How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Find all the different shapes that can be made by joining five
equilateral triangles edge to edge.
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?
Find out what a "fault-free" rectangle is and try to make some of
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
A Sudoku with clues given as sums of entries.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
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....?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
This challenge extends the Plants investigation so now four or more children are involved.
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
A package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Can you find all the different triangles on these peg boards, and
find their angles?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
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 find all the different ways of lining up these Cuisenaire
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
How many different triangles can you make on a circular pegboard that has nine pegs?
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
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?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
In this matching game, you have to decide how long different events take.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
An activity making various patterns with 2 x 1 rectangular tiles.