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?
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?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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?
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
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?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
56 406 is the product of two consecutive numbers. What are these
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
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?
Got It game for an adult and child. How can you play so that you know you will always win?
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.
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 three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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.
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?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Number problems at primary level that may require determination.
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 find any perfect numbers? Read this article to find out more...
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.
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
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?
Help share out the biscuits the children have made.
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.
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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.
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?
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?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
An investigation that gives you the opportunity to make and justify
If you have only four weights, where could you place them in order
to balance this equaliser?
Yasmin and Zach have some bears to share. Which numbers of bears
can they share so that there are none left over?
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?
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?
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?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?