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Broad Topics > Numbers and the Number System > Odd and even numbers

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What Could it Be?

Stage: 1 Challenge Level: Challenge Level:1

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

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Play to 37

Stage: 2 Challenge Level: Challenge Level:1

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

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Square Subtraction

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

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Take Three Numbers

Stage: 2 Challenge Level: Challenge Level:1

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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Odd Times Even

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This problem looks at how one example of your choice can show something about the general structure of multiplication.

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Two Numbers Under the Microscope

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

This investigates one particular property of number by looking closely at an example of adding two odd numbers together.

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Largest Even

Stage: 1 Challenge Level: Challenge Level:1

How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?

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Pairs of Numbers

Stage: 1 Challenge Level: Challenge Level:1

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

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Curious Number

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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How Odd

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

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Light the Lights

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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I Like ...

Stage: 1 Challenge Level: Challenge Level:1

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

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Exploring Simple Mappings

Stage: 3 Challenge Level: Challenge Level:1

Explore the relationship between simple linear functions and their graphs.

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Even and Odd

Stage: 1 Challenge Level: Challenge Level:1

This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?

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Lots of Biscuits!

Stage: 1 Challenge Level: Challenge Level:1

Help share out the biscuits the children have made.

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Venn Diagrams

Stage: 1 and 2 Challenge Level: Challenge Level:1

Use the interactivities to complete these Venn diagrams.

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Magic Vs

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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What Do You Need?

Stage: 2 Challenge Level: Challenge Level:1

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?

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More Carroll Diagrams

Stage: 2 Challenge Level: Challenge Level:1

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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Carroll Diagrams

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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Various Venns

Stage: 2 Challenge Level: Challenge Level:1

Use the interactivities to complete these Venn diagrams.

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Domino Sorting

Stage: 1 Challenge Level: Challenge Level:1

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

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Domino Pick

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Odds and Evens

Stage: 3 and 4 Challenge Level: Challenge Level:1

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

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Number Differences

Stage: 2 Challenge Level: Challenge Level:1

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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More Numbers in the Ring

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

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Ring a Ring of Numbers

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

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Share Bears

Stage: 1 Challenge Level: Challenge Level:1

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

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Break it Up!

Stage: 1 and 2 Challenge Level: Challenge Level:1

In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.

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Odd Squares

Stage: 2 Challenge Level: Challenge Level:1

Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?

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Picturing Square Numbers

Stage: 3 Challenge Level: Challenge Level:1

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

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A Mixed-up Clock

Stage: 2 Challenge Level: Challenge Level:1

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?

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Make 37

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

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Grouping Goodies

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Number Round Up

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

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Always, Sometimes or Never? Number

Stage: 2 Challenge Level: Challenge Level:1

Are these statements always true, sometimes true or never true?

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Always, Sometimes or Never?

Stage: 1 and 2 Challenge Level: Challenge Level:1

Are these statements relating to odd and even numbers always true, sometimes true or never true?

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Take One Example

Stage: 1 and 2

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.

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Magic Letters

Stage: 3 Challenge Level: Challenge Level:1

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

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Odds, Evens and More Evens

Stage: 3 Challenge Level: Challenge Level:1

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

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Pairs of Legs

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

How many legs do each of these creatures have? How many pairs is that?

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Cube Bricks and Daisy Chains

Stage: 1 Challenge Level: Challenge Level:1

Daisy and Akram were making number patterns. Daisy was using beads that looked like flowers and Akram was using cube bricks. First they were counting in twos.

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Becky's Number Plumber

Stage: 2 Challenge Level: Challenge Level:1

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?

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Sorting Numbers

Stage: 1 Challenge Level: Challenge Level:1

Use the interactivity to sort these numbers into sets. Can you give each set a name?

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Three Spinners

Stage: 2 Challenge Level: Challenge Level:1

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

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One of Thirty-six

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Reasonable Algebra

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Use algebra to reason why 16 and 32 are impossible to create as the sum of consecutive numbers.

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Bina-ring

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Investigate powers of numbers of the form (1 + sqrt 2).

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Lattice Points

Stage: 5 Challenge Level: Challenge Level:1

Why are there only a few lattice points on a hyperbola and infinitely many on a parabola?

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Numbers as Shapes

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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