This workshop is aimed at practicing the numeracy encountered when baking/cooking in a kitchen. The end recipe in each section is real, making this a good maths exercise to do at home, with tasty results.

**Please make sure you have adult supervision when baking.**

If you have a favourite family recipe, passed down through the generations, the chances are, the weights will be in pounds (lb) and ounces (oz) - This is known as the *'Imperial System'*. Nowadays, most kitchen scales and equipment use the *'Metric System'*, kilograms (kg) and grams (g). So how do we convert imperial measurements to metric?

Nowadays we tend to have an internet-enabled device to hand, a quick search and you can easily find out how many grams are in 8 ounces. However, what if you are having a birthday party and need to bake a cake, but the internet has gone down?

If you are using a recipe that lists lbs and oz, you will need to convert them all into oz. To do this you need to know that 1lb = 16oz.

Example: A recipe needs 1lb 6oz of flour. How many ounces is this? 1lb = 16oz so 1lb 6oz = 16oz + 6oz = 22 ounces

Work out how many ounces are in each of the following

- 3 lb
- 1
^{1}/_{2}lb ^{3}/_{4}lb- 4 lb 10 oz
- 2
^{1}/_{8}lb

Now you have a recipe where all the measurements are in ounces. How do we convert this to grams? If we were to be totally accurate, we would use 1oz = 28.35g. However, because we are in a kitchen rather than a laboratory, and because we will use the same value throughout the recipe, it is simpler and more common to use 1oz = 25g

Example: A recipe needs 4oz of sugar, how many grams is that? Using 1oz = 25g, 4oz = 4 x 25g = 100g

Using 1oz = 25g calculate how many grams are in each of the below:

- 2 oz
- 3
^{1}/_{2}oz ^{1}/4 oz- 5
^{3}/_{8}oz - 1 lb 2 oz

Now, let's put all this to the test with the below recipe.

- Preheat the oven to 180°C and grease a 20cm (8in) cake tin.
- Break up 9oz of plain chocolate into a heatproof bowl and place it over simmering water to melt
- In a large bowl, beat together 4oz of butter and 3
^{1}/_{2}oz of caster sugar until light and fluffy - Add two-thirds of the now, melted chocolate, along with
^{1}/_{2}lb of ground almonds and 4 egg yolks. Beat the mixture well - In another bowl, whisk 4 egg whites until it forms stiff foam peaks. Now, fold this into the cake mixture.
- Transfer the mixture to the baking tin, level off the surface, bake for 50-55 minutes.
- Leave to cool for 5-10 minutes before removing it from the tin onto a cooling rack
- Whilst cooling, put 2oz of butter with the remaining melted chocolate in a pan. Heat gently, stirring the mixture constantly until melted. Then pour over the top of the cake.
- Decorate with 1oz of white chocolate shavings or sliced almonds.

- The first thing you will need to do, is work out what ingredients are needed (there are 6 different ingredients in total).
- How much of each ingredient is required?
- Now, how many grams of each? Remember to use 1oz = 25g.
- Test your answers by following the above recipe - weigh everything (except the eggs) in grams as calculated.

When baking, you generally start with a recipe that makes a set amount. What if you want to make more or less than the set amount?

To do this we need to know about scaling. This involves taking a recipe and increasing or decreasing the measurements to make the amount we want.

How much do we need to increase or decrease the recipe?

Example: a recipe makes 12 cupcakes but we need 24. This means we need to double the recipe.

How much do we need to increase or decrease each of the below recipes?

- A recipe makes 24 cookies, we need 12
- A recipe makes 8 eclairs, we need 24
- A recipe needs 3 eggs but we only have 2
- A recipe needs 1kg of flour but we only have 750g
- We need 36 cupcakes but the recipe makes 24

Now we know what we need to do to the recipe we need to work out how that changes the ingredient amounts. The main thing to remember is that we need to change all the amounts equally.

Example: If we need to halve a recipe, we need to halve the amount of **each** ingredient (divide each amount by 2)

One major problem when scaling baking recipes is checking if it's possible and whether we have enough of all the ingredients. There's no such thing as half an egg for example, so it will not be possible to correctly scale a recipe that requires this.

Work out how much of each ingredient would be needed for the below:

- A recipe requires 800g of flour, 400g of sugar and 400g of butter for a large crumble. We only want to make a crumble halve the size.
- A recipe requires 3 eggs, 600g of flour and 300g sugar, but we only have 2 eggs and want to make as much as we can
- A recipe needs 250g of flour, 100g of butter and 2 eggs. We want to make three times the amount
- We need to multiply a recipe that needs 100g of flour, 200g of ground almonds and 50g of sugar by 150%
- A recipe needs 2 eggs, 400g of flour and 200g of sugar. We want to make as much as possible with what we have, which is 6 eggs, 1kg of flour and 750g of sugar

Now, let's put all this to the test with the below recipe.

Note: tsp = teaspoon and tbsp = tablespoon

- 3kg unsalted butter
- 4.5kg brown sugar
- 20 eggs
- 20 tsp vanilla extract
- 4.5kg plain flour
- 80 tbsp cocoa powder
- 10 tsp bicarbonate of soda
- 15 tsp baking powder
- 20 pinchs of salt
- 3kg dark chocolate chips
- 3kg milk chocolate chips
- 3kg white chocolate chips

The problem with this recipe is that it has come from a bakery, therefore the quantities listed are designed to make approx. 600 cookies in an industrial-sized kitchen.

