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

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?

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

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

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

What is the best way to shunt these carriages so that each train can continue its journey?

How will you go about finding all the jigsaw pieces that have one peg and one hole?

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?

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

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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

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?

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

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

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

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

How long does it take to brush your teeth? Can you find the matching length of time?

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

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?

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

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

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.

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

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

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

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

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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?

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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

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?

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?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

The Zargoes use almost the same alphabet as English. What does this birthday message say?

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?