Relate Addition to Subtraction

**Addition **is putting numbers together to make a new sum.

It is the **opposite **of subtraction.

In this lesson, we'll show you what that means. But first, let's learn about **fact families.** They'll help us understand how addition and subtraction are related.

🤔Do you know that equations have families, too?

👉They're called **fact families.**

**Fact families** are groups of equations that are **related **to each other.

But how can equations be **related?**

Let's look at one **fact family**.

5 + 2 = 7

2 + 5 = 7

7 - 2 = 5

7 - 5 = 2

Can you think of ways they are related?

✅ They all have the same three numbers: 5, 2, and 7

✅ They all use addition or subtraction.

Let's learn to make fact families using a cool trick - Math Mountains!

**Math Mountains **help you figure out how numbers are related.

Here's the math mountain:

Do you see how it looks like a mountain? ⛷

Each of the boxes will have one number from our equation in it.

The box at the top is the **total. **The two boxes below are the **two parts.**

👉When you **add **the **two parts,** you always get the **total **at the top.

👉When you take **one part away **from the total, you get the **other part.**

Here's a math mountain with our addition problem 5 + 2 = 7:

The **sum **will always be in the **top **box.

The two addends will always be in the bottom boxes.

From this, we can see that:

5 + 2 = 7

We can also see this:

2 + 5 = 7

They are **related equations.**

👉They are from the same math mountain.

Here's the fun part!

😺You can use the same math mountain to find two related subtraction equations!

How?

👉We can subtract **one part **from the **total **to get the **other part!**

Let's try subtracting "2" from the total:

What **related equation **do we get?

7 - 2 = 5

Great job! 😺

So far we've used our math mountain to find 3 **related **equations:

7 - 2 = 5

2 + 5 = 7

5 + 2 = 7

Can we use the same math mountain to figure out one more related equation?

Yes! We can subtract 5 from 7.

7 - 5 = 2

When you take one **part away **from the **total,** you get the **other part!**

Great job! 🤗 That’s how you create **fact families!**

👉You write the **two addition **and **two subtraction equations **that describe the same math mountain!

Here's the most important part of math mountains:

👉You can use them to solve **both addition **and **subtraction **problems!

Take a look.

Let's write the **related equations **for this math mountains.

Let's start with the addition equations:

🤓We can add the **two parts **(8 and 7) to get the **total **(15), in either order.

Can you figure out how to create the other 2 **related **subtraction equations?

Let's start by taking away one part from the total.

That makes the 3rd **related **equation:

15 - 8 = 7

Now let's subtract the other part (7) from the total (15).

This makes the 4th **related equation **in our fact family:

15 - 7 = 8

Let’s try to write a fact family for this equation:

3 + 2 = 5

How should we start?

Let's make a math mountain! 🤗

Follow these steps to write all the equations in the fact family:

👉 Write **two **addition equations by **switching the addends.**

👉 Write **one subtraction equation **by subtracting the **left side of the mountain.**

👉 Write **one more subtraction equation** by subtracting the **right side of the mountain.**

What do we get?

3 + 2 = 5

2 + 3 = 5

5 - 2 = 3

5 - 3 = 2

You’ve got it! 💪

So what did we learn?

👉 **Related equations **belong to one fact family.

👉 We can use a **Math Mountain **to find related equations.

Great job! 🤗 Now, you can practice what you've just learned!

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