{"CFDocument":{"identifier":"82282a10-050e-11e8-83a3-2d90e6e9552c","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFDocuments/82282a10-050e-11e8-83a3-2d90e6e9552c","creator":"Smarter Balanced_Math Claim 1 Item Specifications","title":"HS Mathematics Item Specification C1 TB","lastChangeDateTime":"2022-09-23T23:26:02+00:00","officialSourceURL":"https://images.smarterbalanced.org/content/Documents/Item%20Specs/Math_Item_Specs/Claim1_mathematics_HS_specs/HS_1B_NQ_Spec_V3_phase3.docx","publisher":"Smarter Balanced Assessment Consortium","subject":["Math"],"subjectURI":[{"title":"Math","identifier":"d41fb0f6-b390-11e7-9a98-233b080813ce","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFSubjects/d41fb0f6-b390-11e7-9a98-233b080813ce"}],"adoptionStatus":"Draft","notes":"HS_1B_NQ_Spec_V3_phase3"},"CFItems":[{"identifier":"8b7eeee6-050e-11e8-8105-69e04658d252","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8b7eeee6-050e-11e8-8105-69e04658d252","fullStatement":"Tasks for this target will require students to demonstrate understanding of operations with rational and irrational numbers. Tasks that ask students to explain why operations with rational and irrational numbers lead to either rational or irrational numbers will contribute evidence to Claim 3.","CFItemType":"Clarification","CFItemTypeURI":{"title":"Clarification","identifier":"f6e54927-6d0a-4ed6-94f7-3ee1f5ca4fcf","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/f6e54927-6d0a-4ed6-94f7-3ee1f5ca4fcf"},"abbreviatedStatement":"Clarifications","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:17:43+00:00"},{"identifier":"8cba5994-050e-11e8-a464-1762cc6e729c","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8cba5994-050e-11e8-a464-1762cc6e729c","fullStatement":"Item Writing and Scoring Guidelines","CFItemType":"Section Heading","CFItemTypeURI":{"title":"Section Heading","identifier":"ab8e8fdc-baaa-400f-9dc8-7b737f8b86ff","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/ab8e8fdc-baaa-400f-9dc8-7b737f8b86ff"},"educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:17:43+00:00"},{"identifier":"8cbad022-050e-11e8-8fe5-b7921f8ce7a9","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8cbad022-050e-11e8-8fe5-b7921f8ce7a9","fullStatement":"Students should be able to identify the difference between a rational and an irrational number.","CFItemType":"Range ALD","CFItemTypeURI":{"title":"Range ALD","identifier":"4c380133-6f2b-4606-9a4d-aa87b9980467","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/4c380133-6f2b-4606-9a4d-aa87b9980467"},"abbreviatedStatement":"Level 1","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:18:04+00:00"},{"identifier":"8cba9486-050e-11e8-a081-0ffb900fcd7a","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8cba9486-050e-11e8-a081-0ffb900fcd7a","fullStatement":"RANGE Achievement Level Descriptors (Range ALDs)","CFItemType":"Range ALD","CFItemTypeURI":{"title":"Range ALD","identifier":"4c380133-6f2b-4606-9a4d-aa87b9980467","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/4c380133-6f2b-4606-9a4d-aa87b9980467"},"educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:07:48+00:00"},{"identifier":"8cbaed50-050e-11e8-8bcb-d5ce2abaaa10","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8cbaed50-050e-11e8-8bcb-d5ce2abaaa10","fullStatement":"Students should be able to perform operations on rational and irrational numbers.","CFItemType":"Range ALD","CFItemTypeURI":{"title":"Range ALD","identifier":"4c380133-6f2b-4606-9a4d-aa87b9980467","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/4c380133-6f2b-4606-9a4d-aa87b9980467"},"abbreviatedStatement":"Level 2","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:18:17+00:00"},{"identifier":"8cbb0844-050e-11e8-805b-a119faa7b55c","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8cbb0844-050e-11e8-805b-a119faa7b55c","fullStatement":"Students should be able to understand and explain that the sum and product of a rational number and a nonzero irrational number are irrational.","CFItemType":"Range ALD","CFItemTypeURI":{"title":"Range ALD","identifier":"4c380133-6f2b-4606-9a4d-aa87b9980467","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/4c380133-6f2b-4606-9a4d-aa87b9980467"},"abbreviatedStatement":"Level 3","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:18:28+00:00"},{"identifier":"8cbb2432-050e-11e8-9009-9fc2768037d5","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8cbb2432-050e-11e8-9009-9fc2768037d5","fullStatement":"Students should be able to provide a specific example given a generalization statement, such as the sum of a rational number and an irrational number is irrational.","CFItemType":"Range ALD","CFItemTypeURI":{"title":"Range ALD","identifier":"4c380133-6f2b-4606-9a4d-aa87b9980467","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/4c380133-6f2b-4606-9a4d-aa87b9980467"},"abbreviatedStatement":"Level 4","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:18:41+00:00"},{"identifier":"8cbb888c-050e-11e8-8e96-dd7a83e61ac1","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8cbb888c-050e-11e8-8e96-dd7a83e61ac1","fullStatement":"The student provides examples of addition or multiplication problems that will have sums or products of a specified type (rational or irrational).","CFItemType":"Evidence Required","CFItemTypeURI":{"title":"Evidence Required","identifier":"62ae8acf-e478-4213-a2d2-aebec5b898df","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/62ae8acf-e478-4213-a2d2-aebec5b898df"},"abbreviatedStatement":"Evidence Required 1","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-02-16T15:01:47+00:00"},{"identifier":"8cbb411a-050e-11e8-b608-3d4f4945480f","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8cbb411a-050e-11e8-b608-3d4f4945480f","fullStatement":"Evidence Required","CFItemType":"Evidence Required","CFItemTypeURI":{"title":"Evidence Required","identifier":"62ae8acf-e478-4213-a2d2-aebec5b898df","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/62ae8acf-e478-4213-a2d2-aebec5b898df"},"educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:07:48+00:00"},{"identifier":"8cbbb942-050e-11e8-909f-d3550c42921d","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8cbbb942-050e-11e8-909f-d3550c42921d","fullStatement":"The student determines whether the sum of two numbers is a rational number or an irrational number.","CFItemType":"Evidence Required","CFItemTypeURI":{"title":"Evidence Required","identifier":"62ae8acf-e478-4213-a2d2-aebec5b898df","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/62ae8acf-e478-4213-a2d2-aebec5b898df"},"abbreviatedStatement":"Evidence Required 