How can we help students make sense of addition and subtraction of negative numbers?
A combination mechanism for a safe comprises thirty-two tumblers
numbered from one to thirty-two in such a way that the numbers in
each wheel total 132... Could you open the safe?
When I type a sequence of letters my calculator gives the product
of all the numbers in the corresponding memories. What numbers
should I store so that when I type 'ONE' it returns 1, and when I
type. . . .
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
Replace each letter with a digit to make this addition correct.
Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.
Whenever two chameleons of different colours meet they change
colour to the third colour. Describe the shortest sequence of
meetings in which all the chameleons change to green if you start
with 12. . . .
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit
numbers such that their total is close to 1500?
Find out about Magic Squares in this article written for students. Why are they magic?!
Find the numbers in this sum
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Find the sum of all three-digit numbers each of whose digits is
Find a great variety of ways of asking questions which make 8.
What is the largest number you can make using the three digits 2, 3
and 4 in any way you like, using any operations you like? You can
only use each digit once.
Are these statements always true, sometimes true or never true?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
Max and Mandy put their number lines together to make a graph. How
far had each of them moved along and up from 0 to get the counter
to the place marked?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
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.
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
Find the next number in this pattern: 3, 7, 19, 55 ...
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
Investigate what happens when you add house numbers along a street
in different ways.
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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?
This is an adding game for two players.
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
Who said that adding couldn't be fun?
Investigate the different distances of these car journeys and find
out how long they take.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Number problems at primary level that may require determination.
In sheep talk the only letters used are B and A. A sequence of
words is formed by following certain rules. What do you notice when
you count the letters in each word?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?