In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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?
Can you complete this jigsaw of the multiplication square?
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.
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.
If you have only four weights, where could you place them in order to balance this equaliser?
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?
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 are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
How many different rectangles can you make using this set of rods?
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
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?
How many different sets of numbers with at least four members can you find in the numbers in this box?
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.
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?
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?
Use the interactivities to complete these Venn diagrams.
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.
A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.
An investigation that gives you the opportunity to make and justify predictions.
Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?
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?
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?
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?
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?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you explain the strategy for winning this game with any target?
Got It game for an adult and child. How can you play so that you know you will always win?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.
Number problems at primary level to work on with others.
Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?
Number problems at primary level that may require resilience.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Given the products of adjacent cells, can you complete this Sudoku?
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
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?
This article for teachers describes how number arrays can be a useful representation for many number concepts.
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
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.