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Session 1, Part B:
Reasoning About Situations
In This Part: Eric the Sheep | Changing the Rules
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Here's a simple number puzzle that leads to a surprisingly challenging investigation. Note 3
It's a hot summer day, and Eric the Sheep is at the end of a line of sheep waiting to be shorn. There are 50 sheep in front of him. Being an impatient sort of sheep, though, every time the shearer takes a sheep from the front of the line to be shorn, Eric sneaks up two places in line.
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Problem B1 | |
Without working out the entire problem, predict how many sheep will get shorn before Eric. Note 4
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Problem B2 | |
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One way to help solve a complicated problem is to solve a smaller version of the same problem. In this activity, you will solve a version of Eric's problem, one with a shorter line. Notice any patterns you find -- they will help you understand and solve the larger problem.
You can use counters, plastic chips, or coins to try out various smaller versions of this problem. Complete the following table:
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Problem B3 |  |
Use the table from Problem B2 to predict how many sheep will get shorn before Eric if there are 50 in line in front of him. |
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Look for a pattern in the table, then extend it. Are you using algebraic thinking? Close Tip |
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Problem B4 | |
Describe the strategies you used to find the answer to Problem B3 and how you could predict the answer for any number of sheep in the line. Is your method for predicting "algebraic"? Why or why not? |
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Problem B5 | |
Work out the solutions for the boxes left blank in the table below:
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Number of sheep in front of Eric | | Sheep shorn before Eric |
37 | | 13 |
296 | | 99 |
1000 | | 334 |
7695 | | 2565 |
37, 38, or 39 | | 13 |
61, 62, or 63 | | 21 |
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hide answers |
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Help: You will have to work backwards for the last two entries. Some problems may have more than one answer. |
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