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Proof through words - number

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In this feature for Primary teachers, we offer a selection of numerical tasks that lend themselves to 'proof through words'. In the accompanying article, we outline three essential features of proof and illustrate what they might look like in the context of words, as opposed to algebraic symbols. The tasks we have included in this feature will help develop your learners' understanding of what constitutes a proof, so that they are well equipped on the mathematical journeys ahead.

You can watch a recording of the webinar in which we discussed the mathematical thinking which can be prompted by these activities.

You may also like to take a look at our Proof Through Words - Geometry feature which offers similar experiences but in a numerical context.

article

Why dialogue matters in primary proof

In this article for Primary teachers, Ems explores three essential features of proof, all of which can be developed in the context of primary mathematics through talk.

Strike it out

problem

Strike it out

Age

5 to 11

Challenge level

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

problem

Even and odd

Age

5 to 7

Challenge level

This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?

problem

Two numbers under the microscope

Age

5 to 7

Challenge level

This investigates one particular property of number by looking closely at an example of adding two odd numbers together.

problem

Next-door numbers

Age

5 to 7

Challenge level

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?

problem

Unravelling sequences

Age

7 to 11

Challenge level

Can you describe what is happening as this program runs? Can you unpick the steps in the process?

problem

An easy way to multiply by 10?

Age

7 to 11

Challenge level

Do you agree with Badger's statements? Is Badger's reasoning 'watertight'? Why or why not?

problem

Mathdoku

Age

7 to 11

Challenge level

Complete the Mathdoku grid using the clues. Can you convince us that the number you have chosen for each square has to be correct?

problem

Take three numbers

Age

7 to 11

Challenge level

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

problem

Neighbourly addition

Age

7 to 14

Challenge level

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

problem

Three neighbours

Age

7 to 14

Challenge level

Take three consecutive numbers and add them together. What do you notice?