s. Compare the average rate of change over the 33-s interval with the average rate of change over consecutive 11-s intervals.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:22:37+00:00"},{"identifier":"f0ebc7fa-4b78-11eb-8b0d-1d425bf29f88","uri":"https://opensalt.net/uri/f0ebc7fa-4b78-11eb-8b0d-1d425bf29f88","fullStatement":"recognize examples of instantaneous rates of change arising from real-world situations, and make connections between instantaneous rates of change and average rates of change (e.g., an average rate of change can be used to approximate an instantaneous rate of change)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.D1.5","notes":"**Sample Problem**: \r\n\r\nIn general, does the speedometer of a car measure instantaneous rate of change (i.e., instantaneous speed) or average rate of change (i.e., average speed)? Describe situations in which the instantaneous speed and the average speed would be the same.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:22:37+00:00"},{"identifier":"f0ebe2da-4b78-11eb-b5ea-b91eefbe796d","uri":"https://opensalt.net/uri/f0ebe2da-4b78-11eb-b5ea-b91eefbe796d","fullStatement":"determine, through investigation using various representations of relationships (e.g., tables of values, graphs, equations), approximate instantaneous rates of change arising from real-world applications (e.g., in the natural, physical, and social sciences) by using average rates of change and reducing the interval over which the average rate of change is determined","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.D1.6","notes":"**Sample Problem**: \r\n\r\nThe distance, d metres, travelled by a falling object in t seconds is represented by d = 5t\u00b2. When t = 3, the instantaneous speed of the object is 30 m/s. Compare the average speeds over different time intervals starting at t = 3 with the instantaneous speed when t = 3. Use your observations to select an interval that can be used to provide a good approximation of the instantaneous speed at t = 3.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:22:37+00:00"},{"identifier":"f0ebfe46-4b78-11eb-9e32-df61a8950e64","uri":"https://opensalt.net/uri/f0ebfe46-4b78-11eb-9e32-df61a8950e64","fullStatement":"make connections, through investigation, between the slope of a secant on the graph of a function (e.g., quadratic, exponential, sinusoidal) and the average rate of change of the function over an interval, and between the slope of the tangent to a point on the graph of a function and the instantaneous rate of change of the function at that point","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.D1.7","notes":"**Sample Problem**: \r\n\r\nUse tangents to investigate the behaviour of a function when the instantaneous rate of change is zero, positive, or negative.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:22:37+00:00"},{"identifier":"244385dc-4b80-11eb-a368-8737d96adc4c","uri":"https://opensalt.net/uri/244385dc-4b80-11eb-a368-8737d96adc4c","fullStatement":"represent a sinusoidal function with an equation, given its graph or its properties, with angles expressed in radians","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.B2.6","notes":"**Sample Problem**: \r\n\r\nA sinusoidal function has an amplitude of 2 units, a period of \u03c0, and a maximum at (0, 3). Represent the function with an equation in two different ways.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:12:57+00:00"},{"identifier":"27aa8270-4b80-11eb-8ec3-338d7e251c61","uri":"https://opensalt.net/uri/27aa8270-4b80-11eb-8ec3-338d7e251c61","fullStatement":"pose problems based on applications involving a trigonometric function with domain expressed in radians (e.g., seasonal changes in temperature, heights of tides, hours of daylight, displacements for oscillating springs), and solve these and other such problems by using a given graph or a graph generated with or without technology from a table of values or from its equation","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.B2.7","notes":"**Sample Problem**: \r\n\r\nThe population size, P, of owls (predators) in a certain region can be modelled by the function P(t) = 1000 + 100 sin (\u03c0t/12), where t represents the time in months. The population size, p, of mice (prey) in the same region is given by p(t) = 20 000 + 4000 cos (\u03c0t/12). Sketch the graphs of these functions, and pose and solve problems involving the relationships between the two populations over time.