Proof Through Words - Number

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.

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.

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?

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.

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?

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.

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?

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?

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?

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?

Three Neighbours 

Age 7 to 14
Challenge Level
Take three consecutive numbers and add them together. What do you notice?

Neighbourly Addition 

Age 7 to 14
Challenge Level
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?