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?
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.
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.
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.
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?
A collection of resources to support work on Factors and Multiples at Secondary level.
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?"
A game in which players take it in turns to choose a number. Can you block your opponent?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
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?
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?
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?
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
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?
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...
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?
Play this game and see if you can figure out the computer's chosen number.
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
An environment which simulates working with Cuisenaire rods.
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
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?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Can you find any perfect numbers? Read this article to find out more...
Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
Can you find any two-digit numbers that satisfy all of these statements?
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...
Find the number which has 8 divisors, such that the product of the divisors is 331776.
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.
How did the the rotation robot make these patterns?
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?
Is there an efficient way to work out how many factors a large number has?
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
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 numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?
Can you find a way to identify times tables after they have been shifted up or down?
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.
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.
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .
When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .
What is the smallest number of answers you need to reveal in order to work out the missing headers?
Follow this recipe for sieving numbers and see what interesting patterns emerge.