Y.2 Add ones to two-digit numbers using a number chart – without regrouping
What does it mean to add ones to a two-digit number?
A two-digit number is made of tens and ones, like 23 (2 tens and 3 ones) or 56 (5 tens and 6 ones). Adding ones means you are joining a smaller number (1, 2, 3, ... up to 9) to the ones place of that two-digit number. Without regrouping means that when you add, the total number of ones is 9 or less. This keeps the addition simple because the tens digit does not change.
- If you have 34 and add 2, you are adding 2 ones to the 4 ones. 4 ones + 2 ones = 6 ones. The number becomes 36.
- If you have 71 and add 5, you are adding 5 ones to the 1 one. 1 one + 5 ones = 6 ones. The number becomes 76.
- If you have 48 and add 3, you are adding 3 ones to the 8 ones. 8 + 3 = 11 ones. This is NOT "without regrouping" because 11 ones makes a new group of ten.
The key question to ask is: Will the ones place total be 9 or less? If the answer is yes, you are adding without regrouping. This is a foundational skill that makes bigger addition easier later.
Understanding the tools: tens, ones, and place value
Place value is the idea that where a digit sits in a number tells you its value. In the number 25, the '2' is in the tens place, meaning 2 groups of ten (or 20). The '5' is in the ones place, meaning 5 single ones. When we see 25, we understand it as 20 + 5. This understanding is crucial for adding correctly.
- The number 63 means 6 tens (60) and 3 ones (3).
- The number 90 means 9 tens (90) and 0 ones (0).
- Adding 4 to 63 means you are only changing the ones: 60 + (3 + 4). This equals 60 + 7, which is 67. The 6 tens remained untouched.
You can think of a two-digit number like a box of markers. The tens digit is the number of full boxes of 10 markers. The ones digit is the number of loose markers outside the box. Adding ones without regrouping is like adding more loose markers without filling up a whole new box.
What is a number chart and how do you read it?
A number chart (such as a 100 chart or 120 chart) is a special grid that shows numbers in order from 1 to 100 (or 120). Numbers go from left to right in rows, and each row usually has 10 numbers. It is a map of our number system. On this map, moving one space to the right adds one. Moving one space down adds ten. This visual pattern helps us see exactly what happens when we add.
- Find 27 on a number chart. The number directly to its right is 28. This shows that 27 + 1 = 28.
- Find 52 on a number chart. The number directly below it is 62. This shows that 52 + 10 = 62.
- To add 4 to 27, start at 27 and move four squares to the right: 28, 29, 30, 31. You land on 31. So, 27 + 4 = 31.
The number chart proves that adding ones keeps you in the same row. If you stay in the same row, the digit in the tens place does not change. This is a powerful visual rule.
The step-by-step strategy for adding with a number chart
Using a number chart is a reliable method to find the correct sum. Follow these steps every time to ensure accuracy: 1. Locate the starting two-digit number. 2. Count the ones you are adding by moving to the right, one square for each one. 3. Identify the number you land on as your answer.
- Problem: 45 + 3
Step 1: Find and point to 45 on the chart.
Step 2: Move three squares to the right: 46 (1), 47 (2), 48 (3).
Step 3: The answer is 48. - Problem: 80 + 6
Step 1: Find and point to 80 on the chart.
Step 2: Move six squares to the right: 81, 82, 83, 84, 85, 86.
Step 3: The answer is 86.
Touch each square as you count. This physical action helps connect counting to the visual movement on the chart and prevents counting errors. Always double-check that you moved the correct number of spaces.
Moving from the chart to mental math
After much practice with the chart, you will start to see the pattern in your head. The mental math rule for adding ones without regrouping is: Keep the tens digit the same. Add the two ones digits together. Combine the original tens digit with the new ones digit to make the answer.
- 33 + 5: Keep the '3' from the tens place. Add the ones: 3 + 5 = 8. Put them together: 3 and 8 is 38.
- 62 + 7: Keep the '6' from the tens place. Add the ones: 2 + 7 = 9. Put them together: 6 and 9 is 69.
- 14 + 4: Keep the '1' from the tens place. Add the ones: 4 + 4 = 8. Put them together: 1 and 8 is 18.
Saying the process out loud helps: "For twenty-four plus three, the tens stay as twenty. Four ones plus three ones is seven ones. Twenty and seven is twenty-seven." This reinforces the place value concept.
Checking your work for accuracy
A good mathematician always checks their answer. For adding ones without regrouping, the best check is to use a second strategy. If you solved with mental math, check by counting on your fingers or using a number chart. If the answers match, you are correct. Also, ask the key question: Does my answer make sense?
- Problem: 58 + 1 = 59
Check: What number comes right after 58? 59. This makes sense. - Problem: 22 + 6 = 28
Check on a Chart: Start at 22, move 6 right: 23, 24, 25, 26, 27, 28. Correct. - Problem: 77 + 2 = 79