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

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

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

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

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

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

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

Sort the houses in my street into different groups. Can you do it in any other ways?

Can you complete this jigsaw of the multiplication square?

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

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

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?

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....?

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

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?

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

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

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

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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?

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.

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

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?

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

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?

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?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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

You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

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

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

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

How will you work out which numbers have been used to create this multiplication square?

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 a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

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

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

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

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

Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?