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T19:10:09+00:00"},{"identifier":"3e4de8f4-4b81-11eb-be4d-bd8c04c5214c","uri":"https://opensalt.net/uri/3e4de8f4-4b81-11eb-be4d-bd8c04c5214c","fullStatement":"solve linear and quadratic trigonometric equations, with and without graphing technology, for the domain of real values from 0 to 2\u03c0, and solve related problems","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.B3.4","notes":"**Sample Problem**:\r\n\r\nSolve the following trigonometric equations for 0 \u2264 x \u2264 2\u03c0, and verify by graphing with technology: 2 sin x + 1 = 0; 2 sin\u00b2 x + sin x \u2013 1 = 0; sin x = cos 2x; cos 2x = 1 .","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T19:11:32+00:00"},{"identifier":"54c6333a-4b85-11eb-8112-d7d5493919b3","uri":"https://opensalt.net/uri/54c6333a-4b85-11eb-8112-d7d5493919b3","fullStatement":"demonstrate an understanding of solving polynomial and simple rational inequalities","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"MHF4U-C4","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:03:47+00:00"},{"identifier":"54c6aaea-4b85-11eb-b388-a932cb2d8d6b","uri":"https://opensalt.net/uri/54c6aaea-4b85-11eb-b388-a932cb2d8d6b","fullStatement":"explain, for polynomial and simple rational functions, the difference between the solution to an equation in one variable and the solution to an inequality in one variable, and demonstrate that given solutions satisfy an inequality (e.g., demonstrate numerically and graphically that the solution to 1/(x + 1) < 5 is x < -1 or x > -(4/5)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.C4.1","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:16:32+00:00"},{"identifier":"54c66314-4b85-11eb-b848-294390434c3c","uri":"https://opensalt.net/uri/54c66314-4b85-11eb-b848-294390434c3c","fullStatement":"Solving Inequalities","CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3"},"language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:00:14+00:00"},{"identifier":"54c6c926-4b85-11eb-933a-07b1928adb6c","uri":"https://opensalt.net/uri/54c6c926-4b85-11eb-933a-07b1928adb6c","fullStatement":"determine solutions to polynomial inequalities in one variable [e.g., solve f(x) \u2265 0, where f(x) = x\u00b3 \u2013 x\u00b2 + 3x \u2013 9] and to simple rational inequalities in one variable by graphing the corresponding functions, using graphing technology, and identifying intervals for which x satisfies the inequalities","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.C4.2","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:16:39+00:00"},{"identifier":"54c6e4d8-4b85-11eb-9a68-eb85a98359d6","uri":"https://opensalt.net/uri/54c6e4d8-4b85-11eb-9a68-eb85a98359d6","fullStatement":"solve linear inequalities and factorable polynomial inequalities in one variable (e.g., x\u00b3 + x\u00b2 > 0) in a variety of ways (e.g., by deter- mining intervals using x-intercepts and evaluating the corresponding function for a single x-value within each interval; by factoring the polynomial and identifying the conditions for which the product satisfies the inequality), and represent the solutions on a number line or algebraically (e.g., for the inequality x4 \u2013 5x\u00b2+ 4 < 0, the solution represented algebraically is \u2013 2 < x < \u2013 1 or 1 < x < 2)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.C4.3","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T19:21:15+00:00"},{"identifier":"8022d604-4b86-11eb-855a-7f31ee79f80e","uri":"https://opensalt.net/uri/8022d604-4b86-11eb-855a-7f31ee79f80e","fullStatement":"determine an equation of a polynomial