How can we help students make sense of addition and subtraction of negative numbers?
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. . . .
There are exactly 3 ways to add 4 odd numbers to get 10. Find all
the ways of adding 8 odd numbers to get 20. To be sure of getting
all the solutions you will need to be systematic. What about. . . .
Find out about Magic Squares in this article written for students. Why are they magic?!
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.
This addition sum uses all ten digits 0, 1, 2...9 exactly once.
Find the sum and show that the one you give is the only
Find a great variety of ways of asking questions which make 8.
What are the missing numbers in the pyramids?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
If you wrote all the possible four digit numbers made by using each
of the digits 2, 4, 5, 7 once, what would they add up to?
This article suggests some ways of making sense of calculations involving positive and negative numbers.
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number.
Cross out the numbers on the same row and column. Repeat this
process. Add up you four numbers. Why do they always add up to 34?
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.
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?
Find the numbers in this sum
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.
Replace each letter with a digit to make this addition correct.
What is the sum of all the digits in all the integers from one to
In the following sum the letters A, B, C, D, E and F stand for six
distinct digits. Find all the ways of replacing the letters with
digits so that the arithmetic is correct.
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?
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?
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?
You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre
jug is full of wine, the others are empty. Can you divide the wine
into three equal quantities?
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was. . . .
Complete these two jigsaws then put one on top of the other. What
happens when you add the 'touching' numbers? What happens when you
change the position of the jigsaws?
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.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
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. . . .
What is the sum of all the three digit whole numbers?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Choose any three by three square of dates on a calendar page.
Circle any number on the top row, put a line through the other
numbers that are in the same row and column as your circled number.
Repeat. . . .
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
This challenge is to make up YOUR OWN alphanumeric. Each letter
represents a digit and where the same letter appears more than once
it must represent the same digit each time.
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?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Find the sum of all three-digit numbers each of whose digits is
The picture shows a lighthouse and many underwater creatures. If
you know the markings on the lighthouse are 1m apart, can you work
out the distances between some of the different creatures?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.
Can you explain how this card trick works?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
This number has 903 digits. What is the sum of all 903 digits?
Delight your friends with this cunning trick! Can you explain how