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?
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?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
Benâ€™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?
"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 ...?
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?
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.
Got It game for an adult and child. How can you play so that you know you will always win?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
56 406 is the product of two consecutive numbers. What are these
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
An investigation that gives you the opportunity to make and justify
Number problems at primary level to work on with others.
Number problems at primary level that may require determination.
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
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?
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?
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
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.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Have a go at balancing this equation. Can you find different ways of doing it?
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?
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?
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
Can you work out some different ways to balance this equation?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
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?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
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?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
Given the products of adjacent cells, can you complete this Sudoku?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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.
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?
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 I. . . .
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?
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?