Rolling That Cube

My dice has inky marks on each face. Can you find the route it has taken? What does each face look like?

Path to Where?

Path to Where?

Yesterday morning, I went for a walk.
Here is a picture which shows the path that I took, looking from above:

Can you describe the shape of the path I took?
Can you imagine where I could have been to walk like this?

In the afternoon I walked a different route. This is what it looked like from above:

Can you tell a story of where I could have been this time?

At the weekend I went for another walk.
This picture shows the path, again looking from above:

What is the shape of the path this time?
Where could I have been for my path to look like this?

Why do this problem?

This problem has two main purposes: to introduce children to recording plan views and to give them the opportunity to think creatively in maths. A good way to introduce this problem might be to invite the children to work in pairs and set up two markers, either in the playground or school hall. They could make up two different routes between the markers and draw them on paper.

Key questions

What sort of route might be the shortest?
What could make you take one of the right angle bends?
What could make you take a really twisty path?

Possible extension

They could then join with another pair and challenge each other to match a walked route with the correct drawing.

Possible support

Encourage children to work with a partner so they can talk their ideas through.