Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
How many ways can you find of tiling the square patio, using square tiles of different sizes?
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
These rectangles have been torn. How many squares did each one have inside it before it was ripped?
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?
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.
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
An activity making various patterns with 2 x 1 rectangular tiles.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
This activity investigates how you might make squares and pentominoes from Polydron.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Can you draw a square in which the perimeter is numerically equal to the area?
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
Find all the different shapes that can be made by joining five equilateral triangles edge to edge.
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.
An investigation that gives you the opportunity to make and justify predictions.
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
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?
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.
Find out what a "fault-free" rectangle is and try to make some of your own.
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?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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?
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?
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Try out the lottery that is played in a far-away land. What is the chance of winning?
Investigate the different ways you could split up these rooms so that you have double the number.
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?