# Farmyard Race Day

### Task 125 ... Years 4 - 8

#### Summary

Students manipulate the six farmyard animals on the racetrack provided. With the first set of clues, they find out the relative finishing positions of the animals when the winner crosses the line. The second set of clues establishes the finishing positions of the racing animals in relation to the position of the dog watching at the side.

#### Materials

• 6 animals and a racetrack board

#### Content

• interpreting directions for location in 2D space
• interpreting the solution of a problem in context
• spatial language such as before, after, between, length, in front, several lengths behind, passed
• problem solving skills - including breaking a problem into parts, working backwards, elimination, 'if-then' reasoning

#### Iceberg

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

Note: Animals provided in this task may vary depending on supply.

This spatial logic task provides several activities involving spatial language and problem solving skills at increasingly difficult levels. It can be simplified or extended to suit varying abilities and encourages students to justify their reasoning to each other.

You may need to emphasise that a length is the distance between one division mark and the next as shown on the track. This is contrary to horse racing parlance, for example, which some students may be familiar with. There are twelve divisions marked altogether. If there is any confusion over the term finishing position, just ask the children to work out where the other animals were when the winner crossed the line.

One teacher commented:

After initial support and guidance, able Year 3 children then repeated the activities by themselves, tried out new race tracks, and readily justified their results using the spatial language and clues provided in the instructions.
1. Finishing positions at the time the winner crossed the finish line:
```1st ... goat
2nd ... duck
3rd ... cow
4th ... pig
5th ... horse
and the dog watched
```
2. Unnecessary information was that the pig did not finish last.
3. Finishing positions at the time the winner crossed the finish line:
```1st ... pig
2nd ... goat
3rd ... duck
4th ... cow
5th ... horse
```
and the dog watched from section between the duck and cow

Extensions

1. In each problem, these are the orders in which the animals finished, but is there more than one way they could be placed in the sections and both keep the order and satisfy the clues?
2. What happens if you give the students any finishing position and ask them to design a set of clues to match?
3. What happens if students ...design their own clues sets for the given race track? ...design their own racetrack? ...design their own clues sets for their own racetrack?
4. Encourage students to justify their reasoning with specific questions. For example for Question 3:
Is it possible that the pig is not in the race?
No.
Why?
Because it says that 3 animals had passed the dog. That means that the dog and 5 animals must be used. Otherwise the winner cannot be 6 lengths in front of the cow.
What changes would you have to make to the instructions to take the pig out of the race?
Change the number of animals that pass the dog or the distance between the winner and the cow.
If you remove the last instruction, could there be another solution?
No, not if the first instruction still remains.

#### 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.

One way to transform this task into a whole class investigation is to draw up a larger size racetrack that the class can stand around and introduce the clues in a fish bowl situation. Clues could be on separate strips of card with one student in charge of each clue. Or you could type out all the clues and project them onto your interactive whiteboard. In either case, their is a reading fluency and comprehension opportunity within the lesson.

Once introduced in this way, partners can quickly sketch the racetrack and find and justify their solution. Further development is suggested by the notes above.

At this stage, Farmyard Race Day does not have a matching lesson on Maths300.

#### 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 Farmyard Views task is an integral part of:

• MWA Space & Logic Years 3 & 4
This task is also included in the Primary Library Kit. Solutions for tasks in the latter kit can be found here.