# 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?

This cameo has a From The Classroom section which contains examples of student work from three levels from schools in three countries, including a PowerPoint presentation from two Year 7 girls.

#### 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

#### Iceberg

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

• 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...

• 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.

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

• 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."
See more in From The Classroom below.

Also:

• Eric the Sheep lining up to be shorn becomes Sneaky Pete queuing for ice cream in this article intended as a teaching craft talking point for a teacher meeting.
• Eric is used as a model for the lesson Learning To Write a Maths Report. Within this lesson you will find an example of a PowerPoint prepared by Year 10 students.
• Eric is used to illustrate Working Like A Mathematician in this video on the You Tube channel of the Association of Teachers of Mathematics (ATM), UK. You can also find it through Mathematics Centre Cube Tube.

For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 17, Eric The Sheep, which includes an Investigation Guide and student PowerPoint publications from Year 7.

Visit Eric The Sheep in Menu Maths Pack D.

#### 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.

## From The Classroom

 In this section you have the opportunity to see how Eric has been explored and reported on in a Year 1 class from the USA, a Year 5 class from the UK and a Year 7 class from a small, remote school in New South Wales. Photos above are from a Year 3 class in Australia.

Year 1 Accelerated Class, Hammond Westside Primary, Louisiana
Miss Langlois

In the first hour with the problem children explored it physically (they became the sheep) then with Poly Plugs. They collected data about some numbers of sheep in front of Jacobi and were fascinated to see that sometimes the number cut (shorn) was the same. In their own way, they recorded what they had done on a journal page. Next day they began the problem again, this time organising their search through the data.

 Literacy and numeracy develop hand in hand when students are learning to work like a mathematician. Miss Greer's regular Year 1 class, Hammond Westside Primary, Louisiana The photos below are from their first hour with the problem. Recording on their journal page was a feature too.

Year 5, St. Edmund's Junior School, England
Matthew Reames
Each week Matthew combines two 'sets' for an investigation session of just over an hour. The two Year 5 classes are split for mathematics into three sets. Matthew takes Sets 1 & 2 in this session.

Sample journal entries from this session are shown below.

 Editor's Interpretation 1. first me and my partner lined up fifty counters not encluding Eric [diagram] hear is a small section of what hapens [diagram] we tried to find out how many sheep were was sawn before him. Editor's Interpretation we were trying to figure out a problem and was 51 sheep one of the sheep was called eric there were 50 sheep in front of eric waiting to be shawn eric really wanted to be shawn so he skipped 2 sheep every 1 sheep gets shawn So what me and my group did we tried to act it out, first with five people then with 7 but it wasn't working So we decided to get 51 little cubes and we put the cubes in a line and eric at the back then we took a cube away and put eric in front of 2 cubes every time until we got an answer.

Year 7, Hillston Central School, New South Wales, Australia
Graeme Smyth
Hi Doug,
Attached is a presentation on Eric the Sheep produced by Tiana and Emma, from Year 7 at Hillston Central School. They selected Eric the Sheep as their task to present to Mr Smyth's maths class. The students in this class have really enjoyed the Working Mathematically approach using the Maths With Attitude kits. They did their presentation in Powerpoint, which has been converted to a pdf.

Thanks,
Graeme

• Eric The Sheep by Tiana and Emma
(To view in full screen use Ctrl L.)
(Editor's Note: Congratulations girls, this is great work.)