How old!

Achievement objectives

NA4-1: Use a range of multiplicative strategies when operating on whole numbers.

NA4-3: Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.

Required materials

See Materials that come with this resource to download:

• How old activity (.pdf)

Activity

I am twice my brother's age and one fifth my mother's age. 

My dad is older than mum by half my brother's age.

All our ages are whole numbers.

I go to school, but my brother doesn't yet.

• How old are we? 

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 situation and the words? (Students may need support to understand that the ages are whole numbers of year, so ages like 1.5 years are not permitted.)
• What is the important information in the problem?
• Is any information that I need not there? What information is that?
• What will my solution look like? (The solution will be the age for each person in the family that meets the conditions.)
• Is it possible that there might be more than one correct answer?

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.

• Do I know some ways to record and organise the information to make solving the problem easier?
• Could I draw a diagram to represent the ages?
• Could I write the clues as algebraic expressions, like a and 4a?
• Would a table help to organise my working with different ages?
• What are the maths skills I need to work this out?
• What might the solution be? What can’t the solution be? Why not?
• What tools (digital or physical) could help my investigation?

Take action

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

• Whose age should I use to start with? Why should I use the age of that person?
• Have I recorded my ideas in a way that helps me to see patterns and helps me see that I have not missed a possible solution?
• Are there any patterns?
• How might I describe the pattern?
• How does the pattern help me to answer the question?
• Does my solution answer the question? How could I check?
• Is there another possible answer or way to solve it?

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 solution? Does it match all the conditions?
• Can I be sure that I have not missed a solution?
• 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? Which strategy might I use to solve a similar problem next time?
• Have I considered all possible cases (ages)?