Apply Properties of Operations as Strategies to Add and...

Section 1

The Story of Adding Tricks ✨

People have been adding and subtracting for a very, very long time! Long ago, people noticed something cool. When you put things together, it does not matter what order you put them in. You still get the same answer! Let's see how people learned these math tricks over the years.

A Long Time Ago 🏺

People in ancient lands like Egypt and Babylon used rocks and sticks to count. They noticed that putting 3 rocks with 2 rocks is the same as putting 2 rocks with 3 rocks!

Ancient Greece 🏛️

Smart thinkers in Greece saw patterns in numbers. They wrote down rules about how numbers work together. These rules help us add faster!

Hundreds of Years Ago 📖

Math teachers gave these rules special names. They called them properties. A property is like a rule that is always true.

Today 🎒

You use these same rules in your classroom every day! They help you solve addition and subtraction problems more easily. You are learning the same tricks people have used for thousands of years!

So here is the big question: What are these special rules, and how can they help YOU add and subtract? Let's find out!

Section 2

The Big Ideas 💡

There are a few special rules — called properties — that help us add and subtract. A property is something that is always true about numbers. Let's learn four of them!

Turn-Around Rule

You can add two numbers in any order and get the same answer! 3 + 5 is the same as 5 + 3. This is called the Commutative Property.

Grouping Rule

When you add three numbers, you can group any two first. (2 + 3) + 4 is the same as 2 + (3 + 4). This is the Associative Property.

Zero Rule

When you add 0 to any number, you get that same number back! 7 + 0 = 7. Zero is called the Identity Element.

Fact Family Rule

Addition and subtraction are opposites! If 4 + 5 = 9, then 9 − 5 = 4. Knowing one fact helps you find the other!

✦ Key Takeaway

Think of adding like putting toys in a box. If you put in 3 cars and then 2 trucks, you have 5 toys. If you put in 2 trucks first and then 3 cars, you still have 5 toys! The order does not change how many you have.

Section 3

See It in Pictures! 🎨

Let's look at pictures that show how the Turn-Around Rule works. When we swap the groups, the total stays the same!

Diagram showing that 3 plus 5 equals 5 plus 3 using colored circles

See? In the top picture, we have 3 blue circles plus 5 pink circles. That makes 8. In the bottom picture, we swapped them! We have 5 pink plus 3 blue. We still get 8!

💡 🌟 Fun Fact

This swap trick only works for addition. It does NOT work for subtraction! 5 − 3 is NOT the same as 3 − 5. Be careful!

Section 4

How These Rules Work 🔧

Now let's look at each rule with numbers. These are like super tools in your math toolbox!

Turn-Around Rule

3 + 5 = 5 + 3

You can flip the numbers around. The answer is still 8!

This is so helpful! If you know that 3 + 5 = 8, then you also know that 5 + 3 = 8. That's like learning two facts for the price of one!

Grouping Rule

(2 + 3) + 4 = 2 + (3 + 4)

Group any two numbers first. You still get 9!

When you add three numbers, you can pick which two to add first. Try it! (2 + 3) is 5, then 5 + 4 = 9. Or do 2 + (3 + 4) — that's 2 + 7 = 9. Same answer!

Zero Rule

6 + 0 = 6

Adding zero does not change the number!

Zero is special. If you have 6 apples and you get 0 more apples, you still have 6 apples. Zero doesn't add anything!

Fact Family

4 + 5 = 9 → 9 − 5 = 4

Addition and subtraction are partners!

If you know an addition fact, you can figure out a subtraction fact! 4 + 5 = 9 tells you that 9 − 5 = 4 and 9 − 4 = 5. That's a whole family of facts!

Section 5

More Helpful Tools 🧰

Let's learn one more awesome trick: Make a 10! When you add two numbers, sometimes you can break one number apart to make a group of 10. This makes adding much easier because 10 is a friendly number.

Diagram showing the Make a 10 strategy to add 8 plus 5 by breaking 5 into 2 and 3

We started with 8 + 5. We broke the 5 into 2 and 3. We moved the 2 over to the 8 to make 10. Then we added the leftover 3. So 10 + 3 = 13!

