Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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!
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
If you have only four weights, where could you place them in order
to balance this equaliser?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Can you complete this jigsaw of the multiplication square?
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?
Use the interactivities to complete these Venn diagrams.
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?"
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 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 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.
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?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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.
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Got It game for an adult and child. How can you play so that you know you will always win?
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?
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?
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?
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?
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
Can you work out some different ways to balance this equation?
A game in which players take it in turns to choose a number. Can you block your opponent?
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?
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.
Have a go at balancing this equation. Can you find different ways of doing it?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
Given the products of diagonally opposite cells - can you complete this Sudoku?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Follow the clues to find the mystery number.
An investigation that gives you the opportunity to make and justify
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
A game that tests your understanding of remainders.
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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 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.
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 adjacent cells, can you complete this Sudoku?
Can you make square numbers by adding two prime numbers together?
An environment which simulates working with Cuisenaire rods.
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. . . .
How many different sets of numbers with at least four members can
you find in the numbers in this box?