2","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:19:06+00:00"},{"identifier":"8cbbe912-050e-11e8-81b0-e537c0860e10","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8cbbe912-050e-11e8-81b0-e537c0860e10","fullStatement":"The student determines whether the product of two numbers is a rational number or an irrational number.","CFItemType":"Evidence Required","CFItemTypeURI":{"title":"Evidence Required","identifier":"62ae8acf-e478-4213-a2d2-aebec5b898df","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/62ae8acf-e478-4213-a2d2-aebec5b898df"},"abbreviatedStatement":"Evidence Required 3","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:19:14+00:00"},{"identifier":"8cbc370a-050e-11e8-bdd7-53d95518ea9b","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8cbc370a-050e-11e8-bdd7-53d95518ea9b","fullStatement":"The student provides an abstract generalization that the sum or product of any two rational numbers is rational, the sum of a rational number and an irrational number is irrational, and the product of a nonzero rational number and an irrational number is irrational.","CFItemType":"Evidence Required","CFItemTypeURI":{"title":"Evidence Required","identifier":"62ae8acf-e478-4213-a2d2-aebec5b898df","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/62ae8acf-e478-4213-a2d2-aebec5b898df"},"abbreviatedStatement":"Evidence Required 4","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:19:35+00:00"},{"identifier":"8cbd1a08-050e-11e8-b8f5-c9286a4a14ad","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8cbd1a08-050e-11e8-b8f5-c9286a4a14ad","fullStatement":"rational number, irrational number, real number","CFItemType":"General Requirements","CFItemTypeURI":{"title":"General Requirements","identifier":"a2c9fb5b-56f1-4d92-af37-4edbbfcce40f","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/a2c9fb5b-56f1-4d92-af37-4edbbfcce40f"},"abbreviatedStatement":"Key/Construct Relevant Vocabulary","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:20:00+00:00"},{"identifier":"8cbccd82-050e-11e8-8a60-31e21f39fba2","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8cbccd82-050e-11e8-8a60-31e21f39fba2","fullStatement":"General Item Information","CFItemType":"General Requirements","CFItemTypeURI":{"title":"General Requirements","identifier":"a2c9fb5b-56f1-4d92-af37-4edbbfcce40f","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/a2c9fb5b-56f1-4d92-af37-4edbbfcce40f"},"educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:07:48+00:00"},{"identifier":"8cbd3740-050e-11e8-acd6-b51d36b9a9c3","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8cbd3740-050e-11e8-acd6-b51d36b9a9c3","fullStatement":"None","CFItemType":"General Requirements","CFItemTypeURI":{"title":"General Requirements","identifier":"a2c9fb5b-56f1-4d92-af37-4edbbfcce40f","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/a2c9fb5b-56f1-4d92-af37-4edbbfcce40f"},"abbreviatedStatement":"Allowable Tools","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:08:04+00:00"},{"identifier":"8cbd52d4-050e-11e8-998e-5700d725829c","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8cbd52d4-050e-11e8-998e-5700d725829c","fullStatement":"Only sums and products of two numbers are used.","CFItemType":"General Requirements","CFItemTypeURI":{"title":"General Requirements","identifier":"a2c9fb5b-56f1-4d92-af37-4edbbfcce40f","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/a2c9fb5b-56f1-4d92-af37-4edbbfcce40f"},"abbreviatedStatement":"Target-Specific Attributes","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:20:27+00:00"},{"identifier":"8cbd6f1c-050e-11e8-afcd-f9106094439b","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8cbd6f1c-050e-11e8-afcd-f9106094439b","fullStatement":"None","CFItemType":"General Requirements","CFItemTypeURI":{"title":"General Requirements","identifier":"a2c9fb5b-56f1-4d92-af37-4edbbfcce40f","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/a2c9fb5b-56f1-4d92-af37-4edbbfcce40f"},"abbreviatedStatement":"Non-Target Constructs","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:08:04+00:00"},{"identifier":"8cbd8b50-050e-11e8-8cc9-d999bdc66944","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8cbd8b50-050e-11e8-8cc9-d999bdc66944","fullStatement":"None","CFItemType":"General Requirements","CFItemTypeURI":{"title":"General Requirements","identifier":"a2c9fb5b-56f1-4d92-af37-4edbbfcce40f","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/a2c9fb5b-56f1-4d92-af37-4edbbfcce40f"},"abbreviatedStatement":"Development Notes","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:08:04+00:00"},{"identifier":"8cbda78e-050e-11e8-90f7-c346311acd55","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8cbda78e-050e-11e8-90f7-c346311acd55","fullStatement":"products or sums of rational and irrational numbers, number type (rational or irrational)","CFItemType":"General Requirements","CFItemTypeURI":{"title":"General Requirements","identifier":"a2c9fb5b-56f1-4d92-af37-4edbbfcce40f","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/a2c9fb5b-56f1-4d92-af37-4edbbfcce40f"},"abbreviatedStatement":"Allowable Stimulus Materials","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:19:49+00:00"},{"identifier":"8cbdc340-050e-11e8-b59f-05c1539a1640","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8cbdc340-050e-11e8-b59f-05c1539a1640","fullStatement":"Item writers should consider the following Language and Visual Element/Design guidelines [1] when developing items.\r\n\r\nLanguage Key Considerations:\r\n\r\n- Use simple, clear, and easy-to-understand language needed to assess the construct or aid in the understanding of the context\r\n\r\n- Avoid sentences with multiple clauses\r\n\r\n- Use vocabulary that is at or below grade level\r\n\r\n- Avoid ambiguous or obscure words, idioms, jargon, unusual names and references\r\n\r\nVisual Elements/Design Key Considerations:\r\n\r\n- Include visual elements only if the graphic is needed to assess the construct or it aids in the understanding of the context\r\n\r\n- Use the simplest graphic possible with the greatest degree of contrast, and include clear, concise labels where necessary\r\n\r\n- Avoid crowding of details and graphics\r\n\r\nItems are selected for a student\u2019s test according to the blueprint, which selects items based on Claims and targets, not task models.\r\n\r\nAs such, careful consideration is given to making sure fully accessible items are available to cover the content of every Claim and target, even if some item formats are not fully accessible using current technology.