✦ Key Takeaway

Making a 10 is like filling up an egg carton! 🥚 If the carton holds 10 eggs and you already have 8, you need 2 more to fill it. Then you count the leftovers. That's exactly what we did with 8 + 5!

Section 6

Let's Solve One Together! ✏️

Here is a problem. Let's use our math tricks to solve it!

Problem: What is 6 + 7?

Step 1 — Use the Make a 10 trickWe want to make 10 from one of these numbers. 6 needs 4 more to make 10. So let's break 7 into 4 and 3.

Step 2 — Break apart the 77 = 4 + 3

Step 3 — Make a 10Now add the 4 to the 6: 6 + 4 = 10

Step 4 — Add the leftover10 + 3 = 13

✅ Answer6 + 7 = 13 🎉

CheckWe could also check with the Turn-Around Rule: 7 + 6 should also be 13. And it is! Great job!

Section 7

Comparing the Tricks 🔍

Each trick is useful in different ways. Let's see when to use each one!

Trick	When to Use It	Example
Turn-Around	When you know one fact and need the other	Know 2 + 8 = 10? Then 8 + 2 = 10!
Grouping	When adding 3 numbers — pick the easiest pair first	3 + 7 + 2 → do 3 + 7 first = 10, then + 2 = 12
Zero	When one number is 0	9 + 0 = 9 (quick!)
Fact Family	When you need a subtraction answer	Know 3 + 4 = 7? Then 7 − 4 = 3!
Make a 10	When one number is close to 10	9 + 6 → 10 + 5 = 15

⚠ ⚠️ Remember!

The Turn-Around Rule does NOT work for subtraction! 5 − 2 = 3, but 2 − 5 is not the same thing. Only addition can be swapped!

✦ Key Takeaway

Think of these tricks like tools in a toolbox. 🧰 A hammer is great for nails, but not for screws. Pick the right tool for the right problem! If you see a number close to 10, use Make a 10. If you need subtraction, think of the fact family.

Section 8

What's Coming Next? 🚀

The tricks you are learning now will help you with bigger numbers soon! In 2nd grade, you will add numbers like 24 + 38. Guess what? You will use the same Make a 10 idea — but with tens and ones! The Turn-Around Rule and Grouping Rule will still be your best friends.

What You Learn Now	What Comes Next
3 + 5 = 5 + 3 (Turn-Around)	23 + 15 = 15 + 23 (still works!)
8 + 5 → Make a 10 → 13	28 + 5 → Make the next 10 (30) → 33
4 + 5 = 9, so 9 − 5 = 4	40 + 50 = 90, so 90 − 50 = 40

See how the same ideas keep working? That's the magic of math properties — they are always true, no matter how big the numbers get! You are building a strong foundation right now. 💪

Section 9

Practice Time! 🏋️

Try these problems on your own. Use the tricks you learned! Click "Show Answer" when you are ready to check.

PROBLEM 1 — WHAT DO YOU KNOW?

If 4 + 6 = 10, what is 6 + 4? Which trick helps you answer this?

PROBLEM 2 — QUICK ADD

What is 5 + 0?

PROBLEM 3 — MAKE A 10

Use the Make a 10 trick to solve: 9 + 4 = ? (Hint: 9 needs just 1 more to make 10!)

PROBLEM 4 — WORD PROBLEM

Emma has 7 crayons. She gets 5 more crayons. How many crayons does she have now? (Try using a math trick to help!)

PROBLEM 5 — THINKING CHALLENGE 🧠

You know that 8 + 6 = 14. Can you use this fact to figure out what 14 − 6 is? Which trick helps you?

Summary

Let's Review! 📝

Today you learned four powerful math tricks called properties! The Turn-Around Rule (Commutative Property) says you can add numbers in any order — 3 + 5 and 5 + 3 both equal 8. The Grouping Rule (Associative Property) says when you add three numbers, you can pick which two to add first. The Zero Rule (Identity Property) says adding 0 to any number gives you that same number. And the Fact Family Rule connects addition and subtraction — if you know 4 + 5 = 9, you also know 9 − 5 = 4!

You also learned a super helpful strategy called Make a 10. When one number is close to 10, you break the other number apart to fill it up to 10, then add the leftovers. These tricks work together to help you add and subtract faster and with more confidence. Keep practicing and you will be a math superstar! ⭐