Resources tagged with: Odd and even numbers

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

Square Subtraction

Age 7 to 11 Challenge Level:

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?

Always, Sometimes or Never? Number

Age 7 to 11 Challenge Level:

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

Next-door Numbers

Age 5 to 7 Challenge Level:

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?

Always, Sometimes or Never?

Age 5 to 11 Challenge Level:

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

Take One Example

Age 5 to 11

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.

Odd Times Even

Age 5 to 7 Challenge Level:

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

Two Numbers Under the Microscope

Age 5 to 7 Challenge Level:

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

Odd Squares

Age 7 to 11 Challenge Level:

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?

Play to 37

Age 7 to 11 Challenge Level:

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.

Take Three Numbers

Age 7 to 11 Challenge Level:

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

Pairs of Numbers

Age 5 to 7 Challenge Level:

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?

Becky's Number Plumber

Age 7 to 11 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?

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?

Number Differences

Age 7 to 11 Challenge Level:

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?

More Numbers in the Ring

Age 5 to 7 Challenge Level:

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?

What Do You Need?

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?

Make 37

Age 7 to 14 Challenge Level:

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.

Part the Piles

Age 7 to 11 Challenge Level:

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

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.

The Set of Numbers

Age 5 to 7 Challenge Level:

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

What Could it Be?

Age 5 to 7 Challenge Level:

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

Prime Magic

Age 7 to 16 Challenge Level:

Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?

What Number?

Age 5 to 7 Short Challenge Level:

I am less than 25. My ones digit is twice my tens digit. My digits add up to an even number.

Pairs of Legs

Age 5 to 7 Challenge Level:

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

Largest Even

Age 5 to 7 Challenge Level:

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

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?

How Odd

Age 5 to 7 Challenge Level:

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?

I Like ...

Age 5 to 7 Challenge Level:

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

Magic Vs

Age 7 to 11 Challenge Level:

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

Diagonal Trace

Age 7 to 11 Challenge Level:

You can trace over all of the diagonals of a pentagon without lifting your pencil and without going over any more than once. Can the same thing be done with a hexagon or with a heptagon?

Carroll Diagrams

Age 5 to 11 Challenge Level:

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

Odd Tic Tac

Age 5 to 7 Challenge Level:

An odd version of tic tac toe

Arrangements

Age 7 to 11 Challenge Level:

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Multiplication Series: Number Arrays

Age 5 to 11

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

Break it Up!

Age 5 to 11 Challenge Level:

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.

The Thousands Game

Age 7 to 11 Challenge Level:

Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?

Domino Sorting

Age 5 to 7 Challenge Level:

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

Red Even

Age 7 to 11 Challenge Level:

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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?

More Carroll Diagrams

Age 7 to 14 Challenge Level:

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

Sets of Four Numbers

Age 7 to 11 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?

Numbers as Shapes

Age 5 to 7 Challenge Level:

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

Number Round Up

Age 5 to 7 Challenge Level:

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.

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?

Magic Crosses

Age 7 to 14 Challenge Level:

Can you find examples of magic crosses? Can you find all the possibilities?

Number Tracks

Age 7 to 11 Challenge Level:

Ben’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?

Venn Diagrams

Age 5 to 11 Challenge Level:

How will you complete these Venn diagrams?

One of Thirty-six

Age 5 to 7 Challenge Level:

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

Ring a Ring of Numbers

Age 5 to 7 Challenge Level:

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

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?