Fluently Add And Subtract Within 5 — CCSS.K.OA.5: Fluently...

SECTION 1

Why Do We Add and Subtract?

People have been adding and subtracting for a very, very long time! Long ago, people needed to count things like sheep, apples, and fish. They wanted to know how many they had when they got more, or how many were left when some went away.

Long Ago

Counting with Fingers

People used their fingers to count things. You have 5 fingers on each hand — perfect for counting to 5!

Old Times

Counting with Stones

People put small stones in piles to keep track of how many animals or crops they had.

Later

Number Symbols

People made up symbols for numbers like 1, 2, 3, 4, and 5. Now we could write math down!

Today

Learning Math in School

Today you learn to add and subtract quickly. This helps you every day — at the store, playing games, and sharing with friends!

So here is the big question: how can you add and subtract numbers up to 5 quickly and correctly? That is what this lesson is all about!

SECTION 2

What Does It Mean to Add and Subtract?

Before we practice, let's learn what adding and subtracting really mean. These are two important actions you can do with numbers.

Adding Means Putting Together

When you add, you put groups together to find out how many in all. The answer gets bigger!

Subtracting Means Taking Away

When you subtract, you take some away from a group. The answer gets smaller!

Within 5 Means 0 to 5

All our numbers today will be 0, 1, 2, 3, 4, or 5. We will not go higher than 5.

Fluently Means Fast and Right

Fluently means you can do it quickly and get the right answer — just like how you know your own name!

✦ KEY TAKEAWAY

Think of adding like putting crayons into a box — you end up with more. Think of subtracting like giving crayons to a friend — you end up with fewer. Your hand has exactly 5 fingers, so you can always use your fingers to help!

SECTION 3

See It! Adding and Subtracting with Pictures

Pictures can help you understand adding and subtracting. Look at the diagram below. It shows adding two groups of stars together and subtracting some stars from a group.

The top part shows adding: 2 stars plus 3 stars make 5 stars in all. The bottom part shows subtracting: start with 5 stars, take away 2 (the faded ones), and 3 are left.

In the top picture, you can see two groups of stars coming together. When you put 2 stars and 3 stars together, you get 5 stars in all. In the bottom picture, you start with 5 stars. The faded stars show the 2 you take away. The 3 bright stars that are left are your answer!

SECTION 4

How Adding and Subtracting Work

When you write an addition or subtraction problem, you use special symbols. The plus sign (+) means add. The minus sign (−) means subtract. The equals sign (=) means "the answer is."

ADDITION

part + part = whole

You put two parts together to find the whole. Example: 1 + 4 = 5

SUBTRACTION

whole − part = part

You start with the whole and take away a part to find what is left. Example: 5 − 1 = 4

ZERO RULE

any number + 0 = that number

Adding zero does not change the number! Example: 3 + 0 = 3. Subtracting zero also keeps the number the same: 3 − 0 = 3.

💡 Helpful Tip

You can count on your fingers! Hold up the first number, then put up more fingers to add or put fingers down to subtract. Count what you see!

SECTION 5

All the Addition and Subtraction Facts Within 5

There are many addition and subtraction facts to learn when working within 5. A fact family is a group of related addition and subtraction facts that use the same numbers. Look at the number line and table below to see all the facts!

The number line at the top shows how you hop forward to add and hop backward to subtract. Below, a fact family shows how the numbers 2, 3, and 5 are connected.

Some important addition and subtraction facts within 5

Addition Fact	Subtraction Fact
0 + 1 = 1	1 − 1 = 0
1 + 1 = 2	2 − 1 = 1
1 + 2 = 3	3 − 2 = 1
2 + 2 = 4	4 − 2 = 2
2 + 3 = 5	5 − 3 = 2
1 + 4 = 5	5 − 4 = 1
0 + 5 = 5	5 − 5 = 0

SECTION 6

Let's Solve a Problem Step by Step

Let's work through a problem together! Pay attention to each step. You can do this!

Example: You have 4 apples. You give 2 to a friend. How many do you have left?

Step 1 — Read the ProblemYou start with 4 apples. You give away 2 apples. The word "give away" tells you to subtract.

Step 2 — Write the Number SentenceWrite the subtraction problem: 4 − 2 = ?

Step 3 — Use Your FingersHold up 4 fingers. Now put 2 fingers down. Count the fingers that are still up: 1, 2. You have 2 fingers still up!

Step 4 — Write the Answer4 − 2 = 2. You have 2 apples left!

4 − 2 = 2

Example: You see 1 bird in a tree. Then 3 more birds come. How many birds are there now?

Step 1 — Read the ProblemYou see 1 bird. Then 3 more come. The words "more come" tell you to add.

Step 2 — Write the Number SentenceWrite the addition problem: 1 + 3 = ?

Step 3 — Count OnStart at 1. Count up 3 more: 2, 3, 4. You land on 4!

Step 4 — Write the Answer1 + 3 = 4. There are 4 birds now!

1 + 3 = 4

SECTION 7

Different Ways to Add and Subtract

There are many ways to find the answer! Some ways might be easier for you than others. Let's look at a few helpful strategies — that's a fancy word for tricks that help you solve problems.

Four strategies for adding and subtracting within 5

Strategy	How It Works	Best For
Counting Fingers	Hold up fingers and count them. Put fingers up to add or down to subtract.	When you are just learning
Counting On	Start with the bigger number in your head. Then count up to add.	Adding small numbers
Using Objects	Use blocks, buttons, or toys. Push them together to add or take some away to subtract.	When you want to touch and see
Knowing by Heart	You just know the answer! Like you know 1 + 1 = 2 without thinking hard.	When you have practiced a lot

✦ KEY TAKEAWAY

Using strategies is like training wheels on a bike. At first you need help, but after practice you can ride on your own! Your goal is to know the facts by heart so you don't need to count every time.

SECTION 8

Getting Ready for Bigger Numbers

Once you can add and subtract within 5 quickly, you are ready for more! Next you will work with numbers up to 10, then up to 20. The same ideas work — the numbers just get bigger.

How today's skills connect to future learning

What You Learn Now	What Comes Next
Add and subtract within 5	Add and subtract within 10
Use fingers and objects	Use a ten frame and drawings
Know facts like 2 + 3 = 5	Know facts like 6 + 4 = 10
Simple word problems	Longer word problems with more steps

Everything you learn about adding and subtracting within 5 is like building a strong base for a tower. The stronger your base, the taller you can build! So keep practicing these facts until you know them by heart.

SECTION 9

Practice Problems

Now it's your turn! Try these problems. Think about the answer first, then check below each one.

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 3 + 2?

PROBLEM 3 — INTERMEDIATE

What is 5 − 3? Use a number line or your fingers to help.

PROBLEM 4 — APPLIED

You have 2 toy cars. Your mom gives you 2 more toy cars. Then you give 1 car to your sister. How many toy cars do you have now?

PROBLEM 5 — CRITICAL THINKING

I am thinking of a number. When I add 3 to my number, I get 5. What is my number? How do you know?

SUMMARY

Let's Remember What We Learned!

In this lesson, you learned how to add and subtract with numbers from 0 to 5. Adding means putting groups together to find how many in all. Subtracting means taking some away to find how many are left. You can use fingers, objects, a number line, or counting on to help you find answers.

You also learned about fact families — related addition and subtraction facts that use the same numbers. The goal is to become fluent, which means you can answer quickly and correctly without counting every time. Keep practicing, and soon these facts will be as easy as saying your name!