Why do this
problem?
This problem is a good example of the use of a "variable"
to represent an unknown quantity so provides useful material
when introducing algebra. It also involves working out
proportions of quantities so can be used while doing work on
ratio and proportion. "Cooking mathematics" links well to work
on proportionality.
Possible approach
You could start by looking at the problem as given with the
whole group. Using some balances to demonstrate how the weight
of the eggs can be used as a measure out the other ingredients
might help some of the class to understand the setting better.
Alternatively, you could begin by getting the class could make
the cakes according to the recipe. No weighing, just balancing,
required. However, if you want to make the finished result look
like the illustration you will need to reserve six cherries -
twelve halves - to put on top of the cakes.
After an introduction to the problem, learners could work in
pairs so that they are able to talk through their ideas with a
partner.
At the end of the lesson you could discuss the different
methods by which the answer was found. Did some learners list
the ingredients as "egg weights" or find the total weight of
the mixture first? Did some pairs solve the problem by using
trial and improvement? If you are using the problem to
introduce, or extend learners' understanding of unknowns, it
might be an appropriate time to use a letter or other symbol to
represent the weight of an egg.
Key questions
How can you find out how much mixture there is altogether?
How many "egg weights" were used of each of the ingredients?
How many "egg weights" were used in the recipe?
How can you find out how much mixture there was?
How can you find out how much of each ingredient there was?
Possible extension
Possible support
Learners might like to try the problem
Blackcurrantiest first.