Eric The Sheep

Task 45 ... Years 2 - 12

Summary

Eric the sheep is lining up to be shorn. He is last in the queue. Each time the shearer takes one sheep from the front of the line, Eric sneaks past two sheep to get closer to the front. If there are 50 sheep in front of Eric to start with, how many will be shorn before Eric gets to the front? 		 

Materials

  • One sheep and at least 50 other counters

Content

  • counting patterns
  • multiplication and division
  • times tables
  • graphing
  • visualisation and generalisation
  • symbolic algebraic representation
  • integer value of a number
Eric The Sheep

Iceberg

A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card. 		   

  • Can you check your answer another way? Possible approaches are:
    • using the counters to make a model
    • acting out
    • seeing a movement pattern which involves three sheep 'leaving' the line on each move (one from the front and two Eric jumps) and so dividing by 3
    • drawing a diagram
    • breaking the problem into smaller parts (fewer sheep) and looking for a pattern...
Strategy: Make a model

Strategy: Draw a diagram
  • If you take the last of these approaches can you represent the data in a table, as a graph...

    Sheep in Front Sheep Shorn
    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, the original challenge on the card, 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.

  • What happens if...?
    • Eric sneaks past 3 sheep, 4 sheep, ...
    • There are 2 shearers, 3 shearers, ...
  • In general, if there are S sheep in the line and Eric sneaks past N each time the shearers take F sheep from the front, work out a formula to find the number of sheep shorn before Eric gets to the front (B).
Extension
How can you tell if a number is a multiple of 3? or 4? or 5? ... Explore Divisibility Tests.

Whole Class Investigation

Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works. 		   

You have to act this one out. It's the only way to start. Bet you already know who you want to make Eric.

Jordan the sheep
From here, encourage small group exploration with counters, cubes or Poly Plug and explore, record and publish guided by the questions above.

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."

Visit Eric The Sheep on Maths300:
Guest ... Member

Visit Eric The Sheep on Poly Plug & Tasks.

Also, Eric is used as a model for the lesson Learning To Write a Maths Report on Maths300. Within this lesson (which is available to members and non-members alike) you will find an example of a PowerPoint prepared by Year 10 students. There are additional PowerPoint examples for members in the Classroom Contribution of the lesson above.

Is it in Maths With Attitude?

Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner. 		   

The Eric The Sheep task is an integral part of:

  • MWA Number & Computation Years 3 & 4
  • MWA Pattern & Algebra Years 7 & 8

The Eric The Sheep lesson is an integral part of:

  • MWA Number & Computation Years 3 & 4
  • MWA Pattern & Algebra Years 9 & 10
This task is also included in the Task Centre Kit for Aboriginal Students and the Secondary Library Kit. Solutions for tasks in the latter kit can be found here.

Green Line
Follow this link to Task Centre Home page.