A game in which players take it in turns to choose a number. Can you block your opponent?
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
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.
Factors and Multiples game for an adult and child. How can you make sure you win this game?
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...
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
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
If you have only four weights, where could you place them in order
to balance this equaliser?
A game that tests your understanding of remainders.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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.
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
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!
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 complete this jigsaw of the multiplication square?
Use the interactivities to complete these Venn diagrams.
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?
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.
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Got It game for an adult and child. How can you play so that you know you will always win?
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.
Given the products of adjacent cells, can you complete this Sudoku?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
Some 4 digit numbers can be written as the product of a 3 digit
number and a 2 digit number using the digits 1 to 9 each once and
only once. The number 4396 can be written as just such a product.
Can. . . .
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?"
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. . . .
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 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?
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.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
Can you find a way to identify times tables after they have been shifted up?
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?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?