Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 1, Part B:

In This Part: Eric the Sheep | Changing the Rules

 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. Problem B1 Without working out the entire problem, predict how many sheep will get shorn before Eric. Note 4

Problem B2

Use the Interactive Activity to complete the following table:

 Number of sheep in front of Eric Sheep shorn before Eric 4 5 6 7 8 9 10 11

 Number of sheep in front of Eric Sheep shorn before Eric 4 2 5 2 6 2 7 3 8 3 9 3 10 4 11 4 hide answers

 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 Look for a pattern in the table, then extend it. Are you using algebraic thinking?

 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:

 Number of sheep in front of Eric Sheep shorn before Eric 37 296 1000 7695 13 21

 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 hide answers

Help: You will have to work backwards for the last two entries. Some problems may have more than one answer.

 "Eric the Sheep" is taken from Maths 300. Permission has been given by the publisher, Curriculum Corporation.