Add And Subtract Within 10 — CCSS.K.OA.2: Solve addition...

SECTION 1

Why Do We Add and Subtract?

People have been adding and subtracting for thousands of years! Long ago, farmers counted their animals. Shopkeepers counted coins. Everyone needed a way to put groups together and take things away.

Adding means putting things together to find out how many you have in all. Subtracting means taking some away to find out how many are left. These are two of the most important things you will ever learn in math!

Long Ago

Counting with Fingers

People used their fingers to count and add small numbers. You have 10 fingers — perfect for adding within 10!

Ancient Times

Pebbles and Stones

People put pebbles in piles to add groups together. They took pebbles away to subtract. These were the first math tools!

Hundreds of Years Ago

The + and − Signs

People invented the plus sign (+) for adding and the minus sign (−) for subtracting. Now we could write math problems down!

Today

You Learn Math!

Now you get to learn how to add and subtract within 10. You can use objects, drawings, and your fingers to help!

So here is the big question: when we hear a story about putting things together or taking things away, how do we figure out the answer? That is what this lesson is all about!

SECTION 2

What Are Addition and Subtraction?

Let's learn the big ideas behind adding and subtracting. These ideas will help you solve all kinds of problems!

Addition Means Joining

When you add, you put two groups together. The answer is called the sum. The sum is always bigger than the parts.

Subtraction Means Taking Away

When you subtract, you start with a group and take some away. The answer is called the difference. The difference is smaller than what you started with.

Use Objects or Drawings

You can use blocks, counters, stickers, or draw circles and dots to help you count. Drawing pictures is a great way to solve word problems!

Within 10

Right now we are working with numbers from 0 to 10. All our answers will be 10 or less. You can use your fingers to check!

✦ KEY TAKEAWAY

Think of adding like filling a basket with apples. If you put 3 apples in and then 4 more apples in, you count them all to find how many you have. Subtracting is like eating some apples from the basket — you count what is left!

SECTION 3

See It! Addition with Pictures

Pictures help us see what is happening in a math problem. Let's look at a picture that shows 3 + 4 = 7. We draw dots for each group, then count them all!

This picture shows 3 blue dots and 4 purple dots. When we put them all together and count, we get 7. That's addition!

Look at the picture above. The blue box has 3 dots. The purple box has 4 dots. At the bottom, we put all the dots in one row and count them. There are 7 dots in all. Drawing dots like this is a great way to solve any addition problem!

SECTION 4

How Addition and Subtraction Work

Let's look at how we write addition and subtraction. We use special signs to show what we are doing.

ADDITION

part + part = whole

The + sign means "put together." The = sign means "is the same as." Example: 2 + 5 = 7.

SUBTRACTION

whole − part = part left over

The − sign means "take away." Example: 8 − 3 = 5. You start with 8 and take away 3. You have 5 left.

Here is a helpful trick! Addition and subtraction are opposites. If 3 + 4 = 7, then 7 − 4 = 3. They undo each other, like zipping and unzipping a jacket!

FACT FAMILY

3 + 4 = 7 → 7 − 4 = 3

A fact family is a group of related addition and subtraction facts that use the same numbers.

🖐️ Helpful Tip!

You can use your fingers to add! Hold up 3 fingers on one hand and 4 on the other. Count them all — 1, 2, 3, 4, 5, 6, 7. The answer is 7!

SECTION 5

See It! Subtraction with Pictures

Now let's see how subtraction works with a picture. We will solve 8 − 3 = 5. We start with 8 things and cross out 3 to take them away. Then we count what is left!

We started with 8 stars. We crossed out 3 (shown in red). The 5 green stars are left. So 8 − 3 = 5!

To subtract with pictures, follow these steps. First, draw the number you start with. Then cross out the number you are taking away. Finally, count the ones that are not crossed out. That is your answer!

Examples of subtraction using pictures

Problem	Draw	Cross Out	Answer
6 − 2	⭐⭐⭐⭐⭐⭐	Cross out 2	4
5 − 1	⭐⭐⭐⭐⭐	Cross out 1	4
9 − 4	⭐⭐⭐⭐⭐⭐⭐⭐⭐	Cross out 4	5

SECTION 6

Solving a Word Problem Step by Step

Word problems tell a little story. Your job is to figure out if you need to add or subtract, and then solve it. Let's try one together!

