# Visualisation, Maths and Kids

Visualising is a great tool when we are solving problems. We can create an image of a situation to make sense of it. Sometime we visualise to explore “what will happen if. . . .?”

Visualising helps kids:

• to explore a model
• to dive into a problem

Visualising to explore a model is particularly useful in situations when the situation is physically unattainable. The situation may not be possible to see for a purpose, such as a maths task in school, where the purpose it to test pupils skills in solving problems related to 3D object.

Cubes within Cubes
We had interlocking cubes (all the same size) in 10 different colours, up to 1000 of each colour. We started with one yellow cube. This was covered all over with a single layer of red cubes:

This was then covered with a layer of blue cubes. Then came a layer of green, followed by black, brown, white, orange, pink and purple for as long as there were enough cubes of that colour to cover the layer that came before.

The unused cubes were put away. The many-layered cube was then broken up and each colour made into cubes. These were just of the one colour and the largest cubes possible made. For example, the red layer made three 2×2×2 cubes with two 1×1×1 cubes left over, whereas the larger layers made much larger cubes as well as smaller ones.

• What colour was the largest cube that was made?
• Which colour was made into the most cubes including the 1×1×1 cubes?

In this problem, it is not possible to see inside a large cube. It is not possible to see the centre of the cube and the surrounding layer at the same time. You need to think in stages and then you visualising strategies to solve the problem.

Go here to play Frogs where the idea is to make the frogs and toads swap places using as few moves as possible.You can try simple visualisation games with your kids. Use a sequence of block in four different colours and ask your child to imagine what would happen if you turn it upside down.

• What would the sequence of colours be from top to bottom? Or from bottom to top?
• Change the order of the blocks, or insert a new colour in the middle.

You can turn the blocks around behind your back or under a cloth.Or you can imagine a clock on the wall and the long hand is pointing to 4 and the short hand between 11 and 12.

• What time is it?
• And what happens if you imagine that there is a mirror behind you and you see the clock in the mirror?
• Or change to a digital clock?