An environment which simulates working with Cuisenaire rods.
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
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?
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.
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?
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.
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.
Can you find a way to identify times tables after they have been shifted up or down?
Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
A collection of resources to support work on Factors and Multiples at Secondary level.
Given the products of diagonally opposite cells - can you complete this Sudoku?
A game in which players take it in turns to choose a number. Can you block your opponent?
Got It game for an adult and child. How can you play so that you know you will always win?
Can you explain the strategy for winning this game with any target?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
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...
I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Given the products of adjacent cells, can you complete this Sudoku?
The clues for this Sudoku are the product of the numbers in adjacent squares.
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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?"
Play this game and see if you can figure out the computer's chosen number.
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.
List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?
Can you find any two-digit numbers that satisfy all of these statements?
Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
How did the the rotation robot make these patterns?
Can you make lines of Cuisenaire rods that differ by 1?
Can you work out what size grid you need to read our secret message?
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
Can you find any perfect numbers? Read this article to find out more...
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
Find the highest power of 11 that will divide into 1000! exactly.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
Find the number which has 8 divisors, such that the product of the divisors is 331776.