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?
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?
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 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.
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?
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?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
Follow the clues to find the mystery number.
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.
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.
Can you complete this jigsaw of the multiplication square?
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?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
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.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you make square numbers by adding two prime numbers together?
Given the products of adjacent cells, can you complete this Sudoku?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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. . . .
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
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?"
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
"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 ...?
Can you work out some different ways to balance this equation?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
Got It game for an adult and child. How can you play so that you know you will always win?
Have a go at balancing this equation. Can you find different ways of doing it?
An environment which simulates working with Cuisenaire rods.
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
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.
An investigation that gives you the opportunity to make and justify
Use the interactivities to complete these Venn diagrams.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Given the products of diagonally opposite cells - can you complete this Sudoku?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
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?
A game that tests your understanding of remainders.
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
Becky created a number plumber which multiplies by 5 and subtracts
4. What do you notice about the numbers that it produces? Can you
explain your findings?
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?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
Number problems at primary level to work on with others.
Number problems at primary level that may require determination.
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’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?