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

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

This challenge is about finding the difference between numbers which have the same tens digit.

My coat has three buttons. How many ways can you find to do up all the buttons?

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?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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?

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

How many different shapes can you make by putting four right- angled isosceles triangles together?

What could the half time scores have been in these Olympic hockey matches?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

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 work out how to balance this equaliser? You can put more than one weight on a hook.

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

Can you find out in which order the children are standing in this line?

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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

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

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

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?

This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

What two-digit numbers can you make with these two dice? What can't you make?

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?