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.
problem
Favourite
Break it up!
Age
5 to 11
Challenge level
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?
problem
Favourite
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
Favourite
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.
problem
Favourite
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?
problem
Favourite
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?
problem
Favourite
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?
problem
Favourite
Always, sometimes or never?
Age
5 to 11
Challenge level
Are these statements relating to odd and even numbers always true, sometimes true or never true?
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
Favourite
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.
problem
Favourite
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?
problem
Favourite
School fair necklaces
Age
5 to 11
Challenge level
How many possible symmetrical necklaces can you find? How do you know you've found them all?