A problem that challenges students to consider the effect of
The problem assumes that students understand ratios (they
understand that if $1/3$ is red it does not mean that the ratio of
red to white is $1:3$) and are able to simplify ratios.
A possible start to using this problem in a classroom could involve
asking students to suggest possible combinations of paints A and B
(or C and D) and their suggestions could be written up for all to
It may be useful to provide students with red and white counters so
that they can simulate the effect of mixing the paints. However,
counters must be used with care; students need to understand that
they must have the same overall number of counters for each paint
Possible follow up questions:
- What is the ratio of red to white paint in these mixes?
- Can any of these ratios be simplified?
- Will any of these combinations produce the same shade of
- Can you list the mixes in order as they become paler?
is a follow-up question to this one.