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Broad Topics > Calculations and Numerical Methods > Multiplication & division

How Old?

Stage: 2 Challenge Level:

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

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?

Doplication

Stage: 2 Challenge Level:

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

Division Rules

Stage: 2 Challenge Level:

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

Journeys in Numberland

Stage: 2 Challenge Level:

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

X Is 5 Squares

Stage: 2 Challenge Level:

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

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?

Machines

Stage: 2 Challenge Level:

What is happening at each box in these machines?

Book Codes

Stage: 2 Challenge Level:

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?

Escape from the Castle

Stage: 2 Challenge Level:

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?

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.

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!

Spiders and Flies

Stage: 1 Challenge Level:

There were 22 legs creeping across the web. How many flies? How many spiders?

Claire's Counting Cards

Stage: 1 Challenge Level:

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

Forgot the Numbers

Stage: 2 Challenge Level:

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

Curious Number

Stage: 2 Challenge Level:

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Zargon Glasses

Stage: 2 Challenge Level:

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Multiply Multiples 1

Stage: 2 Challenge Level:

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Sending Cards

Stage: 2 Challenge Level:

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Next Number

Stage: 2 Short Challenge Level:

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

Stage: 2 Challenge Level:

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

Exploring Number Patterns You Make

Stage: 2 Challenge Level:

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

All the Digits

Stage: 2 Challenge Level:

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Make 100

Stage: 2 Challenge Level:

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

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 Amazing Splitting Plant

Stage: 1 Challenge Level:

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

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?

Double or Halve?

Stage: 1 Challenge Level:

Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?

Sept03 Sept03 Sept03

Stage: 2 Challenge Level:

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

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.

The Tomato and the Bean

Stage: 1 Challenge Level:

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

Being Determined - Primary Number

Stage: 1 and 2 Challenge Level:

Number problems at primary level that may require determination.

Being Thoughtful - Primary Number

Stage: 1 and 2 Challenge Level:

Number problems at primary level that require careful consideration.

Today's Date - 01/06/2009

Stage: 1 and 2 Challenge Level:

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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?

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?

It Was 2010!

Stage: 1 and 2 Challenge Level:

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

Rabbits in the Pen

Stage: 2 Challenge Level:

Using the statements, can you work out how many of each type of rabbit there are in these pens?

Function Machines

Stage: 2 Challenge Level:

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

How Much Did it Cost?

Stage: 2 Challenge Level:

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

Shapes in a Grid

Stage: 2 Challenge Level:

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Multiplication Squares

Stage: 2 Challenge Level:

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Code Breaker

Stage: 2 Challenge Level:

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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.

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.

The Money Maze

Stage: 2 Challenge Level:

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

Twizzle's Journey

Stage: 1 Challenge Level:

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

Fingers and Hands

Stage: 2 Challenge Level:

How would you count the number of fingers in these pictures?

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?