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?
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
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.
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
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.
Can you complete this jigsaw of the multiplication square?
If you have only four weights, where could you place them in order
to balance this equaliser?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
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?
I am thinking of three sets of numbers less than 101. They are the
red set, the green set and the blue set. Can you find all the
numbers in the sets from these clues?
Does a graph of the triangular numbers cross a graph of the six
times table? If so, where? Will a graph of the square numbers cross
the times table too?
Given the products of diagonally opposite cells - can you complete this Sudoku?
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?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
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.
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 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.
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
A game in which players take it in turns to choose a number. Can you block your opponent?
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?
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. . . .
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.
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
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?
A collection of resources to support work on Factors and Multiples at Secondary level.
A game that tests your understanding of remainders.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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.
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?
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?
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Got It game for an adult and child. How can you play so that you know you will always win?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
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. . . .
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 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.
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.
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?
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?
An environment which simulates working with Cuisenaire rods.
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.