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

Constant Counting

Stage: 1 Challenge Level:

You can make a calculator count for you by any number you choose. You can count by ones to reach 24. You can count by twos to reach 24. What else can you count by to reach 24?

What's Left?

Stage: 1 Challenge Level:

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

Six in a Circle

Stage: 1 Challenge Level:

If there is a ring of six chairs and thirty children must either sit on a chair or stand behind one, how many children will be behind each chair?

The Set of Numbers

Stage: 1 Challenge Level:

Can you place the numbers from 1 to 10 in the grid?

Being Resilient - Primary Number

Stage: 1 and 2 Challenge Level:

Number problems at primary level that may require resilience.

Number Tracks

Stage: 2 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?

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?

What Do You Need?

Stage: 2 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?

What Two ...?

Stage: 2 Short Challenge Level:

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

Got it for Two

Stage: 2 Challenge Level:

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

Give Me Four Clues

Stage: 2 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?

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?

One of Thirty-six

Stage: 1 Challenge Level:

Can you find the chosen number from the grid using the clues?

Little Squares

Stage: 1 Challenge Level:

Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?

Odds and Threes

Stage: 2 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.

Money Measure

Stage: 2 Challenge Level:

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

Scoring with Dice

Stage: 2 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 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?

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?

Nineteen Hexagons

Stage: 1 Challenge Level:

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

Becky's Number Plumber

Stage: 2 Challenge Level:

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

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?

Numbers as Shapes

Stage: 1 Challenge Level:

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

Doubling Fives

Stage: 1 Challenge Level:

This activity focuses on doubling multiples of five.

Being Collaborative - Primary Number

Stage: 1 and 2 Challenge Level:

Number problems at primary level to work on with others.

Domino Pick

Stage: 1 Challenge Level:

Are these domino games fair? Can you explain why or why not?

Multiplication Series: Number Arrays

Stage: 1 and 2

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

Grouping Goodies

Stage: 1 Challenge Level:

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

Crossings

Stage: 2 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?

Lots of Lollies

Stage: 1 Challenge Level:

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

Which Is Quicker?

Stage: 2 Challenge Level:

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Path to the Stars

Stage: 2 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?

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'.

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?

Flashing Lights

Stage: 2 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?

Number Detective

Stage: 2 Challenge Level:

Follow the clues to find the mystery number.

What Is Ziffle?

Stage: 2 Challenge Level:

Can you work out what a ziffle is on the planet Zargon?

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?

Down to Nothing

Stage: 2 Challenge Level:

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

In the Money

Stage: 2 Challenge Level:

There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?

Two Primes Make One Square

Stage: 2 Challenge Level:

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

Three Neighbours

Stage: 2 Challenge Level:

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

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.

Sets of Four Numbers

Stage: 2 Challenge Level:

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

Which Numbers? (1)

Stage: 2 Challenge Level:

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

Tiling

Stage: 2 Challenge Level:

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

Stage: 2 Challenge Level:

If you have only four weights, where could you place them in order to balance this equaliser?

Which Numbers? (2)

Stage: 2 Challenge Level:

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

Round and Round the Circle

Stage: 2 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.