Adding a Two-Digit Number and a One-Digit Number - 1st Grade Math

Section 1

Why Do We Add Numbers?

People have been adding things together for a very, very long time! A long time ago, before there were schools or books, people still needed to count. If a farmer had 10 apples in one basket and 5 apples in another basket, the farmer needed to know how many apples there were in all. That is adding!

Let's look at how people learned to add over many years.

Long, Long Ago

People used rocks and sticks to count. They put groups of rocks together to find out how many they had in all. This was the very first kind of adding!

Tally Marks

People started scratching lines on bones and cave walls. Each line stood for one thing. To add, they just drew more lines and counted them all up.

Number Symbols

People in places like Egypt and India made up special symbols for numbers — like the 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0 we use today! This made adding much easier.

The Plus Sign (+)

About 500 years ago, someone came up with the + sign to show adding. Now we all use it! When you see +, it means "put together."

Today!

Now YOU get to learn how to add bigger numbers — numbers all the way up to 100! You are part of this big story of math.

Adding is one of the most useful things you will ever learn. You use it when you count your toys, share snacks with friends, or figure out how many days until your birthday. Today we will learn how to add a two-digit number (like 34) and a one-digit number (like 5).

Section 2

Big Ideas to Know

Before we start adding, let's learn four big ideas. These ideas will help you add like a superstar! 🌟

Ones and Tens

Every two-digit number is made of tens and ones. The number 34 has 3 tens and 4 ones. The tens are the "big" part and the ones are the "little" part.

Add the Ones First

When you add a one-digit number, you are only adding more ones. So you can keep the tens the same and just add the ones together!

Making a New Ten

Sometimes the ones add up to 10 or more. When that happens, you make a new ten! For example, 8 + 5 = 13, which is 1 ten and 3 ones.

Stay Under 100

In this lesson, our answers will always be 100 or less. Don't worry about really big numbers yet — we are building up step by step!

✦

KEY TAKEAWAY

Think of a two-digit number like a piggy bank with two pockets. One pocket holds tens (big coins) and the other pocket holds ones (small coins). When you add a one-digit number, you are only putting more small coins into the ones pocket. If that pocket gets too full (more than 9), you trade 10 small coins for 1 big coin and move it to the tens pocket!

Section 3

Let's See It in Pictures!

Pictures help us understand adding. Let's look at 23 + 5 using blocks. We use long bars for tens and little squares for ones.

Look at the picture! The number 23 has 2 tall blue bars (those are the tens) and 3 small green squares (those are the ones). We are adding 5 more ones (the pink squares). When we put them all together, we still have 2 tens and now we have 8 ones. That gives us 28!

The tens did not change at all. We only changed the ones. That is the secret to this kind of adding!

Section 4

How It Works — Step by Step

Here is a simple plan you can follow every time you add a two-digit number and a one-digit number.

THE ADDING PLAN

Two-digit number + One-digit number

Keep the tens. Add the ones together. That's it!

Let's try 42 + 6.

STEP 1 — BREAK IT APART

42 = 40 + 2

42 is 4 tens (40) and 2 ones (2)

STEP 2 — ADD THE ONES

2 + 6 = 8

Add the ones from 42 (which is 2) and the 6 together

STEP 3 — PUT IT BACK TOGETHER

40 + 8 = 48

The tens (40) plus the new ones (8) gives us 48! ✨

Now let's try one where the ones add up to more than 9. This is called "making a ten." Let's try 37 + 5.

MAKING A TEN — 37 + 5

37 = 30 + 7

Break apart: 3 tens and 7 ones

ADD THE ONES

7 + 5 = 12

12 is more than 9, so we make a new ten! 12 = 10 + 2

PUT IT ALL TOGETHER

30 + 10 + 2 = 42

3 tens + 1 new ten + 2 ones = 42! 🎉

✦

KEY TAKEAWAY

Think of adding ones like filling up an egg carton that holds 10 eggs. If you have 7 eggs and add 5 more, the carton fills up at 10 (that makes a new ten!), and you have 2 eggs left over. So 7 + 5 = 12, which is 1 ten and 2 ones.

Section 5

The Number Line — Jumping Forward!

A number line is like a path with numbers on it. To add, you start at one number and jump forward. Each jump is +1. Let's use it to solve 54 + 3.

See how we started at 54 and made 3 jumps forward? Each jump goes to the next number. After 3 jumps, we landed on 57. So 54 + 3 = 57!

The number line is a great tool. You can draw one on paper or even imagine one in your head. Just start at the bigger number and count forward.

Helpful Addition Chart

Here are some examples of adding a two-digit number and a one-digit number. Can you see the pattern?

Problem	Tens	Ones	Answer
21 + 3	20	1 + 3 = 4	24
35 + 4	30	5 + 4 = 9	39
52 + 7	50	2 + 7 = 9	59
46 + 6	40 → 50	6 + 6 = 12 (new ten!)	52
78 + 5	70 → 80	8 + 5 = 13 (new ten!)	83

Notice: when the ones add up to 10 or more, the tens digit goes up by 1. That is making a new ten!

Section 6

Let's Solve One Together!

Let's solve 67 + 8 step by step. Follow along!

67 + 8

1
Step 1 — Look at the Number

Our problem is 67 + 8. The number 67 is a two-digit number. The number 8 is a one-digit number.
2
Step 2 — Break Apart 67

67 has 6 tens and 7 ones.

