The purpose of this activity is to engage students in solving a problem involving fractions and proportional reasoning.
This activity assumes the students have experience in the following areas:
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.
Three men run a business together.
The proportion of the profit they each get at the end of the month is based on the proportion of the funds they have invested in the business.
The April profit is shared out so that Al gets one third, Bob gets one half and Chuck gets one sixth.
In May, Des joins the group, investing half as much as Bob invested.
What share of the profit can Des expect to get?
The following prompts illustrate how this activity can be structured around the phases of the Mathematics Investigation Cycle.
Introduce the problem. Allow students time to read it and discuss in pairs or small groups.
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.
Allow students time to work through their strategy and find a solution to the problem.
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.
The student chooses a fixed amount that is invested at the start of the business and divides that amount among Al, Bob, and Chuck according to the fractions given. They allocated Des half or Bob’s amount to get a new total and works out the fractions of the new total for each person.
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The student works abstractly with fractions to determine that the new whole is 1 ¼ of the former amount when Des joins the business. They then assign an amount of profit and use the fractions to establish each person’s share of the profit.
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