Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
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....?
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.
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!
Use the interactivities to complete these Venn diagrams.
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?
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?
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?
Here is a chance to play a version of the classic Countdown Game.
Can you complete this jigsaw of the multiplication square?
An environment which simulates working with Cuisenaire rods.
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?
These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
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?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
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.
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. . . .
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?
Choose a symbol to put into the number sentence.
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?
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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 find all the different ways of lining up these Cuisenaire
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 spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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
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.
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 put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
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 was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.