Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
If you have only four weights, where could you place them in order
to balance this equaliser?
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Choose a symbol to put into the number sentence.
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
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....?
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you find all the different ways of lining up these Cuisenaire
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Exchange the positions of the two sets of counters in the least possible number of moves
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you complete this jigsaw of the multiplication square?
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
Can you make the green spot travel through the tube by moving the
yellow spot? Could you draw a tube that both spots would follow?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Here is a chance to play a version of the classic Countdown Game.
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
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?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
How many different triangles can you make on a circular pegboard that has nine pegs?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
Find out what a "fault-free" rectangle is and try to make some of
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
A train building game for 2 players.
What shaped overlaps can you make with two circles which are the
same size? What shapes are 'left over'? What shapes can you make
when the circles are different sizes?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Board Block game for two. Can you stop your partner from being able to make a shape on the board?
What is the greatest number of squares you can make by overlapping
Use the interactivities to complete these Venn diagrams.
Work out the fractions to match the cards with the same amount of
A simulation of target archery practice
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.