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?
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.
An investigation that gives you the opportunity to make and justify
An environment which simulates working with Cuisenaire rods.
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?
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
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?
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?
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?
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
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.
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?
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
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?
Can you complete this jigsaw of the multiplication square?
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?
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?
"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
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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.
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you work out some different ways to balance this equation?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
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...
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
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.
Twice a week I go swimming and swim the same number of lengths of
the pool each time. As I swim, I count the lengths I've done so
far, and make it into a fraction of the whole number of lengths. . . .
Can you find a way to identify times tables after they have been shifted up?
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?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
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?
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.
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
Place four pebbles on the sand in the form of a square. Keep adding
as few pebbles as necessary to double the area. How many extra
pebbles are added each time?
Can you make square numbers by adding two prime numbers together?
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
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?