Here is a rectangle made from squares. What do you notice? What do you wonder?

What are the dimensions of each square? The shape was built outwards, starting with the smallest squares. What dimensions of square would we need to add next? Where would we add it?

In the picture below, three congruent rectangles have been made in different ways with red and blue bricks. The blue bricks are all arranged pointing up and down. The red bricks are arranged going across. If we stick to this rule where blue bricks point in one direction and reds in the other, how else could you make this rectangle?

You might like to explore longer rectangles – this is the same size rectangle as five blue bricks, but we could make rectangles from six, seven or even more blue bricks. The bigger the rectangle you start with, the more ways there are of making it from a mixture of reds and blues in this way. Is there a pattern?

Here are four shapes made out of Lego. Which one doesn’t belong?

Could you make other Lego shapes that belong in a group with some of these ones? Could you make other groups of Lego shapes? Could you make shapes that don’t belong in your groups?

Here is a pattern made from red and white bricks. What do you notice? What do you wonder? Can you figure out how the pattern might have been made? Can you figure out how the pattern might continue?

On Day 19 the challenge was to find all possible pentominoes – the shapes made from 5 squares. Spoilers below – go and try the task first if you want to have a go for yourself.

Here are the twelve possible pentominoes, made out of lego. Some of them have been fitted together to make an enlargement of one of the pentominoes.

Can you make your own set of pentominoes? Can you make enlargements of any of the other shapes? Can you make a rectangle that uses all the pentominoes?

Here is a large square of Lego bricks. What do you notice? What do you wonder?

Can you see any smaller squares in the large square? Can you see any half-squares? If this was the fourth pattern in a sequence, what might the fifth one look like?

Here are two shapes made from Lego. What’s the same? What’s different?

Both shapes use 20 red bricks to make the border. What other shapes can you make with a border made from 20 red bricks? How many yellow bricks would you need to fill in the interior of your shapes?