Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Factors and Multiples game for an adult and child. How can you make sure you win this game?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Use the interactivities to complete these Venn diagrams.
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
A game that tests your understanding of remainders.
If you have only four weights, where could you place them in order
to balance this equaliser?
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.
Can you complete this jigsaw of the multiplication square?
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?
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?"
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 planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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.
Given the products of adjacent cells, can you complete this Sudoku?
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.
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?
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
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
Got It game for an adult and child. How can you play so that you know you will always win?
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?
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.
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 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?
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
Given the products of diagonally opposite cells - can you complete this Sudoku?
This package contains a collection of problems from the NRICH
website that could be suitable for students who have a good
understanding of Factors and Multiples and who feel ready to take
on some. . . .
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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. . . .
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?
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.
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
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.
A collection of resources to support work on Factors and Multiples at Secondary level.
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
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.
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 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?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?