The purpose of this activity is to engage students in using counting strategies, images and/or materials to solve a problem.

This activity assumes the students have experience in the following areas:

- Counting on and back from any number in ones.
- Using materials and images to represent number problems.
- Adding and subtracting simple whole numbers using counting and part-whole strategies.

The problem is sufficiently open ended to allow the students freedom of choice in their approach. It may be scaffolded with guidance that leads to a solution, and/or the students might be given the opportunity to solve the problem independently.

The example responses at the end of the resource give an indication of the kind of response to expect from students who approach the problem in particular ways.

A school has three football fields.

At lunchtime, there is a five-a-side football game on each of the fields.

Two of the teams are made up of year one students and the others are all year two students.

How many of the **players **on the fields are year two students?

Note: Five-a-side means five players on each team. There are no subs.

The following prompts illustrate how this activity can be structured around the phases of the Mathematics Investigation Cycle.

### Make sense

Introduce the problem. Allow ākonga time to read it and discuss in pairs or small groups.

- What do you think the problem is about?
- What information has been given?
- Do I understand all the words, like ‘subs’ and ‘five-a-side.’
- What will an answer to the problem look like?

### Plan approach

Discuss ideas about how to solve the problem. Emphasise that for now you want ākonga to say how they would solve the problem, not to actually solve it.

- What might be useful ways to solve this problem?
- Could I act the problem out? Could I draw a diagram?
- What tools might be useful, such as a counters, and fingers?

### Take action

Allow ākonga time to work through their strategy and find a solution to the problem.

- Am I recording in an organised way so I can keep track of the fruits?
- Does my recording match the information?
- Is my working correct? How can I check? How can I make sure I did not miss any numbers in my counting?
- Do I see any pattern? How might what I know about fives help me?

### Convince yourself and others

Allow ākonga time to check their answers and then either have them pair share with other groups or ask for volunteers to share their solution with the class.

- Have I got an answer? Does my answer seem right? How can I check?
- How can I convince others that I am right?
- What ways can I find to show other people I am right?
- Did I use a good strategy? How does my strategy compare with what others did?
- Would this help me solve a similar problem? How?

### Examples of work

#### Work sample 1

The student creates a diagram of the three fields with two teams of five on each field. They eliminate the Year One players and are left with the Year 2 players. They count to find there are 20 year 2 players.

Click on the image to enlarge it. Click again to close.

#### Work sample 2

The student creates a diagram with numbers to represent the teams. They cross out two teams then find the number of remaining players by counting in fives.