The purpose of this activity is to engage students in solving a problem involving fractions and proportional reasoning.
The background knowledge and skills that need to be established before and/or during this activity are outlined in the diagram below:
- Using diagrams to represent fractions
Shade in 1/4 on this diagram.
- Finding fractions of a value
Find 1/3 of 210.
- Using diagrams to add fractions
Shade in the following fractions to find their sum. 1/3, 1/2.
- Solving word problems
Jane ate three times as many cherries as I did. I ate 14. How may did Jane eat?
- Solving word problems involving proportion
I started my journey on a full tank of petrol, and when I ended it, the gauge read 3/4 full. It took 9 L of petrol to fill up again. How much fuel does the tank hold?
This activity may be carried out with step by step guidance, or by allowing the student to follow their own method of solution. The approach should be chosen in sympathy with students' skills and depth of understanding.
The arithmetic approach (show more)
- The student is able to use a value to divide onto the appropriate proportions in order to solve the problem.
Prompts from the teacher could be:
- How are you going to go about solving this problem? Can you choose a value for the profit to divide between the men?
- If Des had a share, how much would that be?
- What would the profit had to have been for Des to also have a share?
- What are the proportions of the profit shared between all four men?
The conceptual approach (show more)
- The student is able to divide an unknown value into appropriate proportions in order to solve the problem.