Adding and Subtracting Within 100 - 2nd Grade Math

Section 1

Where Did Adding and Subtracting Come From?

People have been adding and subtracting for thousands of years! Long ago, before calculators or even pencils, people needed to count things like sheep, fish, and bags of grain. Let's look at how math grew up over time.

Long, Long Ago

People used pebbles and sticks to count. They would put small stones in piles to keep track of how many animals they had.

About 4,000 Years Ago

People in ancient lands created the abacus, a frame with beads you slide back and forth. It helped people add and subtract faster!

About 1,400 Years Ago

Mathematicians in India and the Arab world gave us the number system we use today — the digits 0 through 9, and the idea of place value (ones, tens, hundreds).

About 500 Years Ago

The + and − signs were first used in books! Before that, people wrote out the words "plus" and "minus."

Today

Now you are learning these same skills! You get to use smart strategies to add and subtract numbers quickly in your head — no pebbles needed!

All these years of work led us to the cool tricks you will learn today. The big question is: How can we add and subtract numbers up to 100 in fast, smart ways?

Section 2

The Big Ideas You Need to Know

Before we start adding and subtracting, let's learn four super-important ideas. These are the tools in your math toolbox!

Place Value

Every digit in a number has a value based on where it sits. In the number 47, the 4 means 40 (four tens) and the 7 means 7 (seven ones).

Break Apart Numbers

You can split a number into tens and ones to make math easier. For example, 36 = 30 + 6. This helps you add or subtract one part at a time.

Make a Ten

Adding is easier when you make a group of ten! If you have 8 + 5, you can take 2 from the 5 to make 10 + 3 = 13.

Addition and Subtraction Are Buddies

These two operations are related! If you know that 25 + 30 = 55, then you also know that 55 − 30 = 25. They undo each other.

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Key Takeaway

Think of numbers like building blocks. A number like 63 is really 6 big blocks (tens) and 3 small blocks (ones). When you add or subtract, you can work with the big blocks and small blocks separately — just like sorting LEGO bricks by size before you build!

Section 3

See It! Place Value Blocks

Let's look at a picture that shows how place value works. In the diagram below, you can see how the number 47 is made of 4 tens and 7 ones.

See how the tall blue blocks are tens and the small yellow blocks are ones? When we add and subtract, we can work with the tens and ones separately. This makes big problems feel easy!

Section 4

Smart Strategies for Adding and Subtracting

Here are the best strategies you can use. Think of them like superpowers for your brain!

Strategy 1: Break Apart (Expanded Form)

Split each number into tens and ones. Add the tens together, add the ones together, then put them back together!

Break Apart Strategy

36 + 42 → (30 + 40) + (6 + 2) = 70 + 8 = 78

Split into tens and ones, add each part, then combine!

Strategy 2: Add Tens, Then Add Ones

Keep one number whole. Then add the tens from the other number. Then add the ones.

Add In Parts

27 + 35 → 27 + 30 = 57 → 57 + 5 = 62

Keep 27 whole, add the 30, then add the 5.

Strategy 3: Make a Ten

Sometimes the ones digits add up past ten. You can borrow from one number to make a nice, round ten.

Make a Ten

48 + 7 → 48 + 2 = 50 → 50 + 5 = 55

Make 48 into 50 first, then add what's left.

Strategy 4: Use Addition to Subtract

Addition and subtraction are best friends! If you need to subtract, you can count up instead.

Think Addition

62 − 45 = ? → 45 + ? = 62 → 45 + 5 = 50, 50 + 12 = 62 → 5 + 12 = 17

Count up from 45 to 62. The answer is 17!

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Key Takeaway

These strategies are like different paths to the same place. Imagine you're walking to a friend's house — you can take the sidewalk, cut through the park, or ride your bike. They all get you there! Pick the strategy that feels easiest for each problem.

Section 5

The Number Line — Your Jumping Tool

A number line is like a road with numbers on it. You can jump forward to add and jump backward to subtract. Let's see how to use it to solve 54 + 28.

We started at 54. We broke 28 into 20 + 8. First we made a big jump of +20 to get to 74. Then we made a small jump of +8 to land on 82. You can use this same trick for subtraction — just jump backward!

Strategy	Best For	Example
Break Apart	Adding two 2-digit numbers	36 + 42 → 70 + 8 = 78
Add in Parts	Adding tens first, then ones	27 + 35 → 57 + 5 = 62
Make a Ten	When one number is close to a ten	48 + 7 → 50 + 5 = 55
Number Line	When you want to see the jumps	54 + 28 → jump 20, jump 8 = 82
Count Up (Think Addition)	Subtraction problems	62 − 45 → 45 + ? = 62 → 17

Section 6

Let's Solve One Together!

Let's work through a problem step by step. We will solve 73 − 48 using the break apart strategy.

