The items in the shopping basket add and multiply to give the same amount. What could their prices be?
Can you work out how many lengths I swim each day?
Given the products of diagonally opposite cells - can you complete this Sudoku?
A collection of resources to support work on Factors and Multiples at Secondary level.
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.
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Given the products of adjacent cells, can you complete this Sudoku?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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...
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?
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
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?
Play this game and see if you can figure out the computer's chosen number.
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?"
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.
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
Got It game for an adult and child. How can you play so that you know you will always win?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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 explain the strategy for winning this game with any target?
A game in which players take it in turns to choose a number. Can you block your opponent?
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?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
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.
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...
How did the the rotation robot make these patterns?
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
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?
Can you find any perfect numbers? Read this article to find out more...
Can you find a way to identify times tables after they have been shifted up or down?
Find the highest power of 11 that will divide into 1000! exactly.
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.
Can you make lines of Cuisenaire rods that differ by 1?
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?
A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?
In how many ways can the number 1 000 000 be expressed as the product of three positive integers?
What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A
An environment which simulates working with Cuisenaire rods.
6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?