Grade by Grade
B. Number · Number Sense: Numbers to 200 and Fractions

Even and Odd Numbers

B1.5About 30 minutes
Learning goals
  • I can explain what makes a number even or odd.
  • I can use pairs or two equal groups to check if a number is even or odd.
  • I can look at the ones digit to tell if a number to 200 is even or odd.

Words to know

pair
A group of two, like a pair of mittens.
even number
A number that can be made into pairs with none left over. It can be split into 2 equal groups.
odd number
A number that has one left over when you make pairs.
ones digit
The last digit of a number. In 146, the ones digit is 6.

Partners at the rink

The Grade 2 class goes skating. The teacher says, "Find a partner!"

If there are 8 children, everyone gets a partner. If there are 7 children, one child is left without a partner.

8 is an even number. 7 is an odd number. Let's find out why.

8: four pairs, none left7: three pairs, one left over
Make pairs. With 8, every dot has a partner. With 7, one dot is left over.

What makes a number even or odd?

  • A number is even if you can put it into pairs with none left over.
  • A number is odd if there is one left over when you make pairs.

Here is another way to think about it:

  • An even number can be shared equally between 2 people.
  • An odd number can't. One is left over.
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6 mittens make 3 pairs, so 6 is even. 5 socks make 2 pairs with 1 sock left over, so 5 is odd.

Counting by 2s shows the even numbers

When you count by 2s from 0, you land on all the even numbers:

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 ...

The numbers you skip are the odd numbers: 1, 3, 5, 7, 9, 11, 13 ...

Even and odd take turns: even, odd, even, odd, all the way up!

01234567891011121314151617181920
The marked numbers are even. The numbers in between are odd.

A shortcut for big numbers

Is 146 even or odd? We don't need to make 146 pairs!

Every ten can be split into pairs: 10 is 5 pairs. Every hundred is 50 pairs. So the hundreds and tens never have one left over.

Only the ones can leave one over. So we just look at the ones digit:

Ones digitEven or odd?
0, 2, 4, 6, 8even
1, 3, 5, 7, 9odd
Look at the last digit to decide.

What about zero?

0 is even. When you have 0 things, there are none left over, and 0 is where counting by 2s starts.

Worked example

Example 1: Socks

Mila has 9 socks in the laundry basket. Is 9 even or odd?

  1. Make pairs: 2, 4, 6, 8. That is 4 pairs.
  2. There is 1 sock left over.

9 is odd. One sock has no partner.

Worked example

Example 2: Sharing grapes

Dad shares 12 grapes between 2 children. Is 12 even or odd?

  1. Give one grape to each child, again and again.
  2. Each child gets 6 grapes. None are left over.

12 is even. It can be shared equally between 2.

Worked example

Example 3: A big number

Is 157 even or odd?

  1. The hundred and the tens (150) can all be put into pairs.
  2. Look at the ones digit: 7.
  3. 7 makes 3 pairs with 1 left over.

157 is odd, because its ones digit, 7, is odd.

Even and odd on your street

On many streets in Canada, the houses on one side have even numbers and the houses on the other side have odd numbers. Take a look on your next walk!

Just for fun

The washing machine is the world's best odd-number maker. Put in 10 socks (even) and somehow only 9 come out (odd)! Where does the lonely partner go?

Hands-on activity

Grab and pair

You need: a bowl of small things (dry beans, pasta, buttons or cereal), and paper with two columns: Even and Odd.

  1. Grab a small handful.
  2. Guess: even or odd?
  3. Line them up in pairs (two rows).
  4. Is one left over? Write the number in the Even or Odd column.
  5. Do it 6 times. Look at the ones digits in each column. What do you notice?

Math talk: "How do you know it's even?"

Your turn

1

Is 6 even or odd?

2

Is 11 even or odd?

3

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Can these 10 apples be shared equally between 2 friends? Is 10 even or odd?

4

Is 134 even or odd?

5

Is 189 even or odd?

6

Write the next three even numbers: 16, 18, __, __, __

7

Write the next three odd numbers: 101, 103, __, __, __

More practice: warm-up

1

Is 4 even or odd?

2

Is 3 even or odd?

3

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Does every sock have a partner?

4

Count by 2s: 2, 4, 6, __, __

5

Is 20 even or odd?

More practice: on your own

1

Sort these numbers into even and odd: 15, 22, 37, 40, 118, 161

2

There are 17 children in a class. Can they all have a partner for a game? Why?

3

Jaden says 120 is odd because 1 is odd. Is he right?

4

What is the even number just before 200? The odd number just before 200?

5

Name an even number between 150 and 155.

Challenge

1

I am an odd number between 170 and 180. My ones digit is the same as my tens digit. What number am I?

2

Add two odd numbers: 3 + 5, 7 + 9, 1 + 11. Are the answers even or odd? Why do you think so?

3

A box has between 10 and 20 crayons. It is an odd number. When you take 1 crayon out, it can be shared equally among 2 kids with 7 each. How many crayons were in the box?

Check your understanding

Quiz

1.

Which number is even?

2.

What makes a number odd?

3.

Is 163 even or odd?

4.

Which group can be shared equally between 2 people?

5.

Which list has only odd numbers?

6.

Which digit tells you if 146 is even or odd?

For parents and teachers

Big idea: A number is even if it can be split into pairs (or two equal groups) with nothing left over. It is odd if one is left over. Because every ten splits into 5 pairs, only the ones digit decides.

Common difficulties:

  • Memorizing the rule without the reason. Before using the ones-digit shortcut, make sure your child can show even and odd with real objects in pairs.
  • Looking at the wrong digit (saying 120 is odd because of the 1). Ask, "Which part can have one left over?"
  • Is 0 even? Yes. It has nothing left over, and counting by 2s starts at 0.

How to help: Use socks, mittens and shoes. Ask "Even or odd?" about the number of people at dinner, apples in a bag, or house numbers on your street.