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10 Sam s Method Sam correctly calculated the number of beads hidden under the cloud. He listed the pattern and showed his calculations. He attempts generalizing a rule to repeat the pattern but does not identify the relationship between the corresponding terms. Sam s Solution Rick s Method Rick uses algebra to determine the patterns of the beads. He generated the rule to determine the next numbers in the pattern. Rick recognized the linear relationship of the black beads and the exponential relationship of the white beads. He also graphed the data. Rick subtracted the correct number of white beads showing in the 4 th and 6 th set of beads. Rick s Solution

11 Beads under the Cloud Student Materials Alpha Version

12 Beads under the Cloud Student Materials Alpha Version Sample Responses to Discuss Here is some work on Beads under the Cloud 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 data. Describe what the student did to calculate a number of beads under the cloud. 3. Explain what the student needs to do to complete or correct his or her solution. s_ Solution

13 Beads under the Cloud Student Materials Alpha Version s_ Solution s_ Solution

14 Timothy s Solution Hannah s Solution

15 Curtis Solution Tony s Solution

16 Claire s Solution Victoria s Solution

17 Sam s Solution Rick s Solution

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