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Learning Math Home
Patterns, Functions, and Algebra
 
Session 1 Part A Part B Part C Homework
 
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Session 1 Materials:
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Session 1, Part B:
Reasoning About Situations (45 minutes)

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

  

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:

Number of sheep in front of Eric

 

Sheep shorn before Eric

4

 

5

 

6

 

7

 

8

 

9

 

10

 

11

 

 

show answers

 

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

Solution  

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.


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Look for a pattern in the table, then extend it. Are you using algebraic thinking?   Close Tip

 

Problem B4

write Reflect  

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 thumbnail
 

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

 

show answers

 

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.

Next > Part B (Continued): Changing the Rules

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