function that satisfies a given set of conditions (e.g., degree of the polynomial, intercepts, points on the function), using methods appropriate to the situation (e.g., using the x-intercepts of the function; using a trial-and-error process with a graphing calculator or graphing soft- ware; using finite differences), and recognize that there may be more than one polynomial function that can satisfy a given set of conditions (e.g., an infinite number of polynomial functions satisfy the condition that they have three given x-intercepts)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.C1.7","notes":"**Sample Problem**: \r\n\r\nDetermine an equation for a fifth-degree polynomial function that intersects the x-axis at only 5, 1, and \u20135, and sketch the graph of the function.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T19:16:36+00:00"},{"identifier":"8199c466-4b86-11eb-beb2-71875479b0c3","uri":"https://opensalt.net/uri/8199c466-4b86-11eb-beb2-71875479b0c3","fullStatement":"determine the equation of the family of polynomial functions with a given set of zeros and of the member of the family that passes through another given point [e.g., a family of polynomial functions of degree 3 with zeros 5, \u20133, and \u20132 is defined by the equation f(x) = k(x \u2013 5)(x + 3)(x + 2), where k is a real number, k \u2260 0; the member of the family that passes through (\u20131, 24) is f(x) = \u20132(x \u2013 5)(x + 3)(x + 2)]","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.C1.8","notes":"**Sample Problem**: \r\n\r\nInvestigate, using graphing technology, and determine a polynomial function that can be used to model the function f(x) = sin x over the interval 0 \u2264 x \u2264 2\u03c0.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T19:17:12+00:00"},{"identifier":"8307cf82-4b86-11eb-a9f6-41764d5b2cfb","uri":"https://opensalt.net/uri/8307cf82-4b86-11eb-a9f6-41764d5b2cfb","fullStatement":"determine, through investigation, and compare the properties of even and odd polynomial functions [e.g., symmetry about the y-axis or the origin; the power of each term; the number of x-intercepts; f(x) = f(\u2013 x) or f(\u2013 x) = \u2013 f (x)], and determine whether a given polynomial function is even, odd, or neither","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.C1.9","notes":"**Sample Problem**: \r\n\r\nInvestigate numerically, graphically, and algebraically, with and without technology, the conditions under which an even function has an even number of x-intercepts.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-01-08T19:17:51+00:00"},{"identifier":"c5481bc6-4b8c-11eb-80c8-afc632173412","uri":"https://opensalt.net/uri/c5481bc6-4b8c-11eb-80c8-afc632173412","fullStatement":"determine, through investigation using a variety of tools and strategies (e.g., using a table of values to calculate slopes of secants or graphing secants and measuring their slopes with technology), the approximate slope of the tangent to a given point on the graph of a function (e.g., quadratic, exponential, sinusoidal) by using the slopes of secants through the given point (e.g., investigating the slopes of secants that approach the tangent at that point more and more closely), and make connections to average and instantaneous rates of change","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.D1.8","language":"en","educationLevel":["12"],"lastChangeDateTime":"2020-12-31T17:23:10+00:00"},{"identifier":"c6f9e5f8-4b8c-11eb-9e32-afe0ce1e2664","uri":"https://opensalt.net/uri/c6f9e5f8-4b8c-11eb-9e32-afe0ce1e2664","fullStatement":"solve problems involving average and instantaneous rates of change, including problems arising from real-world applications, by using numerical and graphical methods (e.g., by using graphing technology to graph a tangent and measure its slope)","CFItemType":"Expectation","CFItemTypeURI":{"title":"Expectation","identifier":"278e0028-95e9-4f74-9827-f1bc7da5e88f","uri":"https://opensalt.net/uri/278e0028-95e9-4f74-9827-f1bc7da5e88f"},"humanCodingScheme":"MHF4U-12.D1.9","notes":"**Sample