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Daily Lego Maths: Day 31

These three squares have the special property that the area of the two smaller squares together is equal to the area of the larger square.

Three squares made from 2 by 2 Lego bricks, arranged so that one edge of each square forms a side of a right-angled triangle. There is a yellow 4 by 4 square and a blue 3 by 3 square. The third square is a 5 by 5 square made up of a 3 by 3 blue square in the top left, with 16 yellow bricks arranged to the right and below to fill in the rest of the square

Can you find some more sets of three squares with this property?
What happens if you arrange them in a triangle?

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Daily Lego Maths: Day 30

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

Squares made from Lego, fitted together to make a rectangle. In the middle are a blue and yellow 1 by 1 square, then a 2 by 2 red square alongside, and continuing outward a yellow 3 by 3, white 5 by 5, blue 8 by 8, white 13 by 13 and blue 21 by 21 squares.

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?

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Daily Lego Maths: Day 29

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?

Three Lego rectangles made from blule and red 4 by 2 bricks. The rectangles are 10 spots across and 4 spots down. The blue bricks are all in 'portrait' orientation and the red bricks are in 'landscape' orientation. Rectangle 1: Blue, blue, a pair of reds, blue. Rectangle 2: blue, a pair of reds, blue, blue. Rectangle 3: pair of reds, blue, pair of reds.

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?

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Daily Lego Maths: Day 28

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

Four shapes made of Lego. Top left: four 2 by 2 white blocks in a square. Top right: four 1 by 4 red blocks in a square. Bottom left: four 2 by 4 red blocks in a rectangle Bottom right: eight 2 by 1 red blocks in a square

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?

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Daily Lego Maths: Day 27

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?

A triangular shape made from white and red 2 by 2 lego bricks on a grey baseboard. The top row has a single white brick in the middle, then each subsequent row has one extra brick down to the bottom row which has 15 bricks. There are single red bricks and inverted red triangles inside the white triangular shape, beginning the fractal pattern known as sierpinski's triangle.
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Daily Lego Maths: Day 26

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.

The twelve possible pentomino shapes made out of Lego. Nine of the shapes have been put together to make an enlarged version of the U shaped pentomino. The U, X and W shapes are below.

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?

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Daily Lego Maths: Day 25

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

A large square made out of smaller lego squares and rectangles. The large square is ten 2 by 2 bricks wide and long. Here are the colours of each row: Row 1: 1 blue, 2 yellow, 3 white, 4 red Row 2: 1 yellow, 2 red, 3 white, 4 red Row 3: 1 yellow, 2 red, 3 white, 4 yellow Rows 4-6: 3 white, 3 blue, 4 yellow Rows 7-10: 2 red, 4 yellow, 4 red This creates a pattern of squares down the diagonals from top left to bottom right.

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?

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Daily Lego Maths: Day 24

Here are two shapes.
What’s the same? What’s different?
What other shapes could you make from these pieces?

Two rectangles made from 2 by 2 red lego bricks, on a grey baseboard. The top rectangle is 6 bricks wide and has 4 rows of bricks. The bottom rectangle is 8 bricks wide and has 3 rows of bricks.

How many different rectangles can you make using exactly 24 bricks?
If you had more bricks, could you make more rectangles?

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Daily Lego Maths: Day 23

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

Two rectangles made from 2 by 2 lego bricks. The top rectangle is 7 by 5 and is red round the outside with a 5 by 3 yellow interior. The bottom rectangle is 9 by 3 and is red round the outside with a 7 by 1 yellow interior.

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?