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Broad Topics > Calculations and Numerical Methods > Multiplication & division Buckets of Thinking

Age 7 to 11 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. Age 7 to 11 Challenge Level:

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

Age 7 to 11 Short Challenge Level:

56 406 is the product of two consecutive numbers. What are these two numbers? How Many Eggs?

Age 7 to 11 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. Being Resourceful - Primary Number

Age 5 to 11 Challenge Level:

Number problems at primary level that require careful consideration. Super Shapes

Age 7 to 11 Short Challenge Level:

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

Age 7 to 11 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? The Deca Tree

Age 7 to 11 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. Odds and Threes

Age 7 to 11 Challenge Level:

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3. Divide it Out

Age 7 to 11 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? The 24 Game

Age 7 to 11 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? Ducking and Dividing

Age 7 to 11 Challenge Level:

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive? Napier's Bones

Age 7 to 11 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? X Is 5 Squares

Age 7 to 11 Challenge Level:

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

Age 7 to 11 Challenge Level:

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15! Rabbits in the Pen

Age 7 to 11 Challenge Level:

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

Age 5 to 11

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

Age 7 to 11 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? Function Machines

Age 7 to 11 Challenge Level:

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

Age 7 to 11 Challenge Level:

This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication. The Pied Piper of Hamelin

Age 7 to 11 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! Rocco's Race

Age 7 to 11 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. Throw a 100

Age 7 to 11 Challenge Level:

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

Age 7 to 11 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? Fair Feast

Age 5 to 11 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? What's My Weight?

Age 7 to 11 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? How Much Did it Cost?

Age 7 to 11 Challenge Level:

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

Age 7 to 11 Challenge Level:

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements? Largest Number

Age 11 to 14 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. Machines

Age 7 to 11 Challenge Level:

What is happening at each box in these machines? Zargon Glasses

Age 7 to 11 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? Magic Potting Sheds

Age 11 to 14 Challenge Level:

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it? Clock Face

Age 7 to 11 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

Age 7 to 11 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. Making Pathways

Age 7 to 11 Challenge Level:

Can you find different ways of creating paths using these paving slabs? Practice Run

Age 7 to 11 Challenge Level:

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

Age 7 to 11 Challenge Level:

Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see? Tom's Number

Age 7 to 11 Challenge Level:

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

Age 7 to 11 Challenge Level:

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

Age 7 to 11 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? Penta Post

Age 7 to 11 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? Clever Keys

Age 7 to 11 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? Sort Them Out (2)

Age 7 to 11 Challenge Level:

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

Age 7 to 11 Challenge Level:

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them? Dividing a Cake

Age 7 to 11 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? How Old?

Age 7 to 11 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? The Clockmaker's Birthday Cake

Age 7 to 11 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? Learning Times Tables

Age 5 to 11 Challenge Level:

In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here. Square Subtraction

Age 7 to 11 Challenge Level:

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it? Jumping

Age 7 to 11 Challenge Level:

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?