[2]\r\n\r\n[1] For more information, refer to the General Accessibility Guidelines at [https://portal.smarterbalanced.org/library/en/general-accessibility-guidelines.pdf](https://portal.smarterbalanced.org/library/en/general-accessibility-guidelines.pdf) \r\n\r\n[2] For more information about student accessibility resources and policies,\r\nrefer to [https://portal.smarterbalanced.org/library/en/usability-accessibility-and-accommodations-guidelines.pdf](https://portal.smarterbalanced.org/library/en/usability-accessibility-and-accommodations-guidelines.pdf)","CFItemType":"Accessibility","CFItemTypeURI":{"title":"Accessibility","identifier":"d19c9ae0-bfe0-11e7-bff4-050398278f5a","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/d19c9ae0-bfe0-11e7-bff4-050398278f5a"},"abbreviatedStatement":"Accessibility Concerns/Guidance","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-02-21T17:11:53+00:00"},{"identifier":"8de69d96-050e-11e8-885f-1fe6e53a4f65","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de69d96-050e-11e8-885f-1fe6e53a4f65","fullStatement":"Task Models","CFItemType":"Task Model","CFItemTypeURI":{"title":"Task Model","identifier":"f66a54af-9e35-46d4-8ba6-66606c888f6c","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/f66a54af-9e35-46d4-8ba6-66606c888f6c"},"educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:17:43+00:00"},{"identifier":"8de771da-050e-11e8-883b-35f359c7feb4","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de771da-050e-11e8-883b-35f359c7feb4","fullStatement":"**Prompt Features:** The student gives an example of either an addition or multiplication problem with either a rational or irrational product or sum.\r\n\r\n**Stimulus Guidelines:**\r\n\r\n- Four or more numbers are given, of which\r\n\r\n - two are rational numbers and\r\n\r\n - two are irrational numbers.\r\n\r\n- The irrational numbers can be $\\pi$ or of the form $a\\sqrt[n]{b}$ where:\r\n\r\n - $a$ is rational;\r\n\r\n - $b$ is an integer such that\r\n\r\n - $b$ is positive when $n$ is even, and\r\n\r\n - $b$ may be negative when $n$ is odd; and\r\n\r\n - $n$ is a whole number such that $\\ 2 \\leq n \\leq 9$.\r\n\r\n- Item difficulty can be adjusted via these example methods, but are not limited to these methods:\r\n\r\n - radicands lead to roots that do or do not simplify to rational numbers\r\n\r\n - sum/product of the radicands does or does not lead to roots that simplify to a rational number\r\n\r\n - integer or fraction coefficients may be added in front of the radicals\r\n\r\n - radicands can be whole numbers or fractions","CFItemType":"Task Description","CFItemTypeURI":{"title":"Task Description","identifier":"b0804d18-bb65-11e7-98c9-83def7a9dccd","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/b0804d18-bb65-11e7-98c9-83def7a9dccd"},"abbreviatedStatement":"Task Description","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-02-16T15:02:43+00:00"},{"identifier":"8de731ac-050e-11e8-a4a3-7dde2d414a35","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de731ac-050e-11e8-a4a3-7dde2d414a35","fullStatement":"Task Model 1","CFItemType":"Task Model","CFItemTypeURI":{"title":"Task Model","identifier":"f66a54af-9e35-46d4-8ba6-66606c888f6c","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/f66a54af-9e35-46d4-8ba6-66606c888f6c"},"educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:08:34+00:00"},{"identifier":"8de78e22-050e-11e8-b3a3-97aa7988c3ce","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de78e22-050e-11e8-b3a3-97aa7988c3ce","fullStatement":"Examples","CFItemType":"Example","CFItemTypeURI":{"title":"Example","identifier":"c685d17c-bb66-11e7-b6af-3f99116007d0","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/c685d17c-bb66-11e7-b6af-3f99116007d0"},"educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:10:34+00:00"},{"identifier":"8de7b42e-050e-11e8-b1e2-99f2b0946e25","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de7b42e-050e-11e8-b1e2-99f2b0946e25","fullStatement":"**Example Stem 1:** Click on **two** numbers whose sum, when added, would be **irrational**.\r\n\r\n| **Numbers** | \\-5 | 3$\\sqrt{2}$ | $\\frac{2}{3}$ | $\\frac{1}{3}$ | $\\sqrt{8}$ |\r\n|-------------|-----|------------|--------------|--------------|-----------|\r\n\r\n
\r\n\r\n**Rubric:**\r\n\r\n(1 point) The student selects two numbers that satisfy the given conditions. Multiple correct responses are possible and will all need to be included in the scoring rubric. Only example responses are shown below.\r\n\r\nExample Stem 1:\r\n\r\n![Formatted Table](https://images.smarterbalanced.org/content/Documents/Item%20Specs/Math_Item_Specs/Claim1_mathematics_HS_specs/HS_1B_NQ_Spec_V3_phase3_files/TM1E1.png)","CFItemType":"Example","CFItemTypeURI":{"title":"Example","identifier":"c685d17c-bb66-11e7-b6af-3f99116007d0","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/c685d17c-bb66-11e7-b6af-3f99116007d0"},"abbreviatedStatement":"Example 1","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-02-09T14:49:04+00:00"},{"identifier":"8de7cff4-050e-11e8-872a-016d6b97ec80","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de7cff4-050e-11e8-872a-016d6b97ec80","fullStatement":"NA","CFItemType":"Accessibility","CFItemTypeURI":{"title":"Accessibility","identifier":"d19c9ae0-bfe0-11e7-bff4-050398278f5a","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/d19c9ae0-bfe0-11e7-bff4-050398278f5a"},"abbreviatedStatement":"Accessibility Note","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:10:34+00:00"},{"identifier":"8de7e912-050e-11e8-a230-f30602d7cca6","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de7e912-050e-11e8-a230-f30602d7cca6","fullStatement":"None","CFItemType":"Allowable Tools","CFItemTypeURI":{"title":"Allowable Tools","identifier":"3e2514d0-fef2-11e7-817c-13e80b100709","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/3e2514d0-fef2-11e7-817c-13e80b100709"},"abbreviatedStatement":"Allowable Tools","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:10:34+00:00"},{"identifier":"8de802b2-050e-11e8-9adc-f566c4497838","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de802b2-050e-11e8-9adc-f566c4497838","fullStatement":"The student is presented with rational and irrational numbers.","CFItemType":"Stimulus","CFItemTypeURI":{"title":"Stimulus","identifier":"1e025133-1d58-4123-9818-22035889162b","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/1e025133-1d58-4123-9818-22035889162b"},"abbreviatedStatement":"Stimulus","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:23:45+00:00"},{"identifier":"8de85b9a-050e-11e8-95e5-c12bd194af13","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de85b9a-050e-11e8-95e5-c12bd194af13","fullStatement":"**Prompt Features:** The student is presented with a list of expressions that contain the sums of rational and/or irrational numbers.