Word Problem: Emma's Crayons

Step 1 — Read the StoryEmma has 4 crayons. Her friend gives her 3 more crayons. How many crayons does Emma have now?

Step 2 — Decide: Add or Subtract?The story says Emma "gets more." Getting more means the group is getting bigger. That tells us we need to add!

Operation: Addition (+)

Step 3 — Draw a PictureDraw 4 circles for the crayons Emma has. Then draw 3 more circles for the crayons her friend gives her. Now you have two groups of circles!

Step 4 — Count Them AllCount all the circles: 1, 2, 3, 4, 5, 6, 7. There are 7 circles in all.

Step 5 — Write the Answer4 + 3 = 7. Emma has 7 crayons now!

Answer: 4 + 3 = 7

Word Problem: Jake's Stickers

Step 1 — Read the StoryJake has 9 stickers. He gives 5 stickers to his sister. How many stickers does Jake have left?

Step 2 — Decide: Add or Subtract?The story says Jake "gives away" stickers. Giving away means the group gets smaller. We need to subtract!

Operation: Subtraction (−)

Step 3 — Draw and Cross OutDraw 9 circles. Now cross out 5 of them because Jake gives those away.

Step 4 — Count What Is LeftCount the circles that are not crossed out: 1, 2, 3, 4. There are 4 left.

Step 5 — Write the Answer9 − 5 = 4. Jake has 4 stickers left!

Answer: 9 − 5 = 4

SECTION 7

Clue Words: Add or Subtract?

Word problems have clue words that help you decide if you should add or subtract. Listening for these words is like being a math detective!

Listen for these words in story problems!

Addition Clue Words	Subtraction Clue Words
in all	take away
altogether	how many are left
more	fewer
total	gave away
both / and	lost / ate / broke

🔍 KEY TAKEAWAY

Think of clue words like road signs. A sign that says "more" or "altogether" points you toward addition. A sign that says "left" or "take away" points you toward subtraction. Read the story carefully and look for these signs!

SECTION 8

Getting Ready for Bigger Numbers

Right now you are a champion at adding and subtracting within 10. But soon you will work with bigger numbers! Let's peek at what comes next.

From within 10 to within 20 and beyond!

What You Know Now	What Comes Next
Add within 10 (e.g., 3 + 5 = 8)	Add within 20 (e.g., 9 + 7 = 16)
Subtract within 10 (e.g., 9 − 4 = 5)	Subtract within 20 (e.g., 15 − 8 = 7)
Use drawings and fingers	Use ten frames and number lines
Simple word problems	Two-step word problems

The great news is that everything you learn now — drawing pictures, using clue words, and counting carefully — will help you with bigger numbers too. You are building a strong math foundation!

SECTION 9

Practice Problems

Now it's your turn! Try these problems. You can draw pictures, use your fingers, or use objects like blocks to help. Take your time and have fun!

PROBLEM 1 — CONCEPTUAL

What does the plus sign (+) tell you to do? What does the minus sign (−) tell you to do?

PROBLEM 2 — BASIC CALCULATION

What is 2 + 6? Draw a picture or use your fingers to find the answer.

PROBLEM 3 — INTERMEDIATE

Mia has 7 grapes. She eats 3 grapes. How many grapes does Mia have left? Write a number sentence and solve.

PROBLEM 4 — APPLIED

There are 5 birds sitting on a fence. Then 4 more birds fly over and sit on the fence too. How many birds are on the fence altogether? Show your work with a drawing.

PROBLEM 5 — CRITICAL THINKING

Leo has some toy cars. His mom gives him 3 more. Now Leo has 10 toy cars. How many toy cars did Leo have at the start?

SUMMARY

What We Learned

In this lesson you learned that addition means putting groups together to find the sum, and subtraction means taking away to find the difference. You can solve problems by drawing pictures, using objects, or counting on your fingers.

When you read a word problem, look for clue words like "in all" and "altogether" for addition, or "left" and "take away" for subtraction. Remember that addition and subtraction are opposites and belong to the same fact family. Keep practicing and you will be ready for bigger numbers soon!