Why do this
problem?
This problem gives work on percentages in an interesting
and challenging way. It also gives you an opportunity to
discuss different ways of estimating and therefore shows
learners how expressions which look very different can give
very close answers.
Possible approach
You could start by showing the group the picture of the
hepta-tree and invite them to give a quick response as to
which ball they think has the highest value and which one the
smallest. Ask them to estimate the value of each ball in
pairs and encourage several pairs to share their method with
everyone. This will bring out the fact that actually the
balls have very similar values.
After this they could work in pairs on the problem itself,
possibly using
this
sheet (which lists the expressions on the balls).
Learners are likely to need pencil and paper or a
mini-whiteboard and pen, and possibly a calculator.
At the end of the lesson encourage the group to discuss the
problem. Finding out how each pair approached it could be
very useful as learners will gain from seeing what others
have done. By sharing calculation strategies, children's
understanding of the relationship between percentages,
fractions and decimals will be deepened and you will be able
to assess how comfortable they are with this area of
mathematics.
Key questions
What do you notice when you estimate the value of each ball?
How could you work out the exact value of this ball?
What do you notice about the numbers you have found?
How do you know which is the highest/lowest number?
Possible extension
Learners could create more percentages like the ones on the
hepta-tree which look different but have very close answers.
These could range like the ones in the problem or approximate
to another number. It would be interesting to talk to children
about how they were coming up with the percentages.
Possible support
Using this sheet
will help children organise their calcuations and it may be
appropriate for some to use a calculator.