\r\n\r\n**Stimulus Guidelines:**\r\n\r\n- Answer choices include 5 or 6 sums.\r\n\r\n- Irrational numbers can be $\\pi$ or of the form $a\\sqrt[n]{b}$ where:\r\n\r\n - $a$ is rational;\r\n\r\n - $b$ is an integer such that\r\n\r\n - $b$ is positive when $n$ is even, and\r\n\r\n - $b$ may be negative when $n$ is odd; and\r\n\r\n - $n$ is a whole number such that $\\ 2 \\leq n \\leq 9$.\r\n\r\n- Item difficulty can be adjusted via these example methods, but is not limited to these methods:\r\n\r\n - radicands lead to roots that do/do not simplify to rational numbers\r\n\r\n - sum/product of the radicands does/does not lead to roots that simplify to a rational number\r\n\r\n - integer or fraction coefficients may be added in front of the radicands\r\n\r\n - radicands can be whole numbers or fractions","CFItemType":"Task Description","CFItemTypeURI":{"title":"Task Description","identifier":"b0804d18-bb65-11e7-98c9-83def7a9dccd","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/b0804d18-bb65-11e7-98c9-83def7a9dccd"},"abbreviatedStatement":"Task Description","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:36:20+00:00"},{"identifier":"8de81c70-050e-11e8-aab3-8509a043cec7","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de81c70-050e-11e8-aab3-8509a043cec7","fullStatement":"Task Model 2a","CFItemType":"Task Model","CFItemTypeURI":{"title":"Task Model","identifier":"f66a54af-9e35-46d4-8ba6-66606c888f6c","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/f66a54af-9e35-46d4-8ba6-66606c888f6c"},"educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:08:40+00:00"},{"identifier":"8de8792c-050e-11e8-9afd-f74a65b27eac","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de8792c-050e-11e8-9afd-f74a65b27eac","fullStatement":"Examples","CFItemType":"Example","CFItemTypeURI":{"title":"Example","identifier":"c685d17c-bb66-11e7-b6af-3f99116007d0","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/c685d17c-bb66-11e7-b6af-3f99116007d0"},"abbreviatedStatement":"Examples","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:36:20+00:00"},{"identifier":"8de89e20-050e-11e8-ac83-9dd00cfac17b","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de89e20-050e-11e8-ac83-9dd00cfac17b","fullStatement":"**Example Stem:** Select the appropriate box to identify each expression as having either a rational or irrational sum.\r\n\r\n| | **Rational** | **Irrational** |\r\n|----------------------------------------|--------------|----------------|\r\n| $5\\sqrt{7}\\ + \\frac{1}{7}$ | | |\r\n| $\\sqrt{4} + 17$ | | |\r\n| $12.4 + ( - 11)$ | | |\r\n| $- \\frac{4}{5}$ +($- 10\\sqrt{10})$ | | |\r\n\r\n**Rubric:** (1 Point) The student correctly identifies the sum as rational or irrational (e.g., Irrational, Rational, Rational, Irrational).","CFItemType":"Example","CFItemTypeURI":{"title":"Example","identifier":"c685d17c-bb66-11e7-b6af-3f99116007d0","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/c685d17c-bb66-11e7-b6af-3f99116007d0"},"abbreviatedStatement":"Example 1","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:36:56+00:00"},{"identifier":"8de8b9be-050e-11e8-a66d-f513641f4b8b","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de8b9be-050e-11e8-a66d-f513641f4b8b","fullStatement":"NA","CFItemType":"Accessibility","CFItemTypeURI":{"title":"Accessibility","identifier":"d19c9ae0-bfe0-11e7-bff4-050398278f5a","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/d19c9ae0-bfe0-11e7-bff4-050398278f5a"},"abbreviatedStatement":"Accessibility Note","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:36:20+00:00"},{"identifier":"8de8d296-050e-11e8-a699-d5b6787371bc","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de8d296-050e-11e8-a699-d5b6787371bc","fullStatement":"The student is presented with a list of expressions that contain the sums of rational and/or irrational numbers.","CFItemType":"Stimulus","CFItemTypeURI":{"title":"Stimulus","identifier":"1e025133-1d58-4123-9818-22035889162b","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/1e025133-1d58-4123-9818-22035889162b"},"abbreviatedStatement":"Stimulus","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:36:20+00:00"},{"identifier":"8de8eccc-050e-11e8-a227-43130db7e3bf","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de8eccc-050e-11e8-a227-43130db7e3bf","fullStatement":"None","CFItemType":"Allowable Tools","CFItemTypeURI":{"title":"Allowable Tools","identifier":"3e2514d0-fef2-11e7-817c-13e80b100709","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/3e2514d0-fef2-11e7-817c-13e80b100709"},"abbreviatedStatement":"Allowable Tools","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:36:20+00:00"},{"identifier":"8de9478a-050e-11e8-9ec3-47d2fd675f90","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de9478a-050e-11e8-9ec3-47d2fd675f90","fullStatement":"**Prompt Features:** The student is presented with a list of expressions that contain the sums of rational and/or irrational numbers.\r\n\r\n**Stimulus Guidelines:**\r\n\r\n- Answer choices include 5 or 6 sums.\r\n\r\n- Irrational numbers can be $\\pi$ or of the form $a\\sqrt[n]{b}$ where:\r\n\r\n - $a$ is rational;\r\n\r\n - $b$ is an integer such that\r\n\r\n - $b$ is positive when $n$ is even, and\r\n\r\n - $b$ may be negative when $n$ is odd; and\r\n\r\n - $n$ is a whole number such that $\\ 2 \\leq n \\leq 9$.\r\n\r\n- Item difficulty can be adjusted via these example methods, but is not limited to these methods:\r\n\r\n - radicands lead to roots that do/do not simplify to rational numbers\r\n\r\n - sum/product of the radicands does/does not lead to roots that simplify to a rational number\r\n\r\n - integer or fraction coefficients may be added in front of the radicands\r\n\r\n - radicands can be whole numbers or fractions","CFItemType":"Task Description","CFItemTypeURI":{"title":"Task Description","identifier":"b0804d18-bb65-11e7-98c9-83def7a9dccd","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/b0804d18-bb65-11e7-98c9-83def7a9dccd"},"abbreviatedStatement":"Task Description","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:38:03+00:00"},{"identifier":"8de90784-050e-11e8-bd20-91da1839c5ba","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de90784-050e-11e8-bd20-91da1839c5ba","fullStatement":"Task Model 2b","CFItemType":"Task Model","CFItemTypeURI":{"title":"Task Model","identifier":"f66a54af-9e35-46d4-8ba6-66606c888f6c","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/f66a54af-9e35-46d4-8ba6-66606c888f6c"},"educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:08:47+00:00"},{"identifier":"8de96346-050e-11e8-9deb-21581a4cfa18","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de96346-050e-11e8-9deb-21581a4cfa18","fullStatement":"Examples","CFItemType":"Example","CFItemTypeURI":{"title":"Example","identifier":"c685d17c-bb66-11e7-b6af-3f99116007d0","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/c685d17c-bb66-11e7-b6af-3f99116007d0"},"educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:10:42+00:00"},{"identifier":"8de988d0-050e-11e8-96e4-3f34473dd67d","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de988d0-050e-11e8-96e4-3f34473dd67d","fullStatement":"**Example Stem:** Select each box in the table where the numbers from corresponding rows and columns will have a **rational** sum.