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?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
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?
Got It game for an adult and child. How can you play so that you know you will always win?
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 ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
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?
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 sets of numbers with at least four members can
you find in the numbers in this box?
An investigation that gives you the opportunity to make and justify
Can you find any perfect numbers? Read this article to find out more...
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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?
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.
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Can you work out some different ways to balance this equation?
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?
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?
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?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
"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 ...?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
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?
Can you find a way to identify times tables after they have been shifted up?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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?
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.
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
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?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Have a go at balancing this equation. Can you find different ways of doing it?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
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?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
56 406 is the product of two consecutive numbers. What are these
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?