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1.01 Odd and even numbers


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We can use what we know about patterns with numbers to help us determine if a number is even or odd.


Example 1

Write the next number in the pattern:

2, \,4, \,6, \,8, \,10, \,12, \,⬚

Worked Solution
Create a strategy

Count how much is added each time and add it to the last given number.

Apply the idea

We can see that 2+2=4 and 4+2=6, and so on. This means we need to add 2 to 12, that is 12+2=14.

2, \,4, \,6, \,8, \,10, \,12, \,14

Idea summary

To find the next number with an increasing pattern, we need to find how much is added each time and add it to last given number.

Odd and even numbers

What are even and odd numbers? How can we determine if a number is even or odd? Let's find out.

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Example 2

Carl has 13 blocks and wants to divide them into two equal groups that are as big as possible. When doing this, Carl doesn't break any of the blocks into pieces.

13 scattered blocks

How many blocks will there be in each group?

Worked Solution
Create a strategy

Share the blocks into two groups, placing one block into the groups one at a time.

Apply the idea
2 groups of 6 blocks with 1 left over.

We can start putting one block into each group as shown.

We can see that there are 6 blocks in each group with one block left over.


Is 13 an even number?

Worked Solution
Create a strategy

If a number is even, then we can equally share it into two equal groups without anything left over.

Apply the idea

We found from part (b) that when we made two equal groups, there was 1 block left over.

So, 13 is not an even number.

Idea summary
  • All even numbers end in 2,4,6,8 or 0.

  • All odd numbers end in 1,3,5,7 or 9.

Even numbers can be split into two equal groups with no remaining numbers left over.



generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing values

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