A challenging activity focusing on finding all possible ways of stacking rods.

Use the clues about the symmetrical properties of these letters to place them on the grid.

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.

How many different symmetrical shapes can you make by shading triangles or squares?

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

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?

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

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

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

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?

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?

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?

This activity investigates how you might make squares and pentominoes from Polydron.

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

In how many ways can you stack these rods, following the rules?

Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .

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

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

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

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?

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....?

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?

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

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.

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?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

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

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

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

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

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

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?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?