\r\n\r\n[Problems with Latex in table.]\r\n\r\n| | $~~~~\\large4~~~~$ | $~~~\\Large\\frac{1}{3}~~~$ | $~~\\large\\sqrt{3}~~$ | $~~~\\large\\pi~~~~$ |\r\n|:----------------------------------:|:-------:|:----------------------------------:|:---------------------:|:----------------:|\r\n| $~~~~~\\large4~~~~~$ | | | | |\r\n|$\\Large\\frac{1}{3}$ | | | | |\r\n| $\\large\\sqrt{3}$ | | | | |\r\n| $\\large\\pi$ | | | | |\r\n\r\n
\r\n\r\n**Rubric:** (1 Point) The student correctly identifies the sum as rational or irrational (e.g., see below).\r\n\r\n![Formatted Table](https://images.smarterbalanced.org/content/Documents/Item%20Specs/Math_Item_Specs/Claim1_mathematics_HS_specs/HS_1B_NQ_Spec_V3_phase3_files/TM2B.png)","CFItemType":"Example","CFItemTypeURI":{"title":"Example","identifier":"c685d17c-bb66-11e7-b6af-3f99116007d0","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/c685d17c-bb66-11e7-b6af-3f99116007d0"},"abbreviatedStatement":"Example 1","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-02-09T14:50:31+00:00"},{"identifier":"8de9a4b4-050e-11e8-a91a-533e0e0880ea","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de9a4b4-050e-11e8-a91a-533e0e0880ea","fullStatement":"NA","CFItemType":"Accessibility","CFItemTypeURI":{"title":"Accessibility","identifier":"d19c9ae0-bfe0-11e7-bff4-050398278f5a","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/d19c9ae0-bfe0-11e7-bff4-050398278f5a"},"abbreviatedStatement":"Accessibility Note","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:10:42+00:00"},{"identifier":"8de9c17e-050e-11e8-876e-1981a854e622","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de9c17e-050e-11e8-876e-1981a854e622","fullStatement":"None","CFItemType":"Allowable Tools","CFItemTypeURI":{"title":"Allowable Tools","identifier":"3e2514d0-fef2-11e7-817c-13e80b100709","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/3e2514d0-fef2-11e7-817c-13e80b100709"},"abbreviatedStatement":"Allowable Tools","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:10:42+00:00"},{"identifier":"8de9dea2-050e-11e8-a168-f14705d0d8a2","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de9dea2-050e-11e8-a168-f14705d0d8a2","fullStatement":"The student is presented with a table of numbers.","CFItemType":"Stimulus","CFItemTypeURI":{"title":"Stimulus","identifier":"1e025133-1d58-4123-9818-22035889162b","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/1e025133-1d58-4123-9818-22035889162b"},"abbreviatedStatement":"Stimulus","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:38:17+00:00"},{"identifier":"8dea3ba4-050e-11e8-9c0a-fd66bd3fb9ef","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8dea3ba4-050e-11e8-9c0a-fd66bd3fb9ef","fullStatement":"**Prompt Features:** The student is prompted to identify products as rational or irrational.\r\n\r\n**Stimulus Guidelines:**\r\n\r\n- The irrational numbers can be $\\pi$ or of the form $a\\sqrt[n]{b}$ where:\r\n\r\n - $a$ is rational;\r\n\r\n - $b$ is an integer such that\r\n\r\n - $b$ is positive when $n$ is even, and\r\n\r\n - $b$ may be negative when $n$ is odd; and\r\n\r\n - $n$ is a whole number such that $\\ 2 \\leq n \\leq 9$.\r\n\r\n- Item difficulty can be adjusted via these example methods, but is not limited to these methods:\r\n\r\n - radicands lead to roots that do/do not simplify to rational numbers\r\n\r\n - sum/product of the radicands does/does not lead to roots that simplify to a rational number\r\n\r\n - integer or fraction coefficients may be added in front of the radicands\r\n\r\n - radicands can be whole numbers or fractions","CFItemType":"Task Description","CFItemTypeURI":{"title":"Task Description","identifier":"b0804d18-bb65-11e7-98c9-83def7a9dccd","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/b0804d18-bb65-11e7-98c9-83def7a9dccd"},"abbreviatedStatement":"Task Description","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:44:55+00:00"},{"identifier":"8de9f978-050e-11e8-8996-03ea99197a28","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8de9f978-050e-11e8-8996-03ea99197a28","fullStatement":"Task Model 3a","CFItemType":"Task Model","CFItemTypeURI":{"title":"Task Model","identifier":"f66a54af-9e35-46d4-8ba6-66606c888f6c","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/f66a54af-9e35-46d4-8ba6-66606c888f6c"},"educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:09:01+00:00"},{"identifier":"8dea597c-050e-11e8-bafd-61386a04181e","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8dea597c-050e-11e8-bafd-61386a04181e","fullStatement":"Examples","CFItemType":"Example","CFItemTypeURI":{"title":"Example","identifier":"c685d17c-bb66-11e7-b6af-3f99116007d0","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/c685d17c-bb66-11e7-b6af-3f99116007d0"},"educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:10:46+00:00"},{"identifier":"8dea8910-050e-11e8-94a2-77938b624bbc","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8dea8910-050e-11e8-94a2-77938b624bbc","fullStatement":"**Example Stem:** Select the appropriate box to identify each expression as having either a rational or irrational product.