B. Number · Adding and Subtracting

What Adding and Subtracting Mean

B2.4 B2.1About 30 minutes

Learning goals

I can tell when a story is about putting groups together (adding).
I can tell when a story is about taking away or comparing (subtracting).
I can read and write the signs +, − and =.
I can show a math story with objects and with a number sentence.

Words to know

add
To put groups together to find how many in all. The sign is + and we say "plus".

sum
The answer when you add. In 3 + 2 = 5, the sum is 5.

subtract
To take some away, or to find how many more. The sign is − and we say "minus".

difference
The answer when you subtract. In 7 − 2 = 5, the difference is 5.

equals (=)
"Is the same amount as." The two sides of = have the same amount.

number sentence
Math written with numbers and signs, like 4 + 3 = 7. It is also called an equation.

Let's start with a story

It is a snowy day in January. Mia has 3 mittens drying on the heater. Her brother puts 2 more mittens beside them.

How many mittens are on the heater now? Let's count them!

🧤🧤🧤🧤🧤

3 mittens and 2 more mittens. Count them all: 1, 2, 3, 4, 5. There are 5 mittens.

When we put groups together to find how many in all, we are adding.

We can write this story as a number sentence:

3 + 2 = 5

We read it like this: "Three plus two equals five."

Sign	Name	What it means
+	plus	put together, join, add more
−	minus	take away, or find how many more
=	equals	is the same amount as

The three math signs you will use every day

The equal sign is like a balance

The equal sign = does not mean "the answer comes next". It means both sides are the same amount.

So 3 + 2 = 5 is true, and 5 = 3 + 2 is true too! Both sides have 5.

Taking away

Now a different story. There are 7 cookies on a plate. Liam eats 2 of them. How many cookies are left?

The group got smaller because some went away. When we take away, we are subtracting.

🍪🍪🍪🍪🍪🍪🍪

Start: 7 cookies on the plate.

🍪🍪🍪🍪🍪

Liam eats 2. Now there are 5 cookies left.

The number sentence is:

7 − 2 = 5

We read it: "Seven minus two equals five."

Comparing

Subtracting also helps us compare two groups to find how many more (or how many fewer).

To compare, line the two groups up and match them one to one. The ones with no partner show the difference.

Worked example

Example 1: Snowballs (adding)

Sam made 4 snowballs. Ali made 3 snowballs. How many snowballs did they make in all?

Think: Are the groups being put together or taken apart? The words in all tell us the groups are being put together. So we add.
Show it. Put out 4 blocks for Sam and 3 blocks for Ali.
Count them all. Or start at 4 and count on 3 more: 5, 6, 7.
Write the number sentence: 4 + 3 = 7.

They made 7 snowballs in all. 4 + 3 = 7.

Start at 4. Jump 3 spaces forward to land on 7.

Worked example

Example 2: Hockey pucks and sticks (comparing)

There are 8 hockey pucks and 5 hockey sticks. How many more pucks than sticks are there?

The words how many more tell us to compare. We subtract.
Line them up. Give each stick a puck partner.
5 pucks have a stick partner. Count the pucks with no partner: 3.
Write the number sentence: 8 − 5 = 3.

There are 3 more pucks than sticks. 8 − 5 = 3.

🏒🏒🏒🏒🏒⚫⚫⚫⚫⚫⚫⚫⚫

Top row: 5 sticks. Bottom row: 8 pucks. Match each stick with a puck. 3 pucks are left without a partner.

Worked example

Example 3: Birds fly away (taking away)

9 geese are on the pond. 4 geese fly away. How many geese are still on the pond?

Some geese fly away, so the group gets smaller. We subtract.
Put out 9 counters. Move 4 of them away.
Count what is left: 5.
Write the number sentence: 9 − 4 = 5.

5 geese are still on the pond. 9 − 4 = 5.

Clue words

Words that often mean add: in all, altogether, total, join, both, how many now.

Words that often mean subtract: left, take away, fly away, eat, how many more, how many fewer, difference.

But always think about the story! Ask: "Are the groups going together, or is something going away?"

Just for fun

Why is the plus sign so friendly?

Because it always brings more friends to the group!

Hands-on activity

Math stories with your toys

You need: 10 small things (toy cars, blocks, buttons, or dry pasta).

A grown-up tells a short story, like "5 cars are in the garage. 2 more drive in."
You act it out with your things.
Say how many there are now.
Write the number sentence on paper, like 5 + 2 = 7.
Now you tell a story and the grown-up acts it out! Try one adding story and one take-away story.

Math talk: "How did you know if it was adding or subtracting?"

Your turn

There are 2 red apples and 4 green apples in a bowl. How many apples in all? Write the number sentence.

6 kids are on the slide. 1 kid goes home. How many kids are still on the slide?

Read this out loud: 5 + 3 = 8

Is this story adding or subtracting? "Dad had 10 maple leaves. The wind blew 3 away."

Mom has 7 loonies. Dad has 4 loonies. How many more loonies does Mom have?

Is 6 = 4 + 2 true or false?

Write your own adding story for 3 + 1 = 4.

More practice: warm-up

🧤🧤🧤🧤 🧤

4 mittens are drying. 1 more mitten is added. How many mittens in all? Write the number sentence.

Which sign means take away: +, − or =?

Read this out loud: 9 − 3 = 6

🍪🍪🍪🍪🍪🍪

There are 6 cookies. 2 cookies get eaten. How many cookies are left?

True or false: 2 + 3 = 5

More practice: on your own

Is this story adding or subtracting? "Nora has 5 toques. Her grandma knits her 2 more." Solve it.

Fish: 🐟🐟🐟🐟🐟🐟🐟

Turtles: 🐢🐢🐢🐢

How many more fish than turtles?

Fill in the blank: 8 = 5 + __

There are 10 canoes at the dock. 4 canoes paddle away. Write the number sentence and solve.

Which number sentence matches this story? "3 robins sit in a tree. 3 more robins land."

3 − 3 = 0
3 + 3 = 6
6 + 3 = 9

Challenge

Find the mistake. Kai says: "There are 9 geese. 5 fly away. 9 + 5 = 14, so there are 14 geese." What did Kai do wrong?

5 kids are at the park. 3 more kids come. Then 2 kids go home. How many kids are at the park now?

Write a subtracting story for 8 − 3 = 5. How do you know your story is subtracting?

Check your understanding

Quiz

Which sign means put together?

There are 8 crayons. 3 break and are thrown away. How many crayons are left?

Ben has 6 stickers. Ana has 2 stickers. How many more stickers does Ben have?

Which number sentence is true?

Which clue words tell you to add?

There are 9 hats and 6 scarves. How many more hats than scarves?

For parents and teachers

Big idea: Adding is joining groups. Subtracting is taking away or comparing two groups. Children should act out stories with real objects before writing number sentences.

Common mistakes:

Thinking "=" means "write the answer here". Show them sentences like 5 = 3 + 2 and 4 + 1 = 3 + 2, and ask "Is it the same amount on both sides?"
Relying only on clue words. "How many more" can mean subtract, but children should picture the story. Ask them to show it with objects.
Recounting from 1 every time. That's fine for now. Later lessons teach counting on.
Forgetting comparing is subtraction. Line up two rows of objects and match them one to one so the extra ones are easy to see.

How to help: Make up quick stories during everyday life ("We have 4 forks on the table and need 6. How many more do we need?"). Ask your child to explain how they know, not just the answer.