If you have only four weights, where could you place them in order
to balance this equaliser?
Can you complete this jigsaw of the multiplication square?
A game that tests your understanding of remainders.
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!
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.
An environment which simulates working with Cuisenaire rods.
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?
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?"
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 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?
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 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.
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...
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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.
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
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 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?
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?
A game in which players take it in turns to choose a number. Can you block your opponent?
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?
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
Given the products of adjacent cells, can you complete this Sudoku?
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 order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
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 diagonally opposite cells - can you complete
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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.
Can you find a way to identify times tables after they have been shifted up?
Use the interactivities to complete these Venn diagrams.
An investigation that gives you the opportunity to make and justify
In this activity, the computer chooses a times table and shifts it.
Can you work out the table and the shift each 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?
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.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
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.