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

Stage: 1 Challenge Level:

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

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?

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?

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 Two ...?

Stage: 2 Short Challenge Level:

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

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?

Skip Counting

Stage: 1 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.

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?

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?

Multiples

Stage: 1 Challenge Level:

This package will help introduce children to, and encourage a deep exploration of, multiples.

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?

Two Primes Make One Square

Stage: 2 Challenge Level:

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

A Dotty Problem

Stage: 2 Challenge Level:

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

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?

Fitted

Stage: 2 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?

Biscuit Decorations

Stage: 1 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?

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?

Factor Track

Stage: 2 Challenge Level:

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

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?

The Set of Numbers

Stage: 1 Challenge Level:

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

Domino Pick

Stage: 2 Challenge Level:

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

Gran, How Old Are You?

Stage: 2 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?

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?

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.

Stage: 2 Challenge Level:

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

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.

One of Thirty-six

Stage: 1 Challenge Level:

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

Fractions in a Box

Stage: 2 Challenge Level:

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

Seven Flipped

Stage: 2 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.

Factor Lines

Stage: 2 Challenge Level:

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

Same Length Trains

Stage: 1 Challenge Level:

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

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?

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?

Which Is Quicker?

Stage: 2 Challenge Level:

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

Tiling

Stage: 2 Challenge Level:

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

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?

Multiples Grid

Stage: 2 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?

Growing Garlic

Stage: 1 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.

Lots of Biscuits!

Stage: 1 Challenge Level:

Help share out the biscuits the children have made.

A Square Deal

Stage: 2 Challenge Level:

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

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?

The Moons of Vuvv

Stage: 2 Challenge Level:

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

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?

Ip Dip

Stage: 1 and 2 Challenge Level:

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

Are You Well Balanced?

Stage: 1 Challenge Level:

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

Numbers as Shapes

Stage: 1 Challenge Level:

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

Curious Number

Stage: 2 Challenge Level:

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

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?

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?

What Is Ziffle?

Stage: 2 Challenge Level:

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