Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Arrange the shapes in a line so that you change either colour or
shape in the next piece along. Can you find several ways to start
with a blue triangle and end with a red circle?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
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.
Can you draw a square in which the perimeter is numerically equal
to the area?
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?
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?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
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
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
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?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
An investigation that gives you the opportunity to make and justify
Find all the different shapes that can be made by joining five
equilateral triangles edge to edge.
Find out what a "fault-free" rectangle is and try to make some of
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
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?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
These practical challenges are all about making a 'tray' and covering it with paper.
This activity investigates how you might make squares and pentominoes from Polydron.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
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
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
Number problems at primary level that require careful consideration.
Can you find all the different ways of lining up these Cuisenaire
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
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.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
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 trains can you make which are the same length as Matt's, using rods that are identical?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?