Maths Week Scotland 2026 - Challenge 3 - Rectangles

Challenge 3 is all about rectangles.

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:

This problem is all about rectangles.

This design is made of dominoes (1 × 2 rectangles).

How many rectangles (of all sizes) does the design contain?

• Think about all the different sizes of rectangles

• Remember that rectangles can overlap each other.

• Remember that any shape with four sides and four right angles is a rectangle.

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

Step 1

Look at all the different possible sizes of rectangle that can be made. Count up the number of rectangles of each size:

• twelve1 × 2 rectangles
• six2 × 3 rectangles
• two2 × 4 rectangles
• two2 × 5 rectangles
• two2 × 6 rectangles
• two 3 × 4 rectangles

Don't forget, there's also the whole rectangle of the design: one4 × 6 rectangle.

There are also four2 × 2 squares. Squares have four sides and four right angles, so they also count as rectangles.

Step 2

Now we can add the total number of each size of rectangle together:

12 + 6 + 2 + 2 + 2 + 2 + 1 + 4 = 31

There are 31 rectangles in total in the design.