A fair dip

Achievement objectives

NA4-2: Understand the addition and subtraction of fractions, decimals, and integers.

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

Required materials

See Materials that come with this resource to download:

• A fair dip activity (.pdf)

Activity

A year 8 class is making a fundraising stall for the school fair.

They have decided to make chocolate-coated strawberries in white, dark, and milk chocolate and to present these in boxes made from origami.

The goal is to raise at least $250 for the school. They plan to sell boxes of six strawberries for $2.

The local supermarket sells punnets of a dozen strawberries for $2.50 and cooking chocolate for $3.95 per bag.

A bag of chocolate should be enough to coat two dozen strawberries.

The boxes take one sheet of coloured paper (10 cents) to make.

• Is this plan going to work?
• How could it be modified to make this fundraising goal realistic?

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 and the words? (Students may not be familiar with profit and how it is the difference between income and cost.)
• Is all the information needed available to you?
• How are budgets usually created in real life?
• What will my solution look like? (The solution will be a decision about whether or not the fund-raiser will make money and justification for that decision.)

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 strategies can I use to get started? (A table format helps to organise the budget calculations.)
• How will I work out the cost of each ingredient? Will I work out that cost per pack or per number of packs?
• How will I need to adjust the ingredient amounts to match my costings?
• Do I have a sense of the likely solution?
• What tools will I use? (A spreadsheet is an obvious tool to use.)

Take action

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

• Am I recording my workings in a systematic way so others can follow it?
• Does my answer seem correct? Does the budget look sound, and are all the costs included?
• Have I worked out each cost per strawberry, pack, and number of packs correctly? How can I check?
• How does my answer match my original prediction? If not, is there a reason to revisit my calculations?
• Is there another possible answer or way to solve it? Can I be 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 solution? Can I show that the solution is correct? How?
• Are my workings clear for someone else to follow?
• How would I convince someone else that I am correct?
• Could I have solved the problem in a more efficient way? How?
• How might I change the fundraiser so it is profitable? (Consider both costs and pricing.)
• What could I try differently next time, with a similar problem?