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Broad Topics > Calculations and Numerical Methods > Addition & subtraction

Super Shapes

Stage: 2 Short Challenge Level:

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

How Many Eggs?

Stage: 2 Challenge Level:

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

Stage: 2 Challenge Level:

Use the information to work out how many gifts there are in each pile.

Buckets of Thinking

Stage: 2 Challenge Level:

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.

Amy's Dominoes

Stage: 2 Challenge Level:

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?

Rocco's Race

Stage: 2 Short Challenge Level:

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.

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.

Calendar Calculations

Stage: 2 Challenge Level:

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 happens?

Oranges and Lemons

Stage: 2 Challenge Level:

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Number Juggle

Stage: 2 Challenge Level:

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

Highest and Lowest

Stage: 2 Challenge Level:

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Sam's Quick Sum

Stage: 2 Challenge Level:

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

Two Number Lines

Stage: 2 Challenge Level:

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?

Clever Keys

Stage: 2 Short Challenge Level:

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?

Magic Squares 4x4

Stage: 2 Challenge Level:

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.

Dividing a Cake

Stage: 2 Challenge Level:

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?

Sometimes We Lose Things

Stage: 2 Challenge Level:

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.

Next Number

Stage: 2 Short Challenge Level:

Find the next number in this pattern: 3, 7, 19, 55 ...

Being Determined - Primary Number

Stage: 1 and 2 Challenge Level:

Number problems at primary level that may require determination.

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.

It Was 2010!

Stage: 1 and 2 Challenge Level:

If the answer's 2010, what could the question be?

How Do You Do It?

Stage: 2 Challenge Level:

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

Six Numbered Cubes

Stage: 2 Challenge Level:

This task combines spatial awareness with addition and multiplication.

Stage: 2 Challenge Level:

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.

Function Machines

Stage: 2 Challenge Level:

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

Penta Post

Stage: 2 Challenge Level:

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?

Brothers and Sisters

Stage: 2 Challenge Level:

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?

The 24 Game

Stage: 2 Challenge Level:

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?

Throw a 100

Stage: 2 Challenge Level:

Can you score 100 by throwing rings on this board? Is there more than way to do it?

Machines

Stage: 2 Challenge Level:

What is happening at each box in these machines?

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?

Clock Face

Stage: 2 Challenge Level:

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

The Clockmaker's Birthday Cake

Stage: 2 Challenge Level:

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

Zios and Zepts

Stage: 2 Challenge Level:

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

The Number Crunching Machine

Stage: 2 Challenge Level:

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

Sept03 Sept03 Sept03

Stage: 2 Challenge Level:

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

Magic Constants

Stage: 2 Challenge Level:

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

The Pied Piper of Hamelin

Stage: 2 Challenge Level:

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

A Rod and a Pole

Stage: 2 Challenge Level:

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?

Hubble, Bubble

Stage: 2 Challenge Level:

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

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?

One Wasn't Square

Stage: 2 Challenge Level:

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

Scoring with Dice

Stage: 2 Challenge Level:

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

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?

Totality

Stage: 1 and 2 Challenge Level:

This is an adding game for two players.

Numbered Cars

Stage: 2 Challenge Level:

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?

Street Sequences

Stage: 1 and 2 Challenge Level:

Investigate what happens when you add house numbers along a street in different ways.

Christmas Shopping

Stage: 2 Challenge Level:

Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?

Back to School

Stage: 2 Challenge Level:

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?