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Broad Topics > Calculations and Numerical Methods > Multiplication & division

Watch the Clock

Stage: 2 Challenge Level:

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

2010: A Year of Investigations

Stage: 1, 2 and 3

This article for teachers suggests ideas for activities built around 10 and 2010.

Practice Run

Stage: 2 Challenge Level:

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

Watching the Wheels Go 'round and 'round

Stage: 2 Challenge Level:

Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.

Factor-multiple Chains

Stage: 2 Challenge Level:

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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?

What's My Weight?

Stage: 2 Short Challenge Level:

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

Pies

Stage: 2 Challenge Level:

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

Being Thoughtful - Primary Number

Stage: 1 and 2 Challenge Level:

Number problems at primary level that require careful consideration.

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?

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.

What's in the Box?

Stage: 2 Challenge Level:

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

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.

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.

I'm Eight

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

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

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?

Clever Santa

Stage: 2 Challenge Level:

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

Sort Them Out (2)

Stage: 2 Challenge Level:

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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?

Next Number

Stage: 2 Short Challenge Level:

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

It Was 2010!

Stage: 1 and 2 Challenge Level:

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

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.

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?

Stage: 2 Challenge Level:

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

Number the Sides

Stage: 2 Challenge Level:

The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?

Method in Multiplying Madness?

Stage: 3 Challenge Level:

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

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?

Being Determined - Primary Number

Stage: 1 and 2 Challenge Level:

Number problems at primary level that may require determination.

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?

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?

Multiplication Square Jigsaw

Stage: 2 Challenge Level:

Can you complete this jigsaw of the multiplication square?

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?

One Million to Seven

Stage: 2 Challenge Level:

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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. . . .

Fair Feast

Stage: 2 Challenge Level:

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

Divide it Out

Stage: 2 Challenge Level:

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

Difficulties with Division

Stage: 1 and 2

This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

Function Machines

Stage: 2 Challenge Level:

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

Tom's Number

Stage: 2 Challenge Level:

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

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?

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.

Machines

Stage: 2 Challenge Level:

What is happening at each box in these machines?

Carrying Cards

Stage: 2 Challenge Level:

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

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?

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?

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?

Diggits

Stage: 3 Challenge Level:

Can you find what the last two digits of the number $4^{1999}$ are?

Skeleton

Stage: 3 Challenge Level:

Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.