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 see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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.
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. . . .
Norrie sees two lights flash at the same time, then one of them
flashes every 4th second, and the other flashes every 5th second.
How many times do they flash together during a whole minute?
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...
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.
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.
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.
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 find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
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.
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
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 jigsaw of the multiplication square?
A game in which players take it in turns to choose a number. Can you block your opponent?
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.
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
What is the smallest number with exactly 14 divisors?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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.
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
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.
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
Given the products of adjacent cells, can you complete this Sudoku?
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.
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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?
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?
Do you know a quick way to check if a number is a multiple of two?
How about three, four or six?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
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?
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
An investigation that gives you the opportunity to make and justify
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?
An environment which simulates working with Cuisenaire rods.
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?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Can you work out what a ziffle is on the planet Zargon?
56 406 is the product of two consecutive numbers. What are these