I find that one of the most difficult concepts for a child in mathematics is to work out the sum they need to do in order to find the answer to a question that’s set in words. I’ve been asked ‘What is the point of algebra?’ or ‘Tell me when I’ll ever use algebra in my life after school?’. The answer to probably both questions is that you’ll use it every day and often without realising it. Every calculation we make involves algebra in one form or another and just because we are not writing out equations, doesn’t mean we’re not doing it. Building on the introduction to algebra in last year’s Olympics Maths Activities, these activities revisit the concept and develop it so that you can use it with KS1 children, right the way through up to Year 6 and the sooner they realise how important and commonplace algebra is, the easier they’ll find it.
Activity One – What’s in the bag?
Year 1 to Year 6
Be able to form number bonds and calculate their answer.
Be able to use prior knowledge to solve a problem where one number is unknown.
Marbles are perfect for this activity but you can use anything uniform such as multilink blocks, ping pong balls etc. Use a cloth bag or anything that can’t be seen through. Show the children you putting 8 marbles into it then adding another 3.
Ask them how many are now in the bag. Get the children to write out the sum on individual whiteboards or paper and show you. 8 + 3 = 11
Do the same but taking out 3 marbles. Now 8 – 3 = 5.
Change now to putting a number of marbles in the bag unseen. Show the children you adding 5 marbles to it then tip the bag out and count the marbles. If there are now 13 marbles, how many were there to begin with?
Ask the children to write out the sum once more and you’re likely to get 8 + 5 = 13. But how did they know to put 8 as the first number? Yes, they’ll have used algebra without thinking about it, to calculate the initial number in the bag.
Repeating the exercise now, ask them to write the sum as the demonstration continues. So this time they need to think of what to replace the unknown number by… suggest ‘n’, add 7 marbles to the bag, tip them out and count 13, so they now have a sum n + 7 = 13. Many will already have worked out how many were in the bag to begin with. Repeat this with subtraction.
Now get the children in pairs to play ‘Think of a number’. One tells the other; ‘I’m thinking of a number, I add/subtract …. and I get …., what is the number I was thinking of?
You should ask the children to write down the sum as it’s spoken.
Can we use this process for multiplication and division too? Ask the children to suggest some examples.
Ask the children to talk with their parents/guardians about times when they might use algebra without knowing it. e.g. ‘I’ve got to be at work for 9 am, if it takes me 20 minutes to get there, when do I have to leave?’ or ‘I need 100g of meat per person for a casserole, how much do I need for four people?’
Activity Two – Number machines
Year 3 to Year 6
Use pictures to help visualise mathematical processes.
Be able to do multi-stage problem solving using a visual process
Show the children a ‘number machine’ and explain how it works; a number is put in one end, the machine performs a mathematical function on it then the answer comes out the other side.
Draw your own, or use the function machine that accompanies the activity and make up cards for numbers and functions to use with it. Begin by placing a number on the input space and a function in the function box then ask for the answer. Gradually increase the level of difficulty for the function before changing the numbers from the input to the output, still using the function cards. Can the children work out the input?
Ask them to write down the sum as it’s performed, finally give them the accompanying worksheet and ask them to write out sums that use the functions and numbers for the output. We’ve deliberately left the function and number boxes blank so you can add your own depending on the age and ability of the children.
Give the children a blank copy of the worksheet and ask them to complete the outputs and functions for a friend to try.
Activity Three – Words Into Sums
Year 3 to Year 6
This activity helps the children to think about the numbers and operations in word problems and
Recognise the required function in word problems
Convert word problems into simple algebra to solve word problems
Write the following word problems on the board and ask the children to tell you if they can see a sum in the words:
My mum gave me £5 to go to the shops to buy some fruit. The cashier gave me £2.65. How much did I spend on fruit?
It’s 35 kilometres from my house to my nan’s, It costs £5 for every seven kilometres by taxi, how much will it cost me to go to see her?
My sunflower grew 15cm on Monday and 12cm on Tuesday, if it’s now 35cm tall, how big was it on Sunday?
Begin by highlighting the numbers in the sentence, then decide whether your answer is going to be bigger or smaller than the number you started with. If smaller, you know it’s likely to be a subtraction or a division, if bigger, then an addition or multiplication.
The best way to get the children started on this is for them to do the reverse of the activity. In other words, give them a simple sum and get them to write a word problem for it. They can then exchange the word problem with a partner and each try to solve them.
Ask the children to write more word problems and bring them in to school. Decide on a ‘top ten’ of the best ones.
For more word problem activities take a look at Collins New Primary Maths Cross-curricular Word Problems