Problem**: \r\n\r\nThe height, h metres, of a ball above the ground can be modelled by the function h(t) = \u2013 5t\u00b2 + 20t, where t is the time in seconds. Use average speeds to determine the approximate instantaneous speed at t = 3.","language":"en","educationLevel":["12"],"lastChangeDateTime":"2021-02-04T13:47:59+00:00"},{"identifier":"c74ee87a-51e8-11eb-88df-a1b4a0613e8a","uri":"https://opensalt.net/uri/c74ee87a-51e8-11eb-88df-a1b4a0613e8a","fullStatement":"Mathematical Processes","CFItemType":"Process","CFItemTypeURI":{"title":"Process","identifier":"b32fbc6e-ca35-422d-a997-07a54bd16ce2","uri":"https://opensalt.net/uri/b32fbc6e-ca35-422d-a997-07a54bd16ce2"},"language":"en","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"lastChangeDateTime":"2021-01-08T20:17:17+00:00"},{"identifier":"01d568de-51e9-11eb-be68-351f66a082ce","uri":"https://opensalt.net/uri/01d568de-51e9-11eb-be68-351f66a082ce","fullStatement":"Problem Solving","CFItemType":"Process","CFItemTypeURI":{"title":"Process","identifier":"b32fbc6e-ca35-422d-a997-07a54bd16ce2","uri":"https://opensalt.net/uri/b32fbc6e-ca35-422d-a997-07a54bd16ce2"},"notes":"**K-8**: develop, select, and apply problem-solving strategies\r\n\r\n**9:12**: develop, select, apply, and compare a variety of problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding","language":"en","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"lastChangeDateTime":"2021-01-08T19:38:37+00:00"},{"identifier":"0fd868f0-51e9-11eb-bd56-cbd571aeafdf","uri":"https://opensalt.net/uri/0fd868f0-51e9-11eb-bd56-cbd571aeafdf","fullStatement":"Reasoning and Proving","CFItemType":"Process","CFItemTypeURI":{"title":"Process","identifier":"b32fbc6e-ca35-422d-a997-07a54bd16ce2","uri":"https://opensalt.net/uri/b32fbc6e-ca35-422d-a997-07a54bd16ce2"},"notes":"**K-8**: develop and apply reasoning skills (e.g., classification, recognition of relationships, use of counter-examples) to justify thinking, make and investigate conjectures, and construct and defend arguments\r\n\r\n**9:12**: develop and apply reasoning skills (e.g., recognition of relationships, generalization through inductive reasoning, use of counter-examples) to make mathematical conjectures, assess conjectures, and justify conclusions, and plan and construct organized mathematical arguments","language":"en","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"lastChangeDateTime":"2021-01-08T19:42:04+00:00"},{"identifier":"123b4f5e-51e9-11eb-bbd8-ff88ee860559","uri":"https://opensalt.net/uri/123b4f5e-51e9-11eb-bbd8-ff88ee860559","fullStatement":"Reflecting","CFItemType":"Process","CFItemTypeURI":{"title":"Process","identifier":"b32fbc6e-ca35-422d-a997-07a54bd16ce2","uri":"https://opensalt.net/uri/b32fbc6e-ca35-422d-a997-07a54bd16ce2"},"notes":"**K-8**: demonstrate that as they solve problems, they are pausing, looking back, and monitoring their thinking to help clarify their understanding (e.g., by comparing and adjusting strategies used, by explaining why they think their results are reasonable, by recording their thinking in a math journal)\r\n\r\n**9:12**: demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions)","language":"en","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"lastChangeDateTime":"2021-01-08T19:42:17+00:00"},{"identifier":"13acbd0a-51e9-11eb-af31-41aac94effe7","uri":"https://opensalt.net/uri/13acbd0a-51e9-11eb-af31-41aac94effe7","fullStatement":"Selecting Tools and [Computational Strategies","CFItemType":"Process","CFItemTypeURI":{"title":"Process","identifier":"b32fbc6e-ca35-422d-a997-07a54bd16ce2","uri":"https://opensalt.net/uri/b32fbc6e-ca35-422d-a997-07a54bd16ce2"},"notes":"**K-8**: select and use a variety of concrete, visual, and electronic learning tools and appropriate strategies to investigate mathematical ideas and to solve problems\r\n\r\n**9:12**: