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Adding and Subtracting Positive and Negative Numbers

Stage: 2, 3 and 4

How can we help students make sense of addition and subtraction of negative numbers?

Chameleons

Stage: 3 Challenge Level:

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. . . .

Score

Stage: 3 Challenge Level:

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. . . .

Magic Squares for Special Occasions

Stage: 3 and 4

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.

Tis Unique

Stage: 3 Challenge Level:

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 possibility.

I'm Eight

Stage: 1, 2, 3 and 4 Challenge Level:

Find a great variety of ways of asking questions which make 8.

Pyramids

Stage: 3 Challenge Level:

What are the missing numbers in the pyramids?

Consecutive Negative Numbers

Stage: 3 Challenge Level:

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

And So on and So On

Stage: 3 Challenge Level:

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?

Making Sense of Positives and Negatives

Stage: 3

This article suggests some ways of making sense of calculations involving positive and negative numbers.

Always the Same

Stage: 3 Challenge Level:

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?

Like Powers

Stage: 3 Challenge Level:

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.

The Patent Solution

Stage: 3 Challenge Level:

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?

Kids

Stage: 3 Challenge Level:

Find the numbers in this sum

Largest Number

Stage: 3 Challenge Level:

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.

Eleven

Stage: 3 Challenge Level:

Replace each letter with a digit to make this addition correct.

Digit Sum

Stage: 3 Challenge Level:

What is the sum of all the digits in all the integers from one to one million?

Aba

Stage: 3 Challenge Level:

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.

Arrange the Digits

Stage: 3 Challenge Level:

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?

Hot Pursuit

Stage: 3 Challenge Level:

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?

Playing Connect Three

Stage: 3 Challenge Level:

In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

Jugs of Wine

Stage: 3 Challenge Level:

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?

Top-heavy Pyramids

Stage: 3 Challenge Level:

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

Pairs

Stage: 3 Challenge Level:

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. . . .

Sorting the Numbers

Stage: 1 and 2 Challenge Level:

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?

The Deca Tree

Stage: 2 Challenge Level:

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.

Weights

Stage: 3 Challenge Level:

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Rod Measures

Stage: 2 Challenge Level:

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?

Clocked

Stage: 3 Challenge Level:

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?

As Easy as 1,2,3

Stage: 3 Challenge Level:

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. . . .

Sam's Quick Sum

Stage: 2 Challenge Level:

What is the sum of all the three digit whole numbers?

Two and Two

Stage: 2 and 3 Challenge Level:

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Four Goodness Sake

Stage: 2 Challenge Level:

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

Calendar Capers

Stage: 3 Challenge Level:

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. . . .

Number Pyramids

Stage: 3 Challenge Level:

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

A Numbered Route

Stage: 2 Challenge Level:

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 possible?

Cows and Sheep

Stage: 2 Challenge Level:

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

Crossed Ends

Stage: 3 Challenge Level:

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

Alphabet Soup

Stage: 3 Challenge Level:

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.

Napier's Bones

Stage: 2 Challenge Level:

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?

Month Mania

Stage: 1 and 2 Challenge Level:

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

Got it Article

Stage: 2 and 3

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Oddly

Stage: 2 Challenge Level:

Find the sum of all three-digit numbers each of whose digits is odd.

Sea Level

Stage: 2 Challenge Level:

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 Two

Stage: 2 and 3 Challenge Level:

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.

Card Trick 2

Stage: 3 Challenge Level:

Can you explain how this card trick works?

First Connect Three for Two

Stage: 2 and 3 Challenge Level:

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.

Sept03 Sept03 Sept03

Stage: 2 Challenge Level:

This number has 903 digits. What is the sum of all 903 digits?

Cunning Card Trick

Stage: 3 Challenge Level:

Delight your friends with this cunning trick! Can you explain how it works?