One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?
Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.
Can you complete this jigsaw of the multiplication square?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
56 406 is the product of two consecutive numbers. What are these two numbers?
This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.
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?
A collection of resources to support work on Factors and Multiples at Secondary level.
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?
Given the products of diagonally opposite cells - can you complete this Sudoku?
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.
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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
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?
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?
Guess the Dominoes for child and adult. Work out which domino your partner has chosen by asking good questions.
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?
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.
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.
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?
Number problems at primary level that may require resilience.
Number problems at primary level to work on with others.
Can you find different ways of creating paths using these paving slabs?
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?
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
Can you make square numbers by adding two prime numbers together?
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.
Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
How many different rectangles can you make using this set of rods?
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?
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?
Can you work out what a ziffle is on the planet Zargon?
How did the the rotation robot make these patterns?
Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.
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?
Are these statements always true, sometimes true or never true?
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
This article for teachers describes how number arrays can be a useful representation for many number concepts.
Find the highest power of 11 that will divide into 1000! exactly.
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?