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?

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?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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?

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?

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?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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

How many trapeziums, of various sizes, are hidden in this picture?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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

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

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?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

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

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

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.

In this matching game, you have to decide how long different events take.

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

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

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....?

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

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

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?

Find out what a "fault-free" rectangle is and try to make some of your own.

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

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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.

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

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

An activity making various patterns with 2 x 1 rectangular tiles.

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?

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?

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.