67 = 60 + 7
3
Step 3 — Add the Ones

Now add the ones: 7 + 8 = ? You might count up from 7: 8, 9, 10, 11, 12, 13, 14, 15. That's 15! 15 is more than 9, so we make a new ten! 15 = 1 ten and 5 ones.

7 + 8 = 15
4
Step 4 — Put It All Together

We had 6 tens and we made 1 new ten. That's 7 tens! We have 5 ones left over.

60 + 10 + 5 = 75
5
Step 5 — The Answer! 🎉

67 + 8 = 75 Great job! We broke the number apart, added the ones, made a new ten, and put it all back together.

Section 7

Tips and Tricks!

Here are some helpful ways to add. Some are fast and some are slow. Pick the one that works best for you!

Strategy	How It Works	Best For
Count On	Start at the bigger number and count up. For 45 + 3, say: 46, 47, 48!	Adding small numbers (1, 2, or 3)
Break Apart	Split the two-digit number into tens and ones. Add the ones, then put it back.	Any problem — works every time!
Make a Ten	Figure out how many to get to the next ten, then add the rest. For 28 + 5: 28 + 2 = 30, then 30 + 3 = 33.	When ones add up past 9
Use Fingers	Start at the big number in your head, then hold up fingers for the small number and count up.	When you're learning — great for checking!

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KEY TAKEAWAY

Think of these strategies like different tools in a toolbox. A hammer is great for nails, and a screwdriver is great for screws. Counting on is great for adding 1, 2, or 3. Breaking apart is great for bigger numbers. You get to pick the best tool for each problem!

One common mistake is forgetting to make a new ten when the ones add up to 10 or more. For example, 38 + 4 is NOT 32. The 8 + 4 = 12, which gives you a new ten. So it's 30 + 12 = 42. Always check: did my ones go past 9?

Section 8

What Comes Next?

You are learning to add a two-digit number and a one-digit number. That is awesome! But math keeps growing. Here is what you will learn soon.

What You Know Now	What Comes Next
Adding a one-digit number (like 34 + 5)	Adding two two-digit numbers (like 34 + 25)!
Answers up to 100	Adding numbers bigger than 100!
Making one new ten	Making new tens AND new hundreds!
Breaking apart numbers	Using this same idea for subtraction too!

The great news is that the same big ideas — tens and ones, breaking apart, making new tens — will help you with ALL of these! The things you learn today are like building blocks for everything that comes next. You are getting ready for bigger math, and you are doing great! 🌟

Section 9

Practice Time! ✏️

Now it's your turn! Try these problems. Think about the steps we learned. Click "Show Answer" when you are ready to check.

Question 1: Problem 1 — Tell Me What You Know

The number 56 has how many tens and how many ones?

Show answer

56 has 5 tens and 6 ones. The 5 is in the tens place and the 6 is in the ones place. 5 tens = 50, and 50 + 6 = 56. Nice work if you got that right!

Question 2: Problem 2 — Simple Adding

What is 32 + 5?

Show answer

32 + 5 = 37. Here's how: 32 has 3 tens and 2 ones. Add the ones: 2 + 5 = 7. The tens stay at 3. So we get 30 + 7 = 37. No new ten needed because 7 is less than 10! 🎉

Question 3: Problem 3 — Making a New Ten

What is 48 + 6?

Show answer

48 + 6 = 54. Break it apart: 48 = 40 + 8. Add the ones: 8 + 6 = 14. That's more than 9, so we make a new ten! 14 = 10 + 4. Now add: 40 + 10 + 4 = 54. The tens went from 4 to 5 because we made a new ten! Great job! ⭐

Question 4: Problem 4 — Story Problem

Emma has 63 crayons in a box. Her friend gives her 9 more crayons. How many crayons does Emma have now?

Show answer

Emma has 72 crayons. We need to find 63 + 9. Break it apart: 63 = 60 + 3. Add the ones: 3 + 9 = 12. Make a new ten! 12 = 10 + 2. Now: 60 + 10 + 2 = 72. Emma has 72 crayons! That's a lot of colors! 🖍️

Question 5: Problem 5 — Think About It

Sam says that 75 + 8 = 73. Is Sam right or wrong? How do you know? What is the correct answer?

Show answer

Sam is wrong! When we add, the answer must be bigger than the number we started with. 73 is smaller than 75, so that can't be right. Let's solve it: 75 = 70 + 5. Add the ones: 5 + 8 = 13. Make a new ten! 13 = 10 + 3. Now: 70 + 10 + 3 = 83. The correct answer is 83. Sam might have subtracted instead of adding. Always remember: adding makes numbers bigger! You're a math detective! 🔍

Summary

What We Learned Today

Summary

Today you learned how to add a two-digit number and a one-digit number with answers up to 100! You learned that every two-digit number is made of tens and ones. When you add a one-digit number, you keep the tens the same and add the ones together. If the ones add up to 10 or more, you make a new ten — the tens digit goes up by one, and you keep the leftover ones.

You can use different strategies: counting on for small numbers, breaking apart for any problem, and making a ten when the ones get big. You practiced with pictures, number lines, and step-by-step math. These same ideas will help you add even bigger numbers someday. You are becoming a great mathematician! 🌟