Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
An investigation that gives you the opportunity to make and justify
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
A game in which players take it in turns to choose a number. Can you block your opponent?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
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!
Can you make square numbers by adding two prime numbers together?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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 interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
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?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
Use the interactivities to complete these Venn diagrams.
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
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?
Follow the clues to find the mystery number.
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
Given the products of adjacent cells, can you complete this Sudoku?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
A challenge that requires you to apply your knowledge of the
properties of numbers. Can you fill all the squares on the board?
Four of these clues are needed to find the chosen number on this
grid and four are true but do nothing to help in finding the
number. Can you sort out the clues and find the number?
Can you complete this jigsaw of the multiplication square?
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
A game that tests your understanding of remainders.
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?