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.

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?

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

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

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

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.

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

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.

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

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?

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?

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

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

Here is a chance to play a version of the classic Countdown Game.

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

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

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

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

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

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.

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.

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

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

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

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

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?

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?

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

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

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

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

Play this game and see if you can figure out the computer's chosen number.

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?

In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

Can you find examples of magic crosses? Can you find all the possibilities?

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

Using compass points, can you describe up to ten paths on this map so that you bring as many gems back home as possible?