What is the greatest number of squares you can make by overlapping three squares?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

Can you picture where this letter "F" will be on the grid if you flip it in these different ways?

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

Move just three of the circles so that the triangle faces in the opposite direction.

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

You have a set of the digits from 0 – 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

A game in which players take it in turns to choose a number. Can you block your opponent?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

How many different triangles can you make on a circular pegboard that has nine pegs?

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

Can you find all the different triangles on these peg boards, and find their angles?

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

Use these four dominoes to make a square that has the same number of dots on each side.

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

How would you move the bands on the pegboard to alter these shapes?

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?