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?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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!
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
Use the interactivities to complete these Venn diagrams.
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?
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?"
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?
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?
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.
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?
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?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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 complete this calculation by filling in the missing numbers? In how many different ways can you do it?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Have a go at balancing this equation. Can you find different ways of doing it?
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?
Can you work out some different ways to balance this equation?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
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.
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.
Got It game for an adult and child. How can you play so that you know you will always win?
Given the products of diagonally opposite cells - can you complete this Sudoku?
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?
An environment which simulates working with Cuisenaire rods.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Given the products of adjacent cells, can you complete this Sudoku?
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?
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.
"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 ...?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Is it possible to draw a 5-pointed star without taking your pencil
off the paper? Is it possible to draw a 6-pointed star in the same
way without taking your pen off?
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?
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?
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?