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.
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
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?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
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?
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?
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!
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
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?
"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 players ...?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
Follow the clues to find the mystery number.
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?
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?
This activity focuses on doubling multiples of five.
Have a go at balancing this equation. Can you find different ways of doing it?
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 place the numbers from 1 to 10 in the grid?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
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.
Got It game for an adult and child. How can you play so that you know you will always win?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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?
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?
Can you find any perfect numbers? Read this article to find out more...
How many trains can you make which are the same length as Matt's, using rods that are identical?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
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?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Help share out the biscuits the children have made.
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?
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
Can you work out some different ways to balance this equation?
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