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Broad Topics > Numbers and the Number System > Factors and multiples

Mystery Matrix

Age 7 to 11 Challenge Level:

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

It Figures

Age 7 to 11 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?

Multiplication Squares

Age 7 to 11 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.

Sweets in a Box

Age 7 to 11 Challenge Level:

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

The Moons of Vuvv

Age 7 to 11 Challenge Level:

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Tiling

Age 7 to 11 Challenge Level:

An investigation that gives you the opportunity to make and justify predictions.

Multiples Grid

Age 7 to 11 Challenge Level:

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Multiply Multiples 3

Age 7 to 11 Challenge Level:

Have a go at balancing this equation. Can you find different ways of doing it?

Multiply Multiples 2

Age 7 to 11 Challenge Level:

Can you work out some different ways to balance this equation?

Multiply Multiples 1

Age 7 to 11 Challenge Level:

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

Curious Number

Age 7 to 11 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?

Zios and Zepts

Age 7 to 11 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?

Abundant Numbers

Age 7 to 11 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?

Neighbours

Age 7 to 11 Challenge Level:

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

Round and Round the Circle

Age 7 to 11 Challenge Level:

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Being Resilient - Primary Number

Age 5 to 11 Challenge Level:

Number problems at primary level that may require resilience.

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?

Fractions in a Box

Age 7 to 11 Challenge Level:

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

Scoring with Dice

Age 7 to 11 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 Square Deal

Age 7 to 11 Challenge Level:

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

Have You Got It?

Age 11 to 14 Challenge Level:

Can you explain the strategy for winning this game with any target?

Seven Flipped

Age 7 to 11 Challenge Level:

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

What's in the Box?

Age 7 to 11 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?

Factor Lines

Age 7 to 14 Challenge Level:

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Two Primes Make One Square

Age 7 to 11 Challenge Level:

Can you make square numbers by adding two prime numbers together?

Sets of Numbers

Age 7 to 11 Challenge Level:

How many different sets of numbers with at least four members can you find in the numbers in this box?

Flashing Lights

Age 7 to 11 Challenge Level:

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

Crossings

Age 7 to 11 Challenge Level:

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

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?

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'.

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?

Number Tracks

Age 7 to 11 Challenge Level:

Benâ€™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?

Multiplication Series: Number Arrays

Age 5 to 11

This article for teachers describes how number arrays can be a useful reprentation for many number concepts.

Money Measure

Age 7 to 11 Challenge Level:

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

Path to the Stars

Age 7 to 11 Challenge Level:

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

Fitted

Age 7 to 11 Challenge Level:

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

Pebbles

Age 7 to 11 Challenge Level:

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Gran, How Old Are You?

Age 7 to 11 Challenge Level:

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

Got it for Two

Age 7 to 14 Challenge Level:

Got It game for an adult and child. How can you play so that you know you will always win?

Being Collaborative - Primary Number

Age 5 to 11 Challenge Level:

Number problems at primary level to work on with others.

Surprising Split

Age 7 to 11 Challenge Level:

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

Times Tables Shifts

Age 7 to 11 Challenge Level:

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Three Dice

Age 7 to 11 Challenge Level:

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

Cuisenaire Environment

Age 5 to 11 Challenge Level:

An environment which simulates working with Cuisenaire rods.

Give Me Four Clues

Age 7 to 11 Challenge Level:

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

Number Detective

Age 5 to 11 Challenge Level:

Follow the clues to find the mystery number.

Making Pathways

Age 7 to 11 Challenge Level:

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

Music to My Ears

Age 7 to 11 Challenge Level:

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?