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Making Pathways

Age 7 to 11
Challenge Level

Making Pathways

We have twelve paving slabs of each different colour.
There are three sizes of slabs for each particular colour which are all the same width. 


The blue has four of one unit length, four of nine unit length and four of twenty-four unit length.
The green has four of one unit length, four of seven unit length and four of twenty-five unit length.
The red has four of one unit length, four of five unit length and four of twenty-nine unit length.
The lengths cannot be broken into smaller pieces.

Challenge 1

If we were thinking of making a path of length 18 in each colour then we might have:

blue                   9 + 9                
green 7+7+1+1+1+1 is counted the same as
red     5+5+5+1+1+1 is counted the same as

For this challenge you cannot break the paving slabs up into smaller pieces.

Can you make three paths of 22, one in each of the three colours?
Now try three paths of 40, one in each of the three colours.
Lastly try 64, one in each of the three colours.

Challenge 2

How many different ways can you make 75?  You cannot mix the colours that are in one path.

Challenge 3

Wouldn't it be good to make eight consecutive lengths of paths that can be made out the blue, green and red - but each separately?

It could look something like this, for the consecutive lengths 59, 60, 61, 62, 63, 64, 65 and 66.
But this is not a solution as it cannot be made without breaking some up into smaller pieces which is not allowed:


Your challenge is to make eight consecutive lengths of path that can be made of each colour separately.

Why do this problem?

This activity challenges pupils to use all four operations and their knowledge of number facts. It is a great opportunity to develop problem-solving skills as the calculations on their own are not enough.

Possible approach

The introduction needs to emphasise the rules of the situation, clearly stating what is allowed. Introduce the activity by working together through the example shown at the start of challenge 1.

If other examples are needed before learners set off on their own, then totals of 30, 31, 33, 34, 35, 42, 43, 46, 48, 49, 50, 51, 52, 53, 58, 59, 60 and 61 could be used as well.

Key questions

Tell me about how you are doing this.
Can you tell me why this is correct?
How are you making sure you obey the rules?

Possible extension

The pupils could set up their own challenges for different slab lengths.

Possible support

Some children may need some connecting cubes to represent the long slabs.