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

### Nineteen Hexagons

##### Age 5 to 7 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?

### Lots of Lollies

##### Age 5 to 7 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?

### Growing Garlic

##### Age 5 to 7 Challenge Level:

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

### One of Thirty-six

##### Age 5 to 7 Challenge Level:

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

### 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.

### 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?

### Same Length Trains

##### Age 5 to 7 Challenge Level:

How many trains can you make which are the same length as Matt's, using rods that are identical?

### Are You Well Balanced?

##### Age 5 to 7 Challenge Level:

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

### 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?

### 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?

### 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?

### 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?

### 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?

### 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?

### 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?

### 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.

### 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.

### Constant Counting

##### Age 5 to 7 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?

### Six in a Circle

##### Age 5 to 7 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?

### 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.

### Skip Counting

##### Age 5 to 7 Challenge Level:

Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from.

### Biscuit Decorations

##### Age 5 to 7 Challenge Level:

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

### Tables Teaser

##### Age 5 to 7 Challenge Level:

How will you work out which numbers have been used to create this multiplication square?

### 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.

### Multiply Multiples 2

##### Age 7 to 11 Challenge Level:

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

### Number Detective

##### Age 5 to 11 Challenge Level:

Follow the clues to find the mystery number.

### Little Squares

##### Age 5 to 7 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?

### What's Left?

##### Age 5 to 7 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?

### Tiling

##### Age 7 to 11 Challenge Level:

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

### 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.

### Doubling Fives

##### Age 5 to 7 Challenge Level:

This activity focuses on doubling multiples of five.

### Mrs Trimmer's String

##### Age 5 to 7 Challenge Level:

Can you help the children in Mrs Trimmer's class make different shapes out of a loop of string?

### Multiply Multiples 3

##### Age 7 to 11 Challenge Level:

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

### Grouping Goodies

##### Age 5 to 7 Challenge Level:

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

### The Set of Numbers

##### Age 5 to 7 Challenge Level:

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

### 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?

### 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?

### 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?

### 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.

### Lots of Biscuits!

##### Age 5 to 7 Challenge Level:

Help share out the biscuits the children have made.

### Domino Pick

##### Age 5 to 7 Challenge Level:

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

### Venn Diagrams

##### Age 5 to 11 Challenge Level:

Use the interactivities to complete these Venn diagrams.

### 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?

### 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?

### Being Resilient - Primary Number

##### Age 5 to 11 Challenge Level:

Number problems at primary level that may require resilience.

### 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?

### Share Bears

##### Age 5 to 7 Challenge Level:

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

### Add the Weights

##### Age 7 to 11 Challenge Level:

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

### 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?