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.
An investigation that gives you the opportunity to make and justify predictions.
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?
There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?
How many different sets of numbers with at least four members can you find in the numbers in this box?
If you have only four weights, where could you place them in order to balance this equaliser?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Number problems at primary level to work on with others.
Number problems at primary level that may require resilience.
Follow the clues to find the mystery number.
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?
Can you make square numbers by adding two prime numbers together?
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 find a way to identify times tables after they have been shifted up?
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
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?
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
Can you find any two-digit numbers that satisfy all of these statements?
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?
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...
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?
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?
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.
Is there an efficient way to work out how many factors a large number has?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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.
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?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
"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 ...?
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
An environment which simulates working with Cuisenaire rods.
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
Got It game for an adult and child. How can you play so that you know you will always win?
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?
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 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?
What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?
Can you explain the strategy for winning this game with any target?
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.