Conjecturing and Generalising at KS1

The "What if..?" questions are such an important part of mathematical thinking. Knowing what to ask means that you understand something about the structure of the problem, and being able to see similarities and differences means you're starting to generalise.

The Add and Take-away Path

Age 5 to 7 Challenge Level:

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

What Was in the Box?

Age 5 to 7 Challenge Level:

This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?

Ring a Ring of Numbers

Age 5 to 7 Challenge Level:

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

How Odd

Age 5 to 7 Challenge Level:

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

Take One Example

Age 5 to 11

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.

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.

Always, Sometimes or Never?live

Age 5 to 11 Challenge Level:

Are these statements relating to odd and even numbers always true, sometimes true or never true?

Sitting Round the Party Tables

Age 5 to 11 Challenge Level:

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Count the Digits

Age 5 to 11 Challenge Level:

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

Break it Up!

Age 5 to 11 Challenge Level:

In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.

School Fair Necklaces

Age 5 to 11 Challenge Level:

How many possible necklaces can you find? And how do you know you've found them all?