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?
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?
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.
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?
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?
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?
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
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.
This package will help introduce children to, and encourage a deep
exploration of, multiples.
Are these domino games fair? Can you explain why or why not?
This activity focuses on doubling multiples of five.
Can you place the numbers from 1 to 10 in the grid?
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?
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?
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
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?
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
On a farm there were some hens and sheep. Altogether there were 8
heads and 22 feet. How many hens were there?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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 cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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.
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
Follow the clues to find the mystery number.
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
An investigation that gives you the opportunity to make and justify
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?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
Can you work out what a ziffle is on the planet Zargon?
"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
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.
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?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
There are a number of coins on a table.
One quarter of the coins show heads.
If I turn over 2 coins, then one third show heads. How many coins are there altogether?
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.
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.