Proportional problem 3: Paint
A particular shade of green is made by mixing 3 litres of blue paint with 5 litres of yellow paint (Figure 23).
How much yellow paint is needed to make this shade of green if you only have 2 litres of blue paint?
Activity 15 Reflecting
Look at the learner’s incorrect response below.
How can you explain the thinking behind this approach?
- There are 3 litres of blue and 5 litres of yellow paint.
- So, there is a total of 8 litres of paint needed.
- There are 2 litres of blue paint.
- So, to make the 8 litres, 6 litres of yellow paint are needed.
This strategy is known as the constant sum strategy. This can be easily tackled using examples for which this strategy is impossible. For instance, if the question had asked ‘How many litres of yellow paint is needed for 12 litres of blue paint?’, the total sum could not have been consistent.
In this particular example, discussions about proportionality and the need for consistency in order to preserve the particular shade of green, may support learners.