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.

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

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### Take one example

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.

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### Next-door Numbers

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

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### Break it up!

In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?

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### Strike it Out

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

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### Sitting round the party tables

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

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### The add and take-away path

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?

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### Count The Digits

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

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### What was in the Box?

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?

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### Always, Sometimes or Never?

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

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### Ring a Ring of Numbers

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

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### How Odd

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?

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### School fair necklaces

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