Dotty Six is a simple dice game that you can adapt in many ways.
How can we help students make sense of addition and subtraction of negative numbers?
This activity is best done with a whole class or in a large group.
Can you match the cards? What happens when you add pairs of the
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
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?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Find the sum of all three-digit numbers each of whose digits is
There are nasty versions of this dice game but we'll start with the nice ones...
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Susie took cherries out of a bowl by following a certain pattern.
How many cherries had there been in the bowl to start with if she
was left with 14 single ones?
Try grouping the dominoes in the ways described. Are there any left
over each time? Can you explain why?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
Can you substitute numbers for the letters in these sums?
Tell your friends that you have a strange calculator that turns
numbers backwards. What secret number do you have to enter to make
141 414 turn around?
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
What is the sum of all the three digit whole numbers?
Choose four of the numbers from 1 to 9 to put in the squares so
that the differences between joined squares are odd.
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.
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
Are these domino games fair? Can you explain why or why not?
This project challenges you to work out the number of cubes hidden
under a cloth. What questions would you like to ask?
Find out about Magic Squares in this article written for students. Why are they magic?!
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten
numbers from the bags above so that their total is 37.
Use the 'double-3 down' dominoes to make a square so that each side
has eight dots.
Find a great variety of ways of asking questions which make 8.
On a farm there were some hens and sheep. Altogether there were 8
heads and 22 feet. How many hens were there?
Explore Alex's number plumber. What questions would you like to
ask? Don't forget to keep visiting NRICH projects site for the
latest developments and questions.
How would you count the number of fingers in these pictures?
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?