When children are curious about why something works, multiple ways of representing the same concept or idea can offer insights and deepen understanding. The problems below will give your learners opportunities to consider different representations, whether they are created by the children themselves or by someone else.
problem
Favourite
Triangle or no triangle?
Age
5 to 7
Challenge level
Here is a selection of different shapes. Can you work out which ones are triangles, and why?
problem
Favourite
Birthday sharing
Age
5 to 7
Challenge level
It's Sahila's birthday and she is having a party. How could you answer these questions using a picture, with things, with numbers or symbols?
problem
Favourite
Catrina's cards
Age
5 to 7
Challenge level
How would you find out how many football cards Catrina has collected?
problem
Magic crosses
Age
7 to 14
Challenge level
Can you find examples of magic crosses? Can you find all the possibilities?
problem
Favourite
Name that triangle!
Age
7 to 11
Challenge level
Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?
game
Favourite
The remainders game
Play this game and see if you can figure out the computer's chosen number.
problem
Favourite
Remainders
Age
7 to 14
Challenge level
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
list
Multiple Representations
Age
11 to 18
Challenge level
Using different representations helps students to think mathematically.