Teaching mathematics
Teaching mathematics

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

Free course

Teaching mathematics

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?

Described image
Figure 19 Tins of paint

Activity 15 Reflecting

Timing: Allow 5 minutes

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.

Discussion

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.

TM_1

Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to university level study, find out more about the types of qualifications we offer, including our entry level Access courses and Certificates.

Not ready for University study then browse over 900 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus