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Squeezy maths

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By John Dabellteacher, writer and Ofsted-trained inspector

Discover ways of drawing the last bit of learning out of simple KS2 concepts

Number 4

Teaching maths involves a lot of squeezing. It’s like a tube of toothpaste. There’s more in there than you think and sometimes you have to squeeze really hard to get it all out. How could you ‘squeeze’ a concept? Let’s think about something really simple – for example, the number 4. These activity ideas are ideal for challenging more able children, in particular.

Using the number 4

There are a number of starting points: the number 4 is an even number, it is a natural number (a positive integer), a composite number (a number with more than two factors), and a square number (since 2 × 2 = 4). We could write the number 4 in different ways, such as a Roman numeral or in tally form. What other ways might there be?

We could leave things there, but we would be wasting a lot of toothpaste still. There’s still more to squeeze and find out. For example, try the following challenge:

Can you use a combination of just four 4s and any operations to write the number 4?
For example, to make the number 4 you could do this calculation: 4 × (4 – 4) + 4 = 4

To help demonstrate this without the brackets, ask the children to write each part of the calculation – ‘4 ×’, ‘4 – 4’ and ‘+ 4’ – on separate pieces of paper or card. These can be used to help the children work out each part of the sum separately and then strung together to make the whole calculation.

You could go even further and extend the challenge to other numbers:

Write the numbers from 0 to 10 using just four 4s and any operations.
For example, 0 = 4 + 4 – 4 – 4, and so on.

See the Activity sheet, ‘4 × 4 challenge’, for instructions plus solutions. Encourage children to work slowly, step by step, in order to reach the result. For example, the number 1 can be reached via the calculation 4 ÷ 4, meaning that one way to reach the number 2 is (4 ÷ 4) + (4 ÷ 4).

More number 4 ideas

You could use the number 4 as a springboard for questions related to things we see around us every day, to improve observational skills. For example:

What number is opposite 4 on:
  • a clock? (10)
  • a dice? (3)
  • a dartboard? (16)

If you have recently covered decimal fractions, you could also use the number 4 as an opportunity to remind children of the concepts:

What numbers are bigger than four but less than five? For example, 4.1, 4.2, 4.56, 4.80, 4.999, and so on.

Number 4 magic

There are also creative investigations involving just the number 4. For example:

Think of any number and write it out in words. Then, count the number of letters it contains and write that down in words on the next line. So:
  • twenty-eight (11 letters)
  • eleven (6 letters)
  • six (3 letters)
  • three (5 letters)
  • five (4 letters)
  • four (4 letters)

Do you always arrive at the number four? Can you explain why?

Squeezy maths is about making the most of mathematical moments, extracting opportunities out of a concept or problem and extending opportunities to challenge and inspire maths thinking and talk. Next time you look at an activity, think about ways to squeeze all the maths out of it!

Number 4 quiz questions

Invite your class to research the answers to these number 4-themed quiz questions.
  • What are plus fours?
    Loose baggy trousers
  • The word ‘four’ has four letters. Can you find another number whose number of letters is equal to its value?
    There aren’t any
  • Why is the number four considered unlucky in Chinese culture?
    The Chinese word for four sounds like their word for ‘death’