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Broad Topics > Calculations and Numerical Methods > Multiplication & division

Exploring Wild & Wonderful Number Patterns

Stage: 2 Challenge Level:

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

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?

Next Number

Stage: 2 Short Challenge Level:

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

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?

Function Machines

Stage: 2 Challenge Level:

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

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?

Numbers Numbers Everywhere!

Stage: 1 and 2

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

Mobile Numbers

Stage: 1 and 2 Challenge Level:

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

Special 24

Stage: 2 Challenge Level:

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.

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?

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?

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.

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?

Mystery Matrix

Stage: 2 Challenge Level:

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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?

Asteroid Blast

Stage: 2 Challenge Level:

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

A-magical Number Maze

Stage: 2 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!

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?

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?

Abundant Numbers

Stage: 2 Challenge Level:

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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?

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.

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?

Shape Times Shape

Stage: 2 Challenge Level:

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

Twenty Divided Into Six

Stage: 2 Challenge Level:

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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?

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.

Route Product

Stage: 2 Challenge Level:

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

Dice and Spinner Numbers

Stage: 2 Challenge Level:

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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?

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.

X Is 5 Squares

Stage: 2 Challenge Level:

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

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.

Machines

Stage: 2 Challenge Level:

What is happening at each box in these machines?

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!

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?

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?

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.

Number Tracks

Stage: 2 Challenge Level:

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

A Mixed-up Clock

Stage: 2 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?

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?

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?

Stage: 2 Challenge Level:

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

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?

It Figures

Stage: 2 Challenge Level:

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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.

Arranging the Tables

Stage: 2 Challenge Level:

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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?

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?

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.