This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
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.
Norrie sees two lights flash at the same time, then one of them
flashes every 4th second, and the other flashes every 5th second.
How many times do they flash together during a whole minute?
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 work out what a ziffle is on the planet Zargon?
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?
56 406 is the product of two consecutive numbers. What are these
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
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?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
Becky created a number plumber which multiplies by 5 and subtracts
4. What do you notice about the numbers that it produces? Can you
explain your findings?
I am thinking of three sets of numbers less than 101. They are the
red set, the green set and the blue set. Can you find all the
numbers in the sets from these clues?
A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.
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 see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
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.
Katie and Will have some balloons. Will's balloon burst at exactly
the same size as Katie's at the beginning of a puff. How many puffs
had Will done before his balloon burst?
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?
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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.
Does a graph of the triangular numbers cross a graph of the six
times table? If so, where? Will a graph of the square numbers cross
the times table too?
Help share out the biscuits the children have made.
Can you place the numbers from 1 to 10 in the grid?
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?
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
This activity focuses on doubling multiples of five.
This package will help introduce children to, and encourage a deep
exploration of, multiples.
A game that tests your understanding of remainders.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
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?
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?
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
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.
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?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
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?
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.
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
A game in which players take it in turns to choose a number. Can you block your opponent?
On a farm there were some hens and sheep. Altogether there were 8
heads and 22 feet. How many hens were there?