How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
Ben’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?
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 sets of numbers with at least four members can
you find in the numbers in this box?
56 406 is the product of two consecutive numbers. What are these
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.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Got It game for an adult and child. How can you play so that you know you will always win?
An investigation that gives you the opportunity to make and justify
Number problems at primary level that may require determination.
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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...
Can you find any perfect numbers? Read this article to find out more...
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
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 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?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
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?
Is there an efficient way to work out how many factors a large number has?
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.
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?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
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 the clues to find the mystery number.
Number problems at primary level to work on with others.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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?
Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
Are these statements always true, sometimes true or never true?
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?
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?
"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 ...?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Can you find a way to identify times tables after they have been shifted up?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
If you have only four weights, where could you place them in order
to balance this equaliser?
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?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?