The purpose of this activity is to engage students in using a non-standard unit to give a measurement involving fractions.

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

- Measuring lengths using common metric units.
- Representing lengths using numbers and units, e.g., 45 cm.
- Using lengths models to represent fractions.
- Add simple fractions and use equations to represent the operations, e.g., ¾ + ¾ = 6/4.

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.

On average the teeth of:

an adult human are 1 ½ cm long.

a great white shark are 7 ½ cm long.

How many adult teeth, stacked end to end, would be needed to make the same length as the great white shark’s tooth?

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

### Make sense

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

- Do I understand the story and the words? (Students must understand that average means typical or normal in this case.)
- What are the important words and symbols? (The meaning of measures is required, such as 7 ½ cm means “seven and one half centimetres.)
- What will my solution look like? (The solution will say how many times an adult human tooth fits into a shark tooth. It might also include some working to explain how the answer was found.)

### Plan approach

Discuss ideas about how to solve the problem. Emphasise that, in the planning phase, you want students to say how they would solve the problem, not to actually solve it.

- What are the maths skills I need to work this out? (Measurement and fraction knowledge and skills are needed.)
- What tools might be useful? (A physical representation and rulers will be helpful.)
- What strategies might I use? Act it out? Create a table? Guess and check?
- How might I work with others?

### Take action

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

- Is my strategy working or should I try something else?
- Am I showing my workings in a way that helps me see patterns?
- Have I got the maths I need, or do I need to ask for help?
- Do my answers seem correct? How can I check my answers?
- Does my solution answer the question?

### Convince yourself and others

Allow students 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.

- What is the answer?
- Is my working clear for someone else to follow?
- How would I convince someone else I am correct?
- Could I have solved the problem in a more efficient way?
- What could I find out next?

### Examples of work

#### Work sample 1

The student creates a ratio for the length of human in centimetres. They use symbols to create equivalent ratios, like 2 teeth = 3 centimetres, and add ratios until 7 1/2 cm is reached.

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

#### Work sample 2

The student creates a linear model of 7 ½ squares to represent the length of a shark’s teeth in centimetres. They ‘step out’ how many counts of 1 ½ fit into the total length.