select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems","language":"en","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"lastChangeDateTime":"2021-01-08T19:43:27+00:00"},{"identifier":"16788136-51e9-11eb-9918-47c1136ef75c","uri":"https://opensalt.net/uri/16788136-51e9-11eb-9918-47c1136ef75c","fullStatement":"Connecting","CFItemType":"Process","CFItemTypeURI":{"title":"Process","identifier":"b32fbc6e-ca35-422d-a997-07a54bd16ce2","uri":"https://opensalt.net/uri/b32fbc6e-ca35-422d-a997-07a54bd16ce2"},"notes":"**K-8**: make connections among mathematical concepts, procedures, and representations, and relate mathematical ideas to other contexts (e.g., other curriculum areas, daily life, sports)\r\n\r\n**9:12**: make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events, art and culture, sports)","language":"en","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"lastChangeDateTime":"2021-01-08T19:43:45+00:00"},{"identifier":"185eaaf2-51e9-11eb-a20b-c1dc7d1de0e5","uri":"https://opensalt.net/uri/185eaaf2-51e9-11eb-a20b-c1dc7d1de0e5","fullStatement":"Representing","CFItemType":"Process","CFItemTypeURI":{"title":"Process","identifier":"b32fbc6e-ca35-422d-a997-07a54bd16ce2","uri":"https://opensalt.net/uri/b32fbc6e-ca35-422d-a997-07a54bd16ce2"},"notes":"**K-8**: select from and create a variety of representations of mathematical ideas (e.g., representations involving physical models, pictures, numbers, variables, graphs), and apply them to solve problems\r\n\r\n**9:12**: create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems","language":"en","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"lastChangeDateTime":"2021-01-08T19:44:05+00:00"},{"identifier":"19fed92c-51e9-11eb-8f1e-735d8d284c9c","uri":"https://opensalt.net/uri/19fed92c-51e9-11eb-8f1e-735d8d284c9c","fullStatement":"Communicating","CFItemType":"Process","CFItemTypeURI":{"title":"Process","identifier":"b32fbc6e-ca35-422d-a997-07a54bd16ce2","uri":"https://opensalt.net/uri/b32fbc6e-ca35-422d-a997-07a54bd16ce2"},"notes":"**K-8**: express and understand mathematical thinking, and engage in mathematical arguments using everyday language, language resources as necessary, appropriate mathematical terminology, a variety of representations, and mathematical conventions\r\n\r\n**9:12**: communicate mathematical thinking orally, visually, and in writing, using mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions","language":"en","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"lastChangeDateTime":"2021-01-08T19:44:19+00:00"},{"identifier":"6953d81e-51ea-11eb-945c-a5c35b3029d3","uri":"https://opensalt.net/uri/6953d81e-51ea-11eb-945c-a5c35b3029d3","fullStatement":"Social-Emotional Learning (SEL)","CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19"},"humanCodingScheme":"A.","notes":"This strand focuses on students\u2019 development and application of social-emotional learning skills to support their learning of math concepts and skills, foster their overall well-being and ability to learn, and help them build resilience and thrive as math learners. As they develop SEL skills, students demonstrate a greater ability to understand and apply the mathematical processes, which are critical to supporting learning in mathematics. In all grades of the mathematics program, the learning related to this strand takes place in the context of learning related to all other strands, and it should be assessed and evaluated within these contexts.","language":"en","educationLevel":["06"],"lastChangeDateTime":"2021-01-08T20:02:14+00:00"},{"identifier":"f22ee214-51ea-11eb-b3f7-219702856349","uri":"https://opensalt.net/uri/f22ee214-51ea-11eb-b3f7-219702856349","fullStatement":"Social-Emotional Learning (SEL) Skills and the Mathematical Processes","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"A1.","language":"en","educationLevel":["06"],"lastChangeDateTime":"2021-01-08T19:51:49+00:00"},{"identifier":"56dad1a0-51eb-11eb-b801-b9f30417d05c","uri":"https://opensalt.net/uri/56dad1a0-51eb-11eb-b801-b9f30417d05c","fullStatement":"Identify and manage emotions","CFItemType":"Specific Outcome","CFItemTypeURI":{"title":"Specific