\r\n\r\n| | **Rational** | **Irrational** |\r\n|---------------------------------------------------------|--------------|----------------|\r\n| $5\\sqrt{7}\\ \\bullet \\frac{1}{7}$ | | |\r\n| $\\sqrt{4} \\bullet 17$ | | |\r\n| $12.4 \\bullet ( - 11)$ | | |\r\n| $- \\frac{4}{5} \\bullet ( - 10\\sqrt{10})\\text{\\ \\ \\ }$ | | |\r\n\r\n**Rubric:** (1 Point) The student correctly identifies the product as rational or irrational (e.g., Irrational, Rational, Rational, Irrational).","CFItemType":"Example","CFItemTypeURI":{"title":"Example","identifier":"c685d17c-bb66-11e7-b6af-3f99116007d0","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/c685d17c-bb66-11e7-b6af-3f99116007d0"},"abbreviatedStatement":"Example 1","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:46:12+00:00"},{"identifier":"8deaa94a-050e-11e8-9f47-a95c242ef0ef","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8deaa94a-050e-11e8-9f47-a95c242ef0ef","fullStatement":"NA","CFItemType":"Accessibility","CFItemTypeURI":{"title":"Accessibility","identifier":"d19c9ae0-bfe0-11e7-bff4-050398278f5a","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/d19c9ae0-bfe0-11e7-bff4-050398278f5a"},"abbreviatedStatement":"Accessibility Note","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:10:46+00:00"},{"identifier":"8deac97a-050e-11e8-b01c-e5c8e49240a3","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8deac97a-050e-11e8-b01c-e5c8e49240a3","fullStatement":"None","CFItemType":"Allowable Tools","CFItemTypeURI":{"title":"Allowable Tools","identifier":"3e2514d0-fef2-11e7-817c-13e80b100709","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/3e2514d0-fef2-11e7-817c-13e80b100709"},"abbreviatedStatement":"Allowable Tools","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:10:46+00:00"},{"identifier":"8deae694-050e-11e8-b737-7dbcc3fe8bcb","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8deae694-050e-11e8-b737-7dbcc3fe8bcb","fullStatement":"The student is presented with a list of expressions that contain the product of rational and/or irrational numbers.","CFItemType":"Stimulus","CFItemTypeURI":{"title":"Stimulus","identifier":"1e025133-1d58-4123-9818-22035889162b","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/1e025133-1d58-4123-9818-22035889162b"},"abbreviatedStatement":"Stimulus","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:45:08+00:00"},{"identifier":"8deb4634-050e-11e8-b919-43c1c41118e5","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8deb4634-050e-11e8-b919-43c1c41118e5","fullStatement":"**Prompt Features:** The student is prompted to identify products as rational or irrational.\r\n\r\n**Stimulus Guidelines:**\r\n\r\n- The irrational numbers can be $\\pi$ or of the form $a\\sqrt[n]{b}$ where:\r\n\r\n - $a$ is rational;\r\n\r\n - $b$ is an integer such that\r\n\r\n - $b$ is positive when $n$ is even, and\r\n\r\n - $b$ may be negative when $n$ is odd; and\r\n\r\n - $n$ is a whole number such that $\\ 2 \\leq n \\leq 9$.\r\n\r\n- Item difficulty can be adjusted via these example methods, but is not limited to these methods:\r\n\r\n - radicands lead to roots that do/do not simplify to rational numbers\r\n\r\n - sum/product of the radicands does/does not lead to roots that simplify to a rational number\r\n\r\n - integer or fraction coefficients may be added in front of the radicands\r\n\r\n - radicands can be whole numbers or fractions","CFItemType":"Task Description","CFItemTypeURI":{"title":"Task Description","identifier":"b0804d18-bb65-11e7-98c9-83def7a9dccd","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/b0804d18-bb65-11e7-98c9-83def7a9dccd"},"abbreviatedStatement":"Task Description","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:47:52+00:00"},{"identifier":"8deb046c-050e-11e8-8aaa-1dc5c44c3248","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8deb046c-050e-11e8-8aaa-1dc5c44c3248","fullStatement":"Task Model 3b","CFItemType":"Task Model","CFItemTypeURI":{"title":"Task Model","identifier":"f66a54af-9e35-46d4-8ba6-66606c888f6c","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/f66a54af-9e35-46d4-8ba6-66606c888f6c"},"educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:09:06+00:00"},{"identifier":"8deb639e-050e-11e8-ad13-db883aefc5ea","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8deb639e-050e-11e8-ad13-db883aefc5ea","fullStatement":"Examples","CFItemType":"Example","CFItemTypeURI":{"title":"Example","identifier":"c685d17c-bb66-11e7-b6af-3f99116007d0","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/c685d17c-bb66-11e7-b6af-3f99116007d0"},"abbreviatedStatement":"Examples","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:10:49+00:00"},{"identifier":"8deb92f6-050e-11e8-ad67-95e3c58f52b5","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8deb92f6-050e-11e8-ad67-95e3c58f52b5","fullStatement":"**Example Stem:** Select each box in the table where the numbers from corresponding rows and columns will have a rational product.\r\n\r\n\r\n| | $~~~\\large4~~~$ | $~~~\\Large\\frac{1}{3}~~~$ | $~~~\\sqrt{3}~~~$ | $~~~-\\sqrt{3}~~~$ |\r\n|:----------------------------------:|:-------:|:----------------------------------:|:---------------------:|:--------------------------------:|\r\n| $~~~~~~~~\\large4~~~~~~~~$ | | | | |\r\n| $\\Large\\frac{1}{3}$| | | | |\r\n| $\\sqrt{3}$ | | | | |\r\n| $-\\sqrt{3}$ | | | | |\r\n\r\n
\r\n\r\n
\r\n\r\n**Rubric:** (1 Point) The student correctly identifies the product as rational or irrational (e.g., see below).\r\n\r\n![Formatted Table](https://images.smarterbalanced.org/content/Documents/Item%20Specs/Math_Item_Specs/Claim1_mathematics_HS_specs/HS_1B_NQ_Spec_V3_phase3_files/TM3B.png)","CFItemType":"Example","CFItemTypeURI":{"title":"Example","identifier":"c685d17c-bb66-11e7-b6af-3f99116007d0","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/c685d17c-bb66-11e7-b6af-3f99116007d0"},"abbreviatedStatement":"Example 1","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-03-27T14:41:07+00:00"},{"identifier":"8debcd84-050e-11e8-9191-9fa578c73fb8","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8debcd84-050e-11e8-9191-9fa578c73fb8","fullStatement":"NA","CFItemType":"Accessibility","CFItemTypeURI":{"title":"Accessibility","identifier":"d19c9ae0-bfe0-11e7-bff4-050398278f5a","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/d19c9ae0-bfe0-11e7-bff4-050398278f5a"},"abbreviatedStatement":"Accessibility Note","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:10:49+00:00"},{"identifier":"8debe92c-050e-11e8-b561-39edf9f82049","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8debe92c-050e-11e8-b561-39edf9f82049","fullStatement":"None","CFItemType":"Allowable Tools","CFItemTypeURI":{"title":"Allowable Tools","identifier":"3e2514d0-fef2-11e7-817c-13e80b100709","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/3e2514d0-fef2-11e7-817c-13e80b100709"},"abbreviatedStatement":"Allowable Tools","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:10:49+00:00"},{"identifier":"8dec0588-050e-11e8-aeed-817bcee2265e","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8dec0588-050e-11e8-aeed-817bcee2265e","fullStatement":"The student is presented with a table of numbers.","CFItemType":"Stimulus","CFItemTypeURI":{"title":"Stimulus","identifier":"1e025133-1d58-4123-9818-22035889162b","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/1e025133-1d58-4123-9818-22035889162b"},"abbreviatedStatement":"Stimulus","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:48:03+00:00"},{"identifier":"8dec65fa-050e-11e8-bd23-373f4368328e","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8dec65fa-050e-11e8-bd23-373f4368328e","fullStatement":"**Prompt Features:** Identify which factors would result in a rational product when multiplied by a given a rational or irrational number.