Investigate the different shaped bracelets you could make from 18
different spherical beads. How do they compare if you use 24 beads?
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.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
"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
An investigation that gives you the opportunity to make and justify
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?
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.
Can you make square numbers by adding two prime numbers together?
Use the interactivities to complete these Venn diagrams.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
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?
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
Can you complete this jigsaw of the multiplication square?
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?
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.
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
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?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
What is the smallest number with exactly 14 divisors?
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!
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?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
Do you know a quick way to check if a number is a multiple of two?
How about three, four or six?
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?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
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?
A game in which players take it in turns to choose a number. Can you block your opponent?
Follow the clues to find the mystery number.
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
A challenge that requires you to apply your knowledge of the
properties of numbers. Can you fill all the squares on the board?
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?
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?
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
Given the products of diagonally opposite cells - can you complete
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
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.
In this activity, the computer chooses a times table and shifts it.
Can you work out the table and the shift each time?
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?
A game that tests your understanding of remainders.
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...
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?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?