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

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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?

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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

An investigation that gives you the opportunity to make and justify predictions.

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

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

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

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Try out the lottery that is played in a far-away land. What is the chance of winning?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

Can you draw a square in which the perimeter is numerically equal to the area?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

These practical challenges are all about making a 'tray' and covering it with paper.

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

Can you find all the different ways of lining up these Cuisenaire rods?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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....?

How many ways can you find of tiling the square patio, using square tiles of different sizes?

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

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

Have a go at balancing this equation. Can you find different ways of doing it?

This challenge extends the Plants investigation so now four or more children are involved.

If you had 36 cubes, what different cuboids could you make?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

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

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.