1. Examining Student Work Jenny Ray, KDE Mathematics Specialist NKCES (Northern Kentucky Region) Jenny.ray@education.ky.gov www.JennyRay.net

2. Quality Core Participant Handbook O Template to Examine Student Work, p. 131 Examination Process (pp. 131-132) 1. Discuss the assignment’s place and purpose. 2. Reach consensus on attributes of high-quality work connected to the assignment 3. Sort student work. 4. Examine student work. 5. Focus on student work that does not meet high-quality standards.

3. Quality Core Worksheet for Examining Student Work O Directions: Using the discussion of Step 2 as a guide, list attributes of each criterion that are specific to the assignment. Then, note the strengths and weaknesses in student work, and identify patterns. O (Criterion: Demonstrates deep conceptual understanding, shows procedural knowledge of mathematical content, demonstrates skill and understanding in problem solving, demonstrates effective communication)

4. Work through the problem O Before assigning student work, complete the task O Preferably, consider multiple entry strategies that students may use O For our analysis purposes, you will work through a task using your method of choice. O Then, you will work through the same problem using another solution strategy

6. Optimization Problems: Boomerangs Analyzing Student Work

7. Alex’s solution P-7

8. Danny’s solution P-8

9. Jeremiah’s solution P-9

10. Tanya's solution P-10

11. Evaluating Sample Responses to Discuss O What do you like about the work? O How has each student organized the work? O What mistakes have been made? O What isn’t clear? O What questions do you want to ask this student? O In what ways might the work be improved? P-11

12. “Take 5” Stretch Break

13. Sidewalk Patterns

14. 1. Draw the next pattern in this series. In Prague some sidewalks are made of small square blocks of stone. The blocks are in different shades to make patterns that are in various sizes.

15. Sidewalk Patterns 3.What do you notice about the number of white blocks and the number of gray blocks? 2.Complete the table below. Pattern number, n1234 Number of white blocks1240 Number of gray blocks13 Total number of blocks25

16. Sidewalk Patterns 4. The total number of blocks can be found by squaring the number of blocks along one side of the pattern. a. Fill in the blank spaces in this list. 25 = 5 2 81 = ___ 169 =___ 289 = 17 2 b. How many blocks will pattern number 5 need? c. How many blocks will pattern n need? 5. a. If you know the total number of blocks in a pattern you can work out the number of white blocks in it Explain how you can do this. b. Pattern number 6 has a total of 625 blocks. How many white blocks are needed for pattern number 6? Show how you figured this out.

17. Student A

18. Student C

19. Student F

20. Student D

21. Watch the animation on the following slide and consider: What aspects of seeing structure and generalizing do you see evident in this work? What are some possible next steps for this student?

22. 4 sets of 1 by 3 rectangles White =4 1 3 4 sets of 2 by 5 rectangles White =4 2 5 4 sets of 3 by 7 rectangles White =4 3 7 4 sets of 1 by 1 and a 3 by 3 Gray =4 1 1+3 3 4 sets of 2 by 2 and a 5 by 5 Gray =4 2 2+5 5 4 sets of 3 by 3 and a 7 by 7 Gray =4 3 3+7 7

23. A student showed the calculations at the right for finding the number of gray squares. O What questions might help him use his thinking to generalize the number of gray tiles?

24. Student A

25. Student B

26. Student C

27. Student E