To use this recipe at home, for a more suitable batch size, we will need to scale it down.

- First of all we need to work out the minimum number of cookies we can make. This will be determined by the eggs - how many cookies would a scaled-down recipe of 1 egg make?
- To have the rest of the amounts scale down to match using just 1 egg, you will need to divide all the quantities by 20 (the original number of eggs)
- Ready to test your now scaled down recipe? The instructions for making these cookies are below.

- In a bowl, whisk together the butter and sugar until they are light and fluffy.
- Add the egg and vanilla and mix well
- In a different large bowl, mix together the flour, cocoa powder, bicarbonate of soda, baking powder and salt
- Stir the first mixture into the second.
- Fold in all three different chocolate chips
- Cover and refrigerate for at least 24 hours - this step makes the cookies softer
- Place the cookie dough somewhere at room temperature for 20-30 minutes
- Pre-heat the oven to 170°C/Gas Mark 3 and line a couple of large baking trays with greaseproof paper or baking parchment
- Split the mixture and roll into 30 evenly sized balls.
- Place the balls on the trays with plenty of space to spread/expand
- Bake for 12-14 minutes. Transfer the cookies on their baking parchment to a wire cooling rack.
- Enjoy!

There is one other form of measurements used in cooking/baking that you may encounter, these are called cups. These measure ingredients by volume instead of weight.

So, how large is a cup?

If you look around your kitchen, you will find lots of different shapes and sizes of 'cups'. Which should you use?

The answer is, it depends on the recipe. It is easiest if a recipe includes all ingredient values in cups. Why?

As long as all the measurements are in values of cups it doesn't matter what size the cup is, as long as you use the same one for all of them. This is because we are keeping the proportions the same.

Example 1: A recipe requires 2 cups of flour, 1 cup of butter and 1 cup of sugar. All ingredients are measured in cups and therefore we can use any cup.

Example 2: A recipe requires 1 cup of flour, 1 medium sized egg and ^{1}/_{2} cup of milk. This cannot just use any size of cup because the egg is a set value not a cup measurement

Just remember, the larger the cup you choose the more recipe you will produce overall

Which of the below recipe(s) could we just use any cup for? If not, why?

- A recipe requires 3 cups of sugar, 1 cup of syrup and 2 cups of oats
- A recipe requires 1 cup of plain flour,
^{1}/_{4}cup of butter and 1 tsp of baking powder - A recipe requires 1 cup of sliced potatoes, 1 tbsp of butter and
^{1}/_{2}cup of sliced mushrooms - A recipe requires 2 eggs,
^{1}/_{4}cup of milk,^{1}/_{8}cup of butter, and ground pepper for seasoning to taste.

So, what if the recipe includes items not measured in cups (like eggs) or you need to make the exact amount specified? For this you need to know the volume of an 'official cup'.

One *legal U.S Cup* used for cooking measurements is 240ml. So, when you need to convert the ingredients to millilitres it would be best to use a jug (especially for calculating part cups) rather than scales or a drinking cup.

Why do we convert to millilitres and not grams? If you are not sure, weigh a cup full of various different objects and compare the results.

Convert each of the below recipe amounts to use millilitres instead of cups

- 2 cups of flour, 1 cup of butter, 50ml of cold water
- 1 egg, 1
^{1}/_{2}cups of plain flour,^{1}/_{4}cup milk ^{1}/_{3}cup of sweetcorn, 1 cup sliced chicken breast, 1 tsp of garlic- 2 cups of pasta per 3 people in 500ml of water, you need to cook pasta for 4

Now, let's put all this to the test with the below recipe.

- Fill a large saucepan
^{3}/_{4}full of cold tap water and place on a hob at maximum setting to boil - Whilst waiting for the water to boil, drizzle 1 tbsp of olive oil into a large sauté pan (a frying pan with lid will work instead)
- Add 1 tsp of crushed garlic to the oil, along with 2 tsp of Italian herbs and 3 cups of beef/quorn mince to the oil and heat on medium. Stir every couple of minutes to prevent sticking
- When water comes to the boil carefully add in 2 cups of pasta and turn down to a simmer
- Add 1
^{1}/_{2}cups of sliced mushrooms and^{2}/_{3}cup of sweetcorn to the sauté pan and stir for two minutes - Pour 500ml of tomato passata into the sauté pan, along with a tin (approx. 400g) of peeled plum tomatoes and a tbsp of tomato pureé
- Simmer the bolognese until the pasta has cooked to required softness.
- Serve and enjoy

- As with any recipe you need to get the ingredients ready first. How much of each ingredient does the recipe ask for (there are 10 ingredients plus tap water)
- As some measurements are in cups, but not all, you will need to convert these to millilitres
- Once ready, give the recipe a go.

If you want to get a thicker bolognese sauce, prepare that first and once the whole thing is simmering, start to boil the water and cook the pasta

In the UK, most of our cooking appliance ovens measure temperatures in gas marks or °C (degrees Celsius). This means that cookbooks produced here give oven temperatures in both.

Some countries, such as the US, use °F (degrees Fahrenheit) on their appliances and recipes.

To convert °F to °C you will need to know the formula:

**(°F - 32) x ^{5}/_{9} = °C**

For example, if we needed to convert 50°F to °C it would be: (50°F - 32) x ^{5}/_{9} = 10°C

Use the above formula to calculate the following temperatures

- 100°F in °C
- 300°F in °C
- 450°F in °C
- 180°C in °F