Tennis costs

Achievement objectives

NA4-4: Apply simple linear proportions, including ordering fractions.

NA4-9: Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns.

Required materials

See Materials that come with this resource to download:

• Tennis costs activity (.pdf)

Activity

Charlie plays tennis, with one ladder competition day each week.

It costs $70 for the season’s subs, and his mother drives him 10 km each way to the tennis club (running costs for the car are 70 cents per km).

• If the season runs for 14 weeks, what is the cost of competing in this tennis club ladder?
• If he finds a way to share transport with another player (so his mother only needs to take him every second week), what would the cost for the season become?
• Are the savings worthwhile?

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 it in pairs or small groups.

• Do I understand the situation? (Students may need background information about finding total costs by multiplying with unit rates.)
• What is the cost? How do you work them out? Which costs are fixed, and what costs vary?
• What information has been given, and what more information might be needed?
• Can I anticipate what the total cost will be? Can I anticipate the cost difference if transport is shared?
• Does this look or sound like a problem I have worked on before? What kind of problem is this?
• What will the answer look like? (A total cost for the 14 weeks and a cost with shared transport factored in. The costs are supported by clear working.)

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? (Rates are integral to the problem.)
• How could I show this problem using numbers, equations, pictures, graphs, tables, or materials? (A ratio table is a good strategy to use.)
• What strategies can I use to get started?
• How much change in the total cost is shared transport likely to cause? How do you know? Can I make an estimate?
• 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.

• Have I shown my working in a clear, systematic way?
• Does my answer seem correct? Is it close to my estimation?
• How could I make sure that I haven’t missed anything?
• Do the costs seem reasonable? Is sharing transport worthwhile? Is there a downside to sharing transport?
• Do my results look the same or different from others? Why could this be?
• Is there another possible answer or way to solve the problem that is more efficient?

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 cost difference between full and shared transport?
• Have I shown clearly how the costs were found?
• How would I convince someone else that my calculations are correct?
• Is there some mathematics that I need to learn?
• What does my answer mean for people who want to share transport costs?