\r\n\r\n**Stimulus Guidelines**:\r\n\r\n- The irrational numbers can be $\\pi$ or of the form $a\\sqrt[n]{b}$ where:\r\n\r\n - $a$ is rational;\r\n\r\n - $b$ is an integer such that\r\n\r\n - $b$ is positive when $n$ is even, and\r\n\r\n - $b$ may be negative when $n$ is odd; and\r\n\r\n - $n$ is a whole number such that $\\ 2 \\leq n \\leq 9$.\r\n\r\n- Item difficulty can be adjusted via these example methods, but is not limited to these methods:\r\n\r\n - radicands lead to roots that do/do not simplify to rational numbers\r\n\r\n - sum/product of the radicands does/does not lead to roots that simplify to a rational number\r\n\r\n - integer or fraction coefficients may be added in front of the radicands\r\n\r\n - radicands can be whole numbers or fractions","CFItemType":"Task Description","CFItemTypeURI":{"title":"Task Description","identifier":"b0804d18-bb65-11e7-98c9-83def7a9dccd","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/b0804d18-bb65-11e7-98c9-83def7a9dccd"},"abbreviatedStatement":"Task Description","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-03-27T14:42:11+00:00"},{"identifier":"8dec2392-050e-11e8-9fe3-ad44347fd685","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8dec2392-050e-11e8-9fe3-ad44347fd685","fullStatement":"Task Model 3c","CFItemType":"Task Model","CFItemTypeURI":{"title":"Task Model","identifier":"f66a54af-9e35-46d4-8ba6-66606c888f6c","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/f66a54af-9e35-46d4-8ba6-66606c888f6c"},"educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:09:12+00:00"},{"identifier":"8dec8472-050e-11e8-bb20-1b6aed48e1fc","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8dec8472-050e-11e8-bb20-1b6aed48e1fc","fullStatement":"Examples","CFItemType":"Example","CFItemTypeURI":{"title":"Example","identifier":"c685d17c-bb66-11e7-b6af-3f99116007d0","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/c685d17c-bb66-11e7-b6af-3f99116007d0"},"abbreviatedStatement":"Examples","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:10:53+00:00"},{"identifier":"8decb4f6-050e-11e8-b4e4-a36159aa51b7","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8decb4f6-050e-11e8-b4e4-a36159aa51b7","fullStatement":"**Example Stem:** Select **all** numbers that will produce a **rational** number when multiplied by $7\\sqrt{5}$.\r\n\r\nA. $- \\frac{1}{5}$\r\n\r\nB. $7\\sqrt{125}$\r\n\r\nC. $5 + \\sqrt{5}$\r\n\r\nD. $3\\sqrt{\\frac{9}{5}}$\r\n\r\n**Rubric:** (1 point) The student correctly identifies the products as rational (e.g., B, D).","CFItemType":"Example","CFItemTypeURI":{"title":"Example","identifier":"c685d17c-bb66-11e7-b6af-3f99116007d0","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/c685d17c-bb66-11e7-b6af-3f99116007d0"},"abbreviatedStatement":"Example 1","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:52:00+00:00"},{"identifier":"8decef20-050e-11e8-a490-f5094ca47584","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8decef20-050e-11e8-a490-f5094ca47584","fullStatement":"NA","CFItemType":"Accessibility","CFItemTypeURI":{"title":"Accessibility","identifier":"d19c9ae0-bfe0-11e7-bff4-050398278f5a","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/d19c9ae0-bfe0-11e7-bff4-050398278f5a"},"abbreviatedStatement":"Accessibility Note","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:10:53+00:00"},{"identifier":"8ded0b9a-050e-11e8-948d-351e91bbee32","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8ded0b9a-050e-11e8-948d-351e91bbee32","fullStatement":"None","CFItemType":"Allowable Tools","CFItemTypeURI":{"title":"Allowable Tools","identifier":"3e2514d0-fef2-11e7-817c-13e80b100709","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/3e2514d0-fef2-11e7-817c-13e80b100709"},"abbreviatedStatement":"Allowable Tools","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:10:53+00:00"},{"identifier":"8ded281e-050e-11e8-86c9-5be0be0ba656","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8ded281e-050e-11e8-86c9-5be0be0ba656","fullStatement":"The student is presented with a rational or irrational number.","CFItemType":"Stimulus","CFItemTypeURI":{"title":"Stimulus","identifier":"1e025133-1d58-4123-9818-22035889162b","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/1e025133-1d58-4123-9818-22035889162b"},"abbreviatedStatement":"Stimulus","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:51:12+00:00"},{"identifier":"8ded86a6-050e-11e8-b8bb-41fd786d5597","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8ded86a6-050e-11e8-b8bb-41fd786d5597","fullStatement":"**Prompt Features:** The student will be prompted to identify sums and products as rational or irrational.\r\n\r\n**Stimulus Guidelines**:\r\n\r\n- The irrational numbers can be $\\pi$ or of the form $a\\sqrt[n]{b}$ where:\r\n\r\n - $a$ is rational;\r\n\r\n - $b$ is an integer such that\r\n\r\n - $b$ is positive when $n$ is even, and\r\n\r\n - $b$ may be negative when $n$ is odd; and\r\n\r\n - $n$ is a whole number such that $\\ 2 \\leq n \\leq 9$.\r\n\r\n- Item difficulty can be adjusted via these example methods, but is not limited to these methods:\r\n\r\n - radicands lead to roots that do/do not simplify to rational numbers\r\n\r\n - sum/product of the radicands does/does not lead to roots that simplify to a rational number\r\n\r\n - integer or fraction coefficients may be added in front of the radicands\r\n\r\n - radicands can be whole numbers or fractions","CFItemType":"Task Description","CFItemTypeURI":{"title":"Task Description","identifier":"b0804d18-bb65-11e7-98c9-83def7a9dccd","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/b0804d18-bb65-11e7-98c9-83def7a9dccd"},"abbreviatedStatement":"Task Description","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:53:39+00:00"},{"identifier":"8ded44fc-050e-11e8-9e78-1770ee01d6bf","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8ded44fc-050e-11e8-9e78-1770ee01d6bf","fullStatement":"Task Model 3d","CFItemType":"Task Model","CFItemTypeURI":{"title":"Task Model","identifier":"f66a54af-9e35-46d4-8ba6-66606c888f6c","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/f66a54af-9e35-46d4-8ba6-66606c888f6c"},"educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:09:18+00:00"},{"identifier":"8deda410-050e-11e8-8f37-0386987bfe89","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8deda410-050e-11e8-8f37-0386987bfe89","fullStatement":"Examples","CFItemType":"Example","CFItemTypeURI":{"title":"Example","identifier":"c685d17c-bb66-11e7-b6af-3f99116007d0","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/c685d17c-bb66-11e7-b6af-3f99116007d0"},"abbreviatedStatement":"Examples","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:10:57+00:00"},{"identifier":"8dedccba-050e-11e8-95db-db6caa33d103","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8dedccba-050e-11e8-95db-db6caa33d103","fullStatement":"**Example Stem:** Select the appropriate box to identify the value of each expression as being rational or irrational.