Maths Week Scotland 2024 - Challenge 1 - Dominoes

Challenge 1 is all about working out the dimensions of a domino within a larger rectangle.

Maths teacher Chris Smith and pupils from Grange Academy are here to explain.

The Maths Week Scotland Daily Challenges have been set by the Scottish Mathematical Council.

So here's the challenge:

One outer rectangle is filled with smaller rectangles.

All the smaller rectangles are dominoes.

The dominoes are special rectangles that are twice as long as they are wide.

The length of the pink domino is 24 cm.

What are the dimensions of the blue domino?

• Try drawing it out and adding the measurements you know.
• How do the sides of different rectangles compare to each other?
• Can you use the outer rectangle to find your answer?

Worked out the answer? Here's how you can do it.

Step 1

If the pink domino has a length of 24cm, then we know its width will be 12cm.

Step 2

The three dominoes underneath the pink domino line up perfectly with its length.

So the width of each of these will be 24 divided by three, which is 8 cm.

Step 3

The length of each of these rectangles will be double 8cm.

2 x 8cm = 16cm

Step 4

We can now work out the width of the outer rectangle by adding the width of the pink domino, 12cm, and the length of the dominoes underneath - 16cm.

12cm + 16cm = 28cm

So, the width of the outer rectangle is 28cm.

Step 5

We can divide the width of the outer rectangle by four to find the width of the blue rectangle.

28cm ÷ 4 = 7 cm

The width of the blue rectangle is 7cm.

Step 6

And once we know the width is 7cm, we can double 7cm to find the length.

7cm x 2 = 14cm

Now you know the dimensions of the blue domino are 14cm by 7cm.