Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Can you complete this jigsaw of the multiplication square?

An environment which simulates working with Cuisenaire rods.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Got It game for an adult and child. How can you play so that you know you will always win?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Can you explain the strategy for winning this game with any target?

How many different rectangles can you make using this set of rods?

Given the products of diagonally opposite cells - can you complete this Sudoku?

The clues for this Sudoku are the product of the numbers in adjacent squares.

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

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?

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?

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 a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

A collection of resources to support work on Factors and Multiples at Secondary level.

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?

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

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?

Factors and Multiples game for an adult and child. How can you make sure you win this game?

A game in which players take it in turns to choose a number. Can you block your opponent?

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.

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.

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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?

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.

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

An investigation that gives you the opportunity to make and justify predictions.

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Given the products of adjacent cells, can you complete this Sudoku?

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?

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

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?

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?

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

56 406 is the product of two consecutive numbers. What are these two numbers?

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 complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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?

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 am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.