Outcome","identifier":"3e5be68c-4f8e-11eb-a0ef-3180514c92f9","uri":"https://opensalt.net/uri/3e5be68c-4f8e-11eb-a0ef-3180514c92f9"},"humanCodingScheme":"6.A1.1","notes":"To the best of their ability, students will learn to identify and manage emotions so they can express and manage their feelings, and show understanding of the feelings of others, as they engage positively in mathematics activities.","language":"en","educationLevel":["06"],"lastChangeDateTime":"2021-01-08T19:54:58+00:00"},{"identifier":"5c5e7dfc-51eb-11eb-8b8d-0f8d58f3bd09","uri":"https://opensalt.net/uri/5c5e7dfc-51eb-11eb-8b8d-0f8d58f3bd09","fullStatement":"Recognize sources of stress and cope with challenges","CFItemType":"Specific Outcome","CFItemTypeURI":{"title":"Specific Outcome","identifier":"3e5be68c-4f8e-11eb-a0ef-3180514c92f9","uri":"https://opensalt.net/uri/3e5be68c-4f8e-11eb-a0ef-3180514c92f9"},"humanCodingScheme":"6.A1.2","notes":"To the best of their ability, students will learn to Recognize sources of stress and cope with challenges so they can work through challenging math problems, understanding that their resourcefulness in using various strategies to respond to stress is helping them build personal resilience.","language":"en","educationLevel":["06"],"lastChangeDateTime":"2021-01-08T19:56:25+00:00"},{"identifier":"5e1b6718-51eb-11eb-bbec-511333639d24","uri":"https://opensalt.net/uri/5e1b6718-51eb-11eb-bbec-511333639d24","fullStatement":"Maintain positive motivation and perseverance","CFItemType":"Specific Outcome","CFItemTypeURI":{"title":"Specific Outcome","identifier":"3e5be68c-4f8e-11eb-a0ef-3180514c92f9","uri":"https://opensalt.net/uri/3e5be68c-4f8e-11eb-a0ef-3180514c92f9"},"humanCodingScheme":"6.A1.3","notes":"To the best of their ability, students will learn to maintain positive motivation and perseverance so they can recognize that testing out different approaches to problems and learning from mistakes is an important part of the learning process, and is aided by a sense of optimism and hope.","language":"en","educationLevel":["06"],"lastChangeDateTime":"2021-01-08T19:57:05+00:00"},{"identifier":"5fab679a-51eb-11eb-8e39-0902a56e9a9d","uri":"https://opensalt.net/uri/5fab679a-51eb-11eb-8e39-0902a56e9a9d","fullStatement":"Build relationships and communicate effectively","CFItemType":"Specific Outcome","CFItemTypeURI":{"title":"Specific Outcome","identifier":"3e5be68c-4f8e-11eb-a0ef-3180514c92f9","uri":"https://opensalt.net/uri/3e5be68c-4f8e-11eb-a0ef-3180514c92f9"},"humanCodingScheme":"6.A1.4","notes":"To the best of their ability, students will learn to build relationships and communicate effectively so they can work collaboratively on math problems \u2013 expressing their thinking, listening to the thinking of others, and practising inclusivity \u2013 and in that way fostering healthy relationships.","language":"en","educationLevel":["06"],"lastChangeDateTime":"2021-01-08T19:57:53+00:00"},{"identifier":"6164df8a-51eb-11eb-9f59-dd145cc54247","uri":"https://opensalt.net/uri/6164df8a-51eb-11eb-9f59-dd145cc54247","fullStatement":"Develop self-awareness and sense of identity","CFItemType":"Specific Outcome","CFItemTypeURI":{"title":"Specific Outcome","identifier":"3e5be68c-4f8e-11eb-a0ef-3180514c92f9","uri":"https://opensalt.net/uri/3e5be68c-4f8e-11eb-a0ef-3180514c92f9"},"humanCodingScheme":"6.A1.5","notes":"To the best of their ability, students will learn to develop self-awareness and sense of identity so they can see themselves as capable math learners, and strengthen their sense of ownership of their learning, as part of their emerging sense of identity and belonging.","language":"en","educationLevel":["06"],"lastChangeDateTime":"2021-01-08T19:58:55+00:00"},{"identifier":"630466e4-51eb-11eb-bf08-055845ba5088","uri":"https://opensalt.net/uri/630466e4-51eb-11eb-bf08-055845ba5088","fullStatement":"Think critically and creatively","CFItemType":"Specific Outcome","CFItemTypeURI":{"title":"Specific Outcome","identifier":"3e5be68c-4f8e-11eb-a0ef-3180514c92f9","uri":"https://opensalt.net/uri/3e5be68c-4f8e-11eb-a0ef-3180514c92f9"},"humanCodingScheme":"6.A1.6","notes":"To the best