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.
Without working out the entire problem, predict how many sheep will get shorn before Eric. Note 4
Problem B2
This activity requires the Flash plug-in, which you can download for free from Macromedia's Web site. If you prefer, you can view the low-tech version of this
activity, which doesn't require the Flash plug-in.
Use the Interactive Activity to complete the following table:
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.
Look for a pattern in the table, then extend it. Are you using algebraic thinking? Close Tip
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?
Video Segment In this video segment, Professor Cossey and the participants discuss strategies for solving a problem with sheep shearing and then discuss the involvement of the number three in all the solutions.
Were you surprised by the different ideas presented in solving this problem?
Which of these ideas reflect algebraic thinking?
You can find this segment on the session video, approximately 7 minutes and 21 seconds after the Annenberg Media logo.
Problem B5
Work out the solutions for the boxes left blank in the table below:
