ERIC THE SHEEP


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ERIC THE SHEEP

MATERIALS

* One sheep - this is Eric
* Fifty [50] counters to stand for the other sheep

TASK

Eric the sheep is lining up to be shorn before the hot summer ahead. There are fifty [50] sheep in front of him. Eric can't be bothered waiting in the queue properly, so he decides to sneak towards the front. Every time Eric passes two sheep, one sheep from the front of the line is taken in to be shorn. How many sheep will be shorn before Eric?

TEACHERS' NOTES - ERIC THE SHEEP

Number/Algebra
Years: 3 - 12

Perhaps because children have personal experience with standing in queues, they find this an appealing task. It is this motivational aspect which leads to a mathematical investigation of appropriate depth for a wide range of ages.

MATHEMATICS CONTENT

Recognising, producing and using patterns in number.

Physical representation of relationships between quantities.

Potential for arithmetic generalisation.

Can be extended to become a high level algebraic problem.

LEARNING FEATURES

Amenable to a variety of problem solving strategies, including:


: acting out
: exploring simpler cases
: looking for a pattern
: applying a rule

Opportunity to involve the whole class physically as sheep in the queue: kinesthetic learning.

RELATED TASKS

Plate Triangles, Task 28

Number Tiles, Task 43

Staircase, Task 51

Double Staircase, Task 61

Square Numbers, Task 111

Tower Of Hanoi, Task 142

Garden Beds, Task 147

4 Arm Shapes, Task 154

Painted Cubes, Task 160

Lovitt, C. & Clarke, D. (1988), MCTP Activity Bank Volume 1, Curriculum Corporation, 'Think Of A Number', p. 277.

EVALUATION / ASSESSMENT

Suppose there were 100 sheep before Eric, Could you work out how many would be shorn before Eric?

Ask the students to write a report of their investigation.

TEACHERS' COMMENTS

My class has a lot of fun with this task. I use it every year to introduce work on pattern. We act it out until everyone who wants to have a turn in the line does so, and then it is easy to continue the investigation because any number of objects in the room can be used as sheep.

Great task, because each time you vary something, you are off on a new investigation.

I like the co-operation which is almost automatically built into this problem. I find most students line up the counters and then use a process like: "OK. I'll move Eric. You move the sheep that are shorn and then we'll count."

SOLUTION

17 sheep are shorn before Eric. One approach is to consider simpler cases and build a pattern.

Number of sheep ahead of Eric	Number shorn before Eric
0	0
1	1
2	1
3	1
4	2
5	2
6	2

So, if the number of sheep before Eric is a multiple of 3, dividing by 3 gives the number shorn before Eric. If the number is not a multiple of 3, dividing the next multiple of 3 by 3 gives the number of sheep shorn.

Fifty is not a multiple of 3. The next multiple of 3 after 50 is 51, and 51 ÷ 3 = 17, so 17 sheep are shorn before Eric.

EXTENSIONS

How can you tell if a number is a multiple of 3?

Try other lengths of sheep lines. What if there were 40 in front of Eric, or 100, or even 1000?
Can you develop a rule to predict the number of sheep shorn?

Suppose Eric gets even sneakier and moves past more than two sheep at a time. Choose some numbers to pass and experiment.

Suppose the boss increases the number of shearers on the line, so that every time Eric moves, more than one sheep has been shorn. Choose some numbers and investigate.

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