This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
Can you draw a square in which the perimeter is numerically equal to the area?
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?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
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.
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.
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?
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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 activity investigates how you might make squares and pentominoes from Polydron.
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?
How many ways can you find of tiling the square patio, using square tiles of different sizes?
These practical challenges are all about making a 'tray' and covering it with paper.
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
How many triangles can you make on the 3 by 3 pegboard?
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
An investigation that gives you the opportunity to make and justify predictions.
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?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?
Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.
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?
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.
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
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....?
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
What happens when you try and fit the triomino pieces into these two grids?
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?
Find your way through the grid starting at 2 and following these operations. What number do you end on?