\r\n\r\n| | **Rational** | **Irrational** |\r\n|-------------------------------------------------------|--------------|----------------|\r\n| $5\\sqrt{7}\\ + \\frac{1}{7}$ | | |\r\n| $12.4 \\bullet ( - 11)$ | | |\r\n| $\\sqrt{4} + 17$ | | |\r\n| $\\left( - 10\\sqrt{10} \\right) \\bullet 10\\sqrt{10}$ | | |\r\n\r\n**Rubric:** (1 Point) Student correctly identifies all sums and products correctly (e.g., Irrational, Rational, Rational, Rational).","CFItemType":"Example","CFItemTypeURI":{"title":"Example","identifier":"c685d17c-bb66-11e7-b6af-3f99116007d0","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/c685d17c-bb66-11e7-b6af-3f99116007d0"},"abbreviatedStatement":"Example 1","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:54:47+00:00"},{"identifier":"8dedeaec-050e-11e8-a6e5-5dff4d400d70","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8dedeaec-050e-11e8-a6e5-5dff4d400d70","fullStatement":"NA","CFItemType":"Accessibility","CFItemTypeURI":{"title":"Accessibility","identifier":"d19c9ae0-bfe0-11e7-bff4-050398278f5a","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/d19c9ae0-bfe0-11e7-bff4-050398278f5a"},"abbreviatedStatement":"Accessibility Note","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:10:57+00:00"},{"identifier":"8dee06da-050e-11e8-bca5-6dce859e0c27","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8dee06da-050e-11e8-bca5-6dce859e0c27","fullStatement":"None","CFItemType":"Allowable Tools","CFItemTypeURI":{"title":"Allowable Tools","identifier":"3e2514d0-fef2-11e7-817c-13e80b100709","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/3e2514d0-fef2-11e7-817c-13e80b100709"},"abbreviatedStatement":"Allowable Tools","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:10:57+00:00"},{"identifier":"8dee2354-050e-11e8-b5f5-f5d6f855b633","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/8dee2354-050e-11e8-b5f5-f5d6f855b633","fullStatement":"The student is presented with expressions that contain the sums and products of rational and/or irrational numbers.","CFItemType":"Stimulus","CFItemTypeURI":{"title":"Stimulus","identifier":"1e025133-1d58-4123-9818-22035889162b","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/1e025133-1d58-4123-9818-22035889162b"},"abbreviatedStatement":"Stimulus","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-01-29T16:53:52+00:00"},{"identifier":"acf45040-0511-11e8-9fbe-570982f3d407","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/acf45040-0511-11e8-9fbe-570982f3d407","fullStatement":"**Example Stem 2:** Click on **two** numbers whose sum, when added, would be **rational**.\r\n\r\n| **Numbers** | \\-5 | 3$\\sqrt{2}$ | $\\frac{2}{3}$ | $\\frac{1}{3}$ | $\\sqrt{7}$ |\r\n|-------------|-----|------------|--------------|--------------|-----------|\r\n\r\n**Rubric:**\r\n\r\n(1 point) The student selects two numbers that satisfy the given conditions. Multiple correct responses are possible and will all need to be included in the scoring rubric. Only example responses are shown below.\r\n\r\nExample Stem 2:\r\n\r\n![Formatted Table](https://images.smarterbalanced.org/content/Documents/Item%20Specs/Math_Item_Specs/Claim1_mathematics_HS_specs/HS_1B_NQ_Spec_V3_phase3_files/TM1E2.png)","CFItemType":"Example","CFItemTypeURI":{"title":"Example","identifier":"c685d17c-bb66-11e7-b6af-3f99116007d0","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/c685d17c-bb66-11e7-b6af-3f99116007d0"},"abbreviatedStatement":"Example 2","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-02-09T14:49:25+00:00"},{"identifier":"c23e3b3c-0511-11e8-bda1-9748dcc97837","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/c23e3b3c-0511-11e8-bda1-9748dcc97837","fullStatement":"**Example Stem 3:** Click on **two** numbers whose product, when multiplied, would be **irrational**.\r\n\r\n| **Numbers** | \\-5 | 3$\\sqrt{2}$ | $\\frac{2}{3}$ | $\\frac{1}{3}$ | $\\sqrt{8}$ |\r\n|-------------|-----|------------|--------------|--------------|-----------|\r\n\r\n**Rubric:**\r\n\r\n(1 point) The student selects two numbers that satisfy the given conditions. Multiple correct responses are possible and will all need to be included in the scoring rubric. Only example responses are shown below.\r\n\r\nExample Stem 3:\r\n\r\n![Formatted Table](https://images.smarterbalanced.org/content/Documents/Item%20Specs/Math_Item_Specs/Claim1_mathematics_HS_specs/HS_1B_NQ_Spec_V3_phase3_files/TM1E3.png)","CFItemType":"Example","CFItemTypeURI":{"title":"Example","identifier":"c685d17c-bb66-11e7-b6af-3f99116007d0","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/c685d17c-bb66-11e7-b6af-3f99116007d0"},"abbreviatedStatement":"Example 3","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2018-02-09T14:49:44+00:00"},{"identifier":"d72ea220-0511-11e8-931a-d337d6476f67","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItems/d72ea220-0511-11e8-931a-d337d6476f67","fullStatement":"**Example Stem 4:** Click on **two** numbers whose product, when multiplied, would be **rational**.\r\n\r\n| **Numbers** | \\-5 | 3$\\sqrt{2}$ | $\\frac{2}{3}$ | $\\frac{1}{3}$ | $\\sqrt{8}$ |\r\n|-------------|-----|------------|--------------|--------------|-----------|\r\n\r\n\r\n**Rubric:**\r\n\r\n(1 point) The student selects two numbers that satisfy the given conditions. Multiple correct responses are possible and will all need to be included in the scoring rubric. Only example responses are shown below.\r\n\r\nExample Stem 4:\r\n\r\n![Formatted Table](https://images.smarterbalanced.org/content/Documents/Item%20Specs/Math_Item_Specs/Claim1_mathematics_HS_specs/HS_1B_NQ_Spec_V3_phase3_files/TM1E4.png)","CFItemType":"Example","CFItemTypeURI":{"title":"Example","identifier":"c685d17c-bb66-11e7-b6af-3f99116007d0","uri":"https://case.smarterbalanced.org/ims/case/v1p0/CFItemTypes/c685d17c-bb66-11e7-b6af-3f99116007d0"},"abbreviatedStatement":"Example 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