of their ability, students will learn to think critically and creatively so they can make connections between math and everyday contexts to help them make informed judgements and decisions.","language":"en","educationLevel":["06"],"lastChangeDateTime":"2021-01-08T19:59:45+00:00"},{"identifier":"5e242424-51ec-11eb-9a49-8b966614b67f","uri":"https://opensalt.net/uri/5e242424-51ec-11eb-9a49-8b966614b67f","fullStatement":"Social-Emotional Learning (SEL)","CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19","uri":"https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/b7ebe6fc-963d-4e71-9b8c-8ea6ff8efd19"},"humanCodingScheme":"A.","notes":"This strand focuses on students\u2019 development and application of social-emotional learning skills to support their learning of math concepts and skills, foster their overall well-being and ability to learn, and help them build resilience and thrive as math learners. As they develop SEL skills, students demonstrate a greater ability to understand and apply the mathematical processes, which are critical to supporting learning in mathematics. In all grades of the mathematics program, the learning related to this strand takes place in the context of learning related to all other strands, and it should be assessed and evaluated within these contexts.","language":"en","educationLevel":["07"],"lastChangeDateTime":"2021-01-08T20:02:40+00:00"},{"identifier":"5e24e666-51ec-11eb-8f9c-93025197c49b","uri":"https://opensalt.net/uri/5e24e666-51ec-11eb-8f9c-93025197c49b","fullStatement":"Recognize sources of stress and cope with challenges","CFItemType":"Specific Outcome","CFItemTypeURI":{"title":"Specific Outcome","identifier":"3e5be68c-4f8e-11eb-a0ef-3180514c92f9","uri":"https://opensalt.net/uri/3e5be68c-4f8e-11eb-a0ef-3180514c92f9"},"humanCodingScheme":"7.A1.2","notes":"To the best of their ability, students will learn to Recognize sources of stress and cope with challenges so they can work through challenging math problems, understanding that their resourcefulness in using various strategies to respond to stress is helping them build personal resilience.","language":"en","educationLevel":["07"],"lastChangeDateTime":"2021-01-08T20:03:08+00:00"},{"identifier":"5e245958-51ec-11eb-8177-0dc92cee4658","uri":"https://opensalt.net/uri/5e245958-51ec-11eb-8177-0dc92cee4658","fullStatement":"Social-Emotional Learning (SEL) Skills and the Mathematical Processes","CFItemType":"Overall Expectation","CFItemTypeURI":{"title":"Overall Expectation","identifier":"d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e","uri":"https://opensalt.net/uri/d2ed6fd4-4523-11eb-9dbd-3d0730c2b36e"},"humanCodingScheme":"A1.","language":"en","educationLevel":["07"],"lastChangeDateTime":"2021-01-08T20:02:48+00:00"},{"identifier":"5e24a4d0-51ec-11eb-ad18-0b106e998bbd","uri":"https://opensalt.net/uri/5e24a4d0-51ec-11eb-ad18-0b106e998bbd","fullStatement":"Identify and manage emotions","CFItemType":"Specific Outcome","CFItemTypeURI":{"title":"Specific Outcome","identifier":"3e5be68c-4f8e-11eb-a0ef-3180514c92f9","uri":"https://opensalt.net/uri/3e5be68c-4f8e-11eb-a0ef-3180514c92f9"},"humanCodingScheme":"7.A1.1","notes":"To the best of their ability, students will learn to identify and manage emotions so they can express and manage their feelings, and show understanding of the feelings of others, as they engage positively in mathematics activities.","language":"en","educationLevel":["07"],"lastChangeDateTime":"2021-01-08T20:02:58+00:00"},{"identifier":"5e250650-51ec-11eb-a482-995db260f5c6","uri":"https://opensalt.net/uri/5e250650-51ec-11eb-a482-995db260f5c6","fullStatement":"Maintain positive motivation and perseverance","CFItemType":"Specific Outcome","CFItemTypeURI":{"title":"Specific Outcome","identifier":"3e5be68c-4f8e-11eb-a0ef-3180514c92f9","uri":"https://opensalt.net/uri/3e5be68c-4f8e-11eb-a0ef-3180514c92f9"},"humanCodingScheme":"7.A1.3","notes":"To the best of their ability, students will learn to maintain positive motivation 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