Math Released Item Grade 4 M03436

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Valerie Lamb
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1 Math Released Item 2017 Grade 4 M03436

2 Anchor Set A1 A8 With Annotations

3 Prompt

4 M03436 Rubric Score Description 3 Student response includes the following 3 elements. Modeling component = 1 point o The student provides a valid equation and solution that represents the number of canoes needed, with work shown. Reasoning component = 2 points o The student provides a valid explanation of why the group s decision is incorrect. o The student provides a valid explanation based on interpretation of the remainder. Sample Student Response: 90-10= =26 with a remainder of 2 The group needs 27 canoes to hold the entire group of 80. The canoeing group s decision is not correct. They did not include the 2 remaining people in the group, 26 x 3 =78. The group needs one more canoe to include the remaining 2 people. Notes: A variety of explanations are possible. As long as the explanation shows a clear understanding of the incorrect thinking of the group, credit should be given. If a computation mistake is made, credit cannot be given for the modeling component, but 2 points can be given if both reasoning components are given. 2 Student response includes 2 of the 3 elements. 1 Student response includes 1 of the 3 elements. 0 Student response is incorrect or irrelevant.

5 A1 Score Point 3

6 Annotation Anchor Paper 1 Score Point 3 This response receives full credit. It includes each of the three required elements. The student shows that 26 canoes are proven to be insufficient, because only 78 people would have a seat on the canoes (3 26 = 78. Since they decided on 26 canoes, only 78 people would be able to go canoeing). The student clearly shows that 27 canoes are needed so that all 80 will have a spot in the canoes with one seat left over (3 27 = 81. If they decided on 27 canoes everyone will be able to go, with an extra seat). This work and explanation addresses both the correct interpretation of the remainder (rubric Element 2) and a correct explanation of why the group s decision is incorrect (rubric Element 3). In addition, as noted above, the reference to an extra seat gives a clear understanding that 80 people want to go canoeing, leaving one seat unfilled since they will now have enough seats for 81 people. Finally, while not explicitly stated that the group s decision is incorrect, it is strongly implied in the overall response to the prompt. Note: Students are not required to use division in order to address this prompt. The approach here shows strong math and reasoning skills and a clear understanding of how to interpret the remainder to determine the correct number of canoes the group needs. In addition, students are not required to show the initial subtraction procedure that determines how many people want to go canoeing (90 10 =80); it is clear from the process that the work and explanation originate from the point that 80 people need a spot in a canoe.

7 A2 Score Point 3

8 Annotation Anchor Paper 2 Score Point 3 This response receives full credit. It includes each of the three required elements. A correct equation and work to determine the number of canoes needed are provided (90 10 = 80, 80 3 = 26 remander 2). Showing work for and getting to 26 r2 is sufficient to satisfy Element 1. While this element includes solving for the correct number of canoes needed, that solution cannot be determined until the remainder is interpreted as required in Element 2. A valid explanation based on the interpretation of the remainder is provided (They need 27 canoes so everyone can go, if there were only 26 canoes 2 people will be left behind). A valid explanation of why the group s decision is incorrect is provided (They need 27 canoes so everyone can go, if there were only 26 canoes 2 people will be left behind). Understanding why the group s decision is incorrect also requires understanding how to interpret the remainder thus one often cannot be solved without understanding and solving the other. In addition, while not explicit that the group s decision is incorrect, it is strongly implied in the overall response to the prompt and an acceptable way in which to address this rubric element.

9 A3 Score Point 2

10 Annotation Anchor Paper 3 Score Point 2 This response receives partial credit. It includes two of the three required elements. A valid equation and work to determine the number of canoes needed are provided (80 3 = 26 with a remainder of 2 people). A valid explanation based on the interpretation of the remainder is provided (They need 27 canoes because... a remainder of 2 people). The reference to 2 people, in the context of the work and the correct number of canoes needed, is an acceptable way to demonstrate understanding of how to interpret the remainder. A valid explanation of why the group s decision is incorrect is not provided. Understanding is demonstrated that 26 canoes are insufficient; however, it is not clearly indicated that two people will be left behind if only 26 canoes are provided. More specificity regarding why the group is incorrect, i.e., 2 people will be left behind, is needed to receive credit for this element.

11 A4 Score Point 2

12 Annotation Anchor Paper 4 Score Point 2 This response receives partial credit. It includes two of the three required elements. An appropriate equation and work to determine the number of canoes needed are provided (3 26 = 78 and there are 80 people because 10 went on a walk). A valid explanation of why the group s decision is incorrect is provided (It was incorrect because if they got 26 canoes 2 people would not beable to have fun). While a partial explanation based on the interpretation of the remainder is provided (2 people), the correct number of canoes needed is not included.

13 A5 Score Point 1

14 Annotation Anchor Paper 5 Score Point 1 This response receives partial credit. It includes one of the three required elements. A correct explanation based on the interpretation of the remainder is provided (they will need 27 because you will have a remainder of 2). No equation or work to determine the number of canoes needed is provided. No explanation of why the group s decision is incorrect is provided. While in many cases the explanation for Element 2 also addresses Element 3, this explanation does not clearly indicate that the group s decision is incorrect or why it is incorrect.

15 A6 Score Point 1

16 Annotation Anchor Paper 6 Score Point 1 This response receives partial credit. It includes one of the three required elements. A correct equation and work to determine the number of canoes needed are provided (90 10 = 80, 80 3 = 26R2). Getting to 26r2 is sufficient for credit for this element. No interpretation of the remainder is provided. No explanation of why the group s decision is incorrect is provided.

17 A7 Score Point 0

18 Annotation Anchor Paper 7 Score Point 0 This response receives no credit. It includes none of the three required elements. No equation or work to determine the number of canoes needed is provided. No clear interpretation of the remainder is provided. While recognition is shown that the group s decision is incorrect, more clarity is necessary regarding the meaning of 1 canoe off, i.e., whether they require 1 more or 1 less canoe.

19 A8 Score Point 0

20 Annotation Anchor Paper 8 Score Point 0 This response receives no credit. It includes none of the three required elements. The equation used to determine the number of canoes needed is incorrect (90 10 = 80 3 =?,? = 25 R5). If only the initial work and/or equation is provided, the solution must be correct (26 R2) in order to adequately address this element. No interpretation of the remainder is provided. No explanation of why the group s decision is incorrect is provided.

21 Practice Set P101 - P105 No Annotations Included

22 P101

23 P102

24 P103

25 P104

26 P105

27 Practice Set Paper Score P101 3 P102 1 P103 1 P104 3 P105 2

Math Released Item Grade 4 PBA Item #17 Number of Baskets VF565302

Math Released Item Grade 4 PBA Item #17 Number of Baskets VF565302 Math Released Item 2015 Grade 4 PBA Item #17 Number of Baskets VF565302 Prompt Rubric Task is worth a total of 6 points. VF565302 Rubric Part A Score Description 2 Student response includes the following