Example Item 1 (Grade 6): Primary Target 3A (Content Domain NF), Secondary Target 1F (CCSS 5.NF.4), Tertiary Target 3F

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1 Task Model 1 DOK Level 2 Target A: Test propositions or conjectures with specific examples Task Expectations: The student is asked to give an example that refutes a proposition or conjecture; or The student is asked to give an example that supports a proposition or conjecture. [Note: Use appropriate mathematical language in asking students for a single example. While a single example can be used to refute a conjecture, it cannot be used to prove one is always true.] Example Item 1 (Grade 6): Primary Target 3A (Content Domain NF), Secondary Target 1F (CCSS 5.NF.4), Tertiary Target 3F Sarah claims that for any fraction multiplied by, the product n will always be less than. A. Drag one number into each box so that the product n is less than. B. Drag one number into each box so that the product n is not less than. Rubric: (1 point) The student drags one number into each box to create an equation where n is less than in Part A, and drags one number into each box to create an equation to show that Sarah s claim is incorrect in Part B (e.g., Part A, Part B ). This exemplar response represents only one possible solution. Other correct responses are possible. Response Type: Drag and Drop 11 Version 2.0

2 Task Model 1 DOK Level 2 Example Item 2 (Grade 8): Primary Target 3A (Content Domain NS), Secondary Target 1A (CCSS 8.NS.1), Tertiary Target 3F Target A: Test propositions or conjectures with specific examples Tom claims: If a rational number is not an integer, then the square root of the number must be irrational. For example, 3.6 is irrational and 1 is irrational. 2 Enter a rational number that is not an integer to show Tom s claim is incorrect. Rubric: (1 point) The student enters a rational number which has a rational square root (e.g., or 2.25). This exemplar response represents only two possible solutions. Other correct responses are possible. Response Type: Equation/Numeric 12 Version 2.0

3 Task Model 2 DOK Levels 3, 4 Target B: Construct, autonomously, chains of reasoning that will justify or refute conjectures Task Expectations: The student is presented with a mathematical phenomenon and a conjecture. Student is asked to identify or construct reasoning that justifies or refutes a conjecture. Example Item 1 (Grade 6): Primary Target 3B (Content Domain G), Secondary Target 1H (CCSS 6.G.2), Tertiary Target 3C Micah constructs a rectangular prism with a volume of 360 cubic units. Micah claims that if the height is 10 units, then the base of the prism must be a square. Use the Connect Line tool to draw a base that shows Micah s claim is incorrect. Rubric: (1 point) The student constructs a rectangle that shows Micah s claim is incorrect (e.g., 4 x 9, 3 x 12, or 2 x 18). Response Type: Graphing 13 Version 2.0

4 Task Model 2 DOK Levels 3, 4 Example Item 2 (Grade 8): Primary Target 3B (Content Domain G), Secondary Target 1G (CCSS 8.G.2), Tertiary Target 3F Two figures are shown on the coordinate grid. Target B: Construct, autonomously, chains of reasoning that will justify or refute conjectures Prove that Figure A and Figure B are congruent. Describe three single transformations that, when performed, would transform Figure A to Figure B. In your response, be sure to identify the transformations in the order they are performed. Rubric: (2 points) The student describes three transformations with sufficient detail to prove that Figure A and Figure B are congruent (e.g., see exemplars). (1 point) The student either describes all three transformations in general terms, without the degree of precision necessary to prove congruency (e.g., rotation, reflection, and translation) or correctly describes two out of three transformations and incorrectly describes the third (e.g., states the rotation is 180 instead of 90 or translates in the wrong direction or an incorrect number of units). Exemplars 4 : 1 st Transformation is to reflect over the y-axis. 2 nd Transformation is to rotate 90 counter-clockwise about the origin. 3 rd Transformation is to translate right by 2 units. 1 st Transformation is to reflect over the x-axis. 2 nd Transformation is to rotate 90 clockwise about the origin. 3 rd Transformation is to translate right by 2 units. Response Type: Short Text (hand scored) 4 Exemplars only represent possible solutions. Typically, many other solutions/responses may receive full credit. The full range of acceptable responses is determined during rangefinding and/or scoring validation. 14 Version 2.0

5 Task Model 3 Target C: State logical assumptions being used Task Expectations: The student is asked to connect a logical basis to its resulting conjecture. The student is presented with a mathematical or real-world scenario where an assumption is made in order to find the solution. Example Item 1 (Grade 7): Primary Target 3C (Content Domain NS), Secondary Target 1B (CCSS 7.NS.2), Tertiary Target 3F In the following equation, a, b, and c are nonzero rational numbers. a b = c Given this equation, drag one value into each box to complete four true equations. Rubric: (2 points) The student is able to complete all four equations correctly (e.g., see solution shown at the right). (1 point) The student is able to complete 3 out of 4 equations correctly. Response Type: Drag and Drop 15 Version 2.0

6 Task Model 4 Task Expectations: The student is given different cases to consider and the student uses or shows reasoning to support the cases. Target D: Use the technique of breaking an argument into cases Example Item 1 (Grade 7): Primary Target 3D (Content Domain NS), Secondary Target 1B (CCSS 7.NS.2), Tertiary Target 3F, Quaternary Target 1C (CCSS 6.NS.4) Rubric: (2 points) The student identifies all the correct conditions that make the argument true (e. g., Statements 1, 3). (1 point) The student identifies the correct conditions that make the argument true, but fails to consider the case of division by zero (e.g., 1, 3, 4). Response Type: Hot Spot 16 Version 2.0

7 Task Model 5 Target E: Distinguish correct reasoning from flawed reasoning Task Expectations: The student is presented with valid or invalid reasoning. If the reasoning is flawed, the student will explain or correct the flaw. The student is asked to select the condition(s) for which an argument does or does not always apply. Two or more approaches or chains of reasoning are given and the student is asked to identify the correct method and justification OR identify the incorrect method/reasoning and the justification. Example Item 1 (Grade 7): Primary Target 3E (Content Domain RP), Secondary Target 1A (CCSS 6.RP.3), Tertiary Target 3C Jane wants to buy the following items at a store. Jeans, $32.99 Earrings, $29.99 T-shirt, $9.99 Shoes, $23.99 Jane will either use coupon A or coupon B to reduce the cost of her purchase. She sees some socks that cost $4.99. Jane thinks that adding socks to her purchase will cost her less than making the purchase without socks. Which option should Jane choose to spend the least amount of money? A. Jane should add the socks to her purchase and then use Coupon A. B. Jane should add the socks to her purchase and then use Coupon B. C. Jane should make the purchase without socks and use Coupon A. D. Jane should make the purchase without socks and use Coupon B. Rubric: (1 point) The student selects the statement that represents correct reasoning (e.g., A). Response Type: Multiple choice, single correct response 17 Version 2.0

8 Task Model 5 Example Item 2 (Grade 7): Primary Target 3E (Content Domain EE), Secondary Target 1D (CCSS 7.EE.3) Target E: Distinguish correct reasoning from flawed reasoning Rubric: (2 points) The student selects the correct steps and plots the correct point on the number line. (e.g., Part A: 1, 2, 4; Part B: 8). (1 point) The student either selects the correct steps or plots the correct point on the number line. Response Type: Hot Spot and Graphing 18 Version 2.0

9 Task Model 5 Example Item 3 (Grade 8): Primary Target 3E (Content Domain RP), Secondary Target 1A (7.RP.3), Tertiary Target 3C Target E: Distinguish correct reasoning from flawed reasoning Rubric: (1 point) The student selects the flawed work (e.g., $90/0.9 = $100 and highlights The bats are on sale for 10% off. ). Response Type: Hot Spot 19 Version 2.0

10 Task Model 6 Task Expectations: The student uses concrete referents to help justify or refute an argument. Target F: Base arguments on concrete referents such as objects, drawings, diagrams, and actions Example Item 1 (Grade 8): Primary Target 3F (Content Domain G), Secondary Target 1E (CCSS 7.G.5), Tertiary Target 3D The base of triangle ABC and the base of triangle DEF lie on line m, as shown in the diagram. The measure of is less than the measure of For each comparison, select the symbol (<, >, =) that makes the relationship between the first quantity and the second quantity true. First Quantity Comparison Second Quantity < > = < > = Interaction: The student selects the symbol from a drop down menu of <, >, =. Rubric: (1 point) The student selects the correct symbol for both comparisons (e.g., >, <) Response Type: Hot Spot 20 Version 2.0

11 Task Model 7 Target G: Determine conditions under which an argument does and does not apply Task Expectations: The student must determine whether a proposition/or conjecture is true for all cases, true for some cases, or not true for any case. In some problems the student must provide justification to support the conclusions. Example Item 1 (Grade 7): Primary Target 3G (Content Domain G), Secondary Target 1F (CCSS 7.G.5), Tertiary Target 3A Determine whether each statement is true for all cases, true for some cases, or not true for any case. Statement Two vertical angles form a linear pair. True for all True for some Not true for any If two angles are supplementary and congruent, they are right angles. The sum of two adjacent angles is 90. If the measure of an angle is 35, then the measure of its complement is 55. The measure of an exterior angle of a triangle is greater than every interior angle of the triangle. Rubric: (1 point) The student can classify each statement correctly (e.g., see table below). Response Type: Hot Spot 21 Version 2.0

12 Task Model 7 Target G: Determine conditions under which an argument does and does not apply Example Item 2 (Grade 8): Primary Target 3G (Content Domain G), Secondary Target 1G (CCSS 8.G.3) A sequence of transformations is applied to a polygon. Identify each sequence of transformations where the resulting polygon has a greater area than the original polygon. A. Reflect over the x-axis, dilate about the origin by a scale factor of, translate up 5 units B. Rotate 90 counterclockwise around the origin, dilate about the origin by a scale factor of C. Dilate about the origin by a scale factor of, rotate 180 clockwise around the origin, translate down 2 units D. Dilate about the origin by a scale factor of 2, reflect over the y-axis, dilate about the origin by a scale factor of Rubric: (1 point) The student identifies all the correct conditions that make the argument true (e.g., B, D) Response Type: Multiple Choice, multiple correct response 22 Version 2.0