Solving 73 − 48

1
Step 1 — Understand the Problem

We want to find 73 − 48. That means we start with 73 and take away 48.
2
Step 2 — Break Apart 48

Let's split 48 into tens and ones: 48 = 40 + 8. Now we can subtract in two easy steps!
3
Step 3 — Subtract the Tens

Start with 73 and subtract 40:

73 − 40 = 33
4
Step 4 — Subtract the Ones

Now take away the 8 from 33. Tip: You can think of this as 33 − 3 = 30, then 30 − 5 = 25. That's the "make a ten" trick inside the bigger problem!

33 − 8 = 25
5
Step 5 — Check Your Work

Since subtraction and addition are buddies, let's check: 25 + 48 = ? 25 + 40 = 65. Then 65 + 8 = 73. ✓ Yes! We got back to 73, so our answer is correct!

Final Answer

73 − 48 = 25

Section 7

Which Strategy Should I Pick?

You might wonder: which strategy is the best? The truth is, they are all great! Different problems work better with different strategies. Let's compare them.

Strategy	Strengths (What's Great)	Watch Out For
Break Apart	Works with any two numbers. Very organized.	Lots of steps. You need to remember all the parts.
Add/Subtract in Parts	Fewer steps. Keep one number whole.	The second step can sometimes be tricky.
Make a Ten	Super fast when a number is close to a ten!	Not always helpful if numbers aren't near a ten.
Number Line	You can see the jumps. Great for understanding.	Takes a little time to draw.
Think Addition	Makes subtraction easier if you know addition facts.	Needs strong addition skills first.

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Key Takeaway

Choosing a math strategy is like choosing a crayon. You have a whole box of colors, and you pick the one that looks best for what you're drawing. Try different strategies and see which one feels most comfortable to you!

Section 8

What Comes Next?

The strategies you are learning now are building blocks for bigger math! Soon you will use these same ideas with even larger numbers. Let's peek at what's ahead.

What You Do Now (2nd Grade)	What You'll Do Next (3rd Grade and Beyond)
Add and subtract within 100	Add and subtract within 1,000!
Break numbers into tens and ones	Break numbers into hundreds, tens, and ones
Use the "make a ten" trick	Use "make a hundred" and other rounding tricks
Use addition to check subtraction	Use multiplication and division (they're buddies too!)

Everything you learn today makes tomorrow's math easier. You're building a strong math brain, one step at a time!

Section 9

Practice Time! 🎉

Try these problems on your own. Take your time, pick a strategy, and check your answers when you're ready!

Question 1: Problem 1 — Think About It

In the number 63, what does the digit 6 mean? What does the digit 3 mean?

Show answer

The 6 is in the tens place, so it means 60 (six tens). The 3 is in the ones place, so it means 3 (three ones). Together, 60 + 3 = 63. Understanding place value is the key to all our adding and subtracting strategies! Great job if you got this! 🌟

Question 2: Problem 2 — Basic Addition

Solve using any strategy: 34 + 25 = ?

Show answer

Let's use the break apart strategy! Split the numbers: 30 + 20 = 50. Then 4 + 5 = 9. Now put them together: 50 + 9 = 59. The answer is 59! You're doing awesome! 🎉

Question 3: Problem 3 — Subtraction Challenge

Solve: 81 − 37 = ?

Show answer

Let's subtract in parts. Break 37 into 30 + 7. First: 81 − 30 = 51. Then: 51 − 7 = ? We can think: 51 − 1 = 50, then 50 − 6 = 44. So 81 − 37 = 44. Check: 44 + 37 = 44 + 30 + 7 = 74 + 7 = 81. ✓ It works! Nice thinking! 🧠

Question 4: Problem 4 — Real-World Problem

You have 56 stickers. Your friend gives you 28 more stickers. How many stickers do you have now?

Show answer

We need to solve 56 + 28. Let's use the add in parts strategy. Start with 56. Add the tens: 56 + 20 = 76. Now add the ones: 76 + 8. We can make a ten! 76 + 4 = 80, then 80 + 4 = 84. You now have 84 stickers! That's a lot of stickers! 🌈

Question 5: Problem 5 — Super Thinker Challenge

Sam says: "I know that 45 + 38 = 83. So 83 − 38 must equal 45." Is Sam right? Explain how you know.

Show answer

Yes, Sam is right! 🎯 Addition and subtraction are opposite operations — they undo each other. If 45 + 38 = 83, then taking 38 away from 83 brings you right back to 45. It's like walking 38 steps forward and then 38 steps backward — you end up right where you started! This is called the relationship between addition and subtraction, and it's one of the most powerful ideas in math. You can always use it to check your work!

Summary

Let's Remember What We Learned!

Summary

You learned that every number has tens and ones, and understanding place value helps you break numbers apart into easier pieces. You discovered several smart strategies: the break apart strategy splits both numbers into tens and ones, the add in parts strategy keeps one number whole while adding or subtracting pieces of the other, and the make a ten trick helps when a number is close to a round number like 10, 20, 30, and so on.

You also learned that a number line lets you see your jumps, and that addition and subtraction are related operations — if you know an addition fact, you know a subtraction fact too! Remember, there is no single "best" strategy. The best strategy is the one that helps you solve the problem quickly and correctly. Keep practicing, and soon you'll be adding and subtracting within 100 like a true math superstar! ⭐