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1 Grades 4-6 Mathematics Formative Assessment Lesson Designed and revised by Kentucky Department of Education Mathematics Specialists Field- tested by Kentucky Mathematics Leadership Network Teachers If you encounter errors or other issues, please contact the KDE team at: Created for the sole purpose of assisting teachers as they develop student understanding of Kentucky s Core Academic Standard through the use of highly effective teaching and learning. Not intended for sale.

6 The methods used by Katrina, Dawn, Jim, Eddie, Andrew & Brandon all lead to the correct solution. However, Dawn s work is incomplete because it does not give the final answer of 24. Dawn s pictorial model uses the tray as the one whole and subtracts amounts while at the same time showing the fractional parts of the whole. In the end there would be 12 equal size sections and 2 cookies could fit in each so the approach could lead to correct solution, it is just incomplete. Katrina & Jim use similar pictorial methods by actually drawing out cookies by working backwards. Eddie uses a bar model to work backwards. Andrew uses fraction multiplication and Brandon solves with equations. Robin, Britney & Charlie all use incorrect methods. Robin attempts to use pictures, Britney uses division & Charlie confuses the amount eaten with the amount left.

7 Mrs. James left a tray of cookies on the counter early one morning. Larry walked by before lunch and decided to take 1/3 of the cookies on the tray. Later that afternoon Barry came in and ate 1/4 of the remaining cookies. After supper Terry saw the tray of cookies and ate 1/2 of the cookies remaining at that time. The next morning Mrs. James found the tray with only 6 cookies left. How many cookies were on the tray when Mrs. James first left it on the counter?

8 Sample Responses to Discuss Here is some work on Where are the Cookies? from students in another class. For each piece of work: 1. Write the name of the student whose solution you are analyzing. 2. Describe the problem solving approach the student used. For example, you might: Describe the way the student has organized the solution. Describe what the student did to calculate the number of cookies that started on the tray. 3. Explain what the student needs to do to complete or correct his or her solution. s_ Solution

9 s_ Solution s_ Solution

10 Katrina s Solution Dawn s Solution

11 Robin s Solution Britney s Solution

12 Charlie s Solution Jim s Solution

13 Eddie s Solution Andrew s Solution

14 Brandon s Solution

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