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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?

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. . . .

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. . . .

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.

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.

I'm Eight

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

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

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.

Pyramids

Stage: 3 Challenge Level:

What are the missing numbers in the pyramids?

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?

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?

Kids

Stage: 3 Challenge Level:

Find the numbers in this sum

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?

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?

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.

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.

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?

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.

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?

Eleven

Stage: 3 Challenge Level:

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

Making Sense of Positives and Negatives

Stage: 3

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

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.

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. . . .

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?

Sam's Quick Sum

Stage: 2 Challenge Level:

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

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. . . .

Oddly

Stage: 2 Challenge Level:

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

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?

Countdown

Stage: 2 and 3 Challenge Level:

Here is a chance to play a version of the classic Countdown Game.

Stage: 1 and 2 Challenge Level:

Who said that adding couldn't be fun?

Connect Three

Stage: 3 Challenge Level:

Can you be the first to complete a row of three?

Weights

Stage: 3 Challenge Level:

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

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.

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?

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?

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.

Consecutive Numbers

Stage: 2 and 3 Challenge Level:

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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?

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.

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.

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.

Card Trick 2

Stage: 3 Challenge Level:

Can you explain how this card trick works?

Sept03 Sept03 Sept03

Stage: 2 Challenge Level:

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

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?

Digit Sum

Stage: 3 Challenge Level:

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

Make 37

Stage: 2 and 3 Challenge Level:

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.

GOT IT Now

Stage: 2 and 3 Challenge Level:

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

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.

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. . . .