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 see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
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.
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?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
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?
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?
Number problems at primary level to work on with others.
If you have only four weights, where could you place them in order
to balance this equaliser?
This activity focuses on doubling multiples of five.
Got It game for an adult and child. How can you play so that you know you will always win?
Number problems at primary level that may require determination.
Are these domino games fair? Can you explain why or why not?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
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.
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
Can you place the numbers from 1 to 10 in the grid?
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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?
Can you work out what a ziffle is on the planet Zargon?
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
56 406 is the product of two consecutive numbers. What are these
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?
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
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?
Can you make square numbers by adding two prime numbers together?
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?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
In this problem we are looking at sets of parallel sticks that
cross each other. What is the least number of crossings you can
make? And the greatest?
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?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
Can you work out some different ways to balance this equation?
An investigation that gives you the opportunity to make and justify
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
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.
Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?