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?
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?
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?
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?
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.
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.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?
56 406 is the product of two consecutive numbers. What are these two numbers?
A collection of resources to support work on Factors and Multiples at Secondary level.
How many different rectangles can you make using this set of rods?
Can you work out some different ways to balance this equation?
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?
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
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.
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.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
A game in which players take it in turns to choose a number. Can you block your opponent?
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?
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you explain the strategy for winning this game with any target?
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?
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?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
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?
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.
Number problems at primary level that may require resilience.
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.
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.
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?
Number problems at primary level to work on with others.
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?
An investigation that gives you the opportunity to make and justify predictions.
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
Can you find different ways of creating paths using these paving slabs?
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?
Are these statements always true, sometimes true or never true?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?