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?
If you have only four weights, where could you place them in order
to balance this equaliser?
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!
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?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
An environment which simulates working with Cuisenaire rods.
Can you complete this jigsaw of the multiplication square?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Choose a symbol to put into the number sentence.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Here is a chance to play a version of the classic Countdown Game.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Work out how to light up the single light. What's the rule?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
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....?
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 find all the different ways of lining up these Cuisenaire
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
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?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
A generic circular pegboard resource.
How many different triangles can you make on a circular pegboard that has nine pegs?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Can you find all the different triangles on these peg boards, and
find their angles?
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?
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
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!
Ahmed has some wooden planks to use for three sides of a rabbit run
against the shed. What quadrilaterals would he be able to make with
the planks of different lengths?