If there is a ring of six chairs and thirty children must either
sit on a chair or stand behind one, how many children will be
behind each chair?
Find the squares that Froggie skips onto to get to the pumpkin
patch. She starts on 3 and finishes on 30, but she lands only on a
square that has a number 3 more than the square she skips from.
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
This activity focuses on doubling multiples of five.
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
You can make a calculator count for you by any number you choose.
You can count by ones to reach 24. You can count by twos to reach
24. What else can you count by to reach 24?
Can you make square numbers by adding two prime numbers together?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
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?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
This package will help introduce children to, and encourage a deep
exploration of, multiples.
Can you place the numbers from 1 to 10 in the grid?
Are these domino games fair? Can you explain why or why not?
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
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?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
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.
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?
56 406 is the product of two consecutive numbers. What are these
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
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?
On a farm there were some hens and sheep. Altogether there were 8
heads and 22 feet. How many hens were there?
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
Have a go at balancing this equation. Can you find different ways of doing it?
Look at the squares in this problem. What does the next square look
like? I draw a square with 81 little squares inside it. How long
and how wide is my square?
Is it possible to draw a 5-pointed star without taking your pencil
off the paper? Is it possible to draw a 6-pointed star in the same
way without taking your pen off?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
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 complete this jigsaw of the multiplication square?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Can you work out some different ways to balance this equation?
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
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 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?
"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
Factor track is not a race but a game of skill. The idea is to go
round the track in as few moves as possible, keeping to the rules.
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
If you have only four weights, where could you place them in order
to balance this equaliser?
Follow the clues to find the mystery number.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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.
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
An environment which simulates working with Cuisenaire rods.