How many different sets of numbers with at least four members can
you find in the numbers in this box?
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
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?
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.
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?
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?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
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?
56 406 is the product of two consecutive numbers. What are these
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.
Can you make square numbers by adding two prime numbers together?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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 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?
"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
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
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 complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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 find a way to identify times tables after they have been shifted up?
An investigation that gives you the opportunity to make and justify
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
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 find any perfect numbers? Read this article to find out more...
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
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.
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?
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
An environment which simulates working with Cuisenaire rods.
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?
Follow the clues to find the mystery number.
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?
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.
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
A game in which players take it in turns to choose a number. Can you block your opponent?
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?
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Find the highest power of 11 that will divide into 1000! exactly.
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
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.
When the number x 1 x x x is multiplied by 417 this gives the
answer 9 x x x 0 5 7. Find the missing digits, each of which is
represented by an "x" .
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
The number 8888...88M9999...99 is divisible by 7 and it starts with
the digit 8 repeated 50 times and ends with the digit 9 repeated 50
times. What is the value of the digit M?