Planning tool

Students can:

• write an expression or equation from a worded problem using pronumerals
• manipulate pronumerals in expressions mathematically and recognise the relationship between variables and how they change
• take a systematic approach to make algebra achievable and meaningful
• apply arithmetic rules to expressions involving variables.

Some students may:

• believe that pronumerals stand for a specific amount or unit of measurement.
• confuse the variable 'x' with the multiplication symbol.
• not recognise that an algebraic expression can be an answer to a problem; they feel that there should always be a numerical answer.
• think that 3x + 2x = 5x² or that 3x × 2x = 6x.
• add together unlike terms. For example, 2x + 3y ≠ 5xy or 2x + 7 ≠ 9x.

The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention

• We are learning how to do maths with letters (variables).
• We are learning how to transform everyday scenarios into mathematical expressions.
• We are learning that the rules we already know about numbers also apply to letters (variables).

Why are we learning about this?

Why? Because mathematics is so much more than numbers. Once we can describe our world with mathematical symbols, we can perform all kinds of interesting calculations about it and make predictions about the future.

What to do

1. Go to the place in your house where the fruits and vegetables are. Wherever that is, I want you to choose a letter to represent that place. Is it the fridge? Then we will call it ƒ. Is it the pantry? We’ll call that p. Maybe it’s the garden; you can call that g. We’ve now created our first ‘variable’.
2. Make a list of three of the fruits or vegetables you find there, for example, 3 apples, 2 cucumbers and 4 tomatoes.
3. Now, instead of referring to them by their name, I want you to select a single letter for each instead. We will also use a + symbol to show that each of vegetable or fruit is on our list. The example above can be shortened to: 3a + 2c + 4t.
4. Let’s combine this information into a mathematical sentence. I’ll do it first. In my fridge there are 3 lemons, 5 onions and 4 potatoes. So, I will turn this information into the mathematical sentence: ƒ = 3l + 5o + 4p
5. You could try repeating this for other parts of your house, for example, my wardrobe has 5 shirts, 3 jeans and 4 T-shirts:
   w = 5s + 3j + 4t

Now that we know how to create mathematical sentences, we need to practise the rules of manipulating them.

Consider this word problem

Raj opens his fridge (ƒ) and finds 3 litres of cow’s milk (c) inside. So ƒ = 3c

A little later, Raj’s mum returns from the supermarket with an extra 2-litre bottle of cow’s milk, along with 2 litres of soy milk (s) and 1 litre of oat milk (o).

Can you update the mathematical sentence above to include the new items?

If you're not sure, this is how I did it.

I did this in two steps.

1. ƒ = 3c + 2c + 2s + 1o
2. ƒ = 5c + 2s + o

Two important rules are illustrated in the example above.

• Firstly, we can only add things together if they have the same letter. We can’t describe Raj’s fridge as ƒ = 8cso because then we wouldn’t know how many litres of each type of milk Raj has.
• Secondly, we can shorten our sentences even more, by removing the number 1 from the front of variables. Whenever you see a variable on its own, there is an invisible 1 hiding in front of it.

Your final task

Before someone at your house goes to the shops, I want you to create a new mathematical sentence about some of the items in your fridge. Then, when they return, I want you to update that sentence to show which items have been increased and which new items have been added.

Success criteria

• I can describe the items I find in different parts of my house using variables and mathematical sentences.
• I can update my mathematical sentences with new information and follow the correct rules about adding variables.