### Pumpkin Pie Problem

Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies?

### The Tree and the Greenhouse

Mum, Dad, Tim and Jill moved into a new house. If they cut down the big tree, will it miss the greenhouse?

### Orange Drink

A 750 ml bottle of concentrated orange squash is enough to make fifteen 250 ml glasses of diluted orange drink. How much water is needed to make 10 litres of this drink?

# Cherry Buns

## Cherry Buns

Sam's grandmother has an old recipe for cherry buns.

To make them, she weighs two eggs. Then she takes the same weight in flour, and in sugar and in butter. She mixes all this together and then she adds half the weight of the $2$ eggs in chopped glace cherries.

She has enough mixture to put $45$ grams in each of $12$ paper cake cases.

What was the weight of one egg?

### 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 to think about how they 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

Learners could try Orange Drink , or Buckets of Thinking or make up some similar problems for friends to try.

### Possible support

Learners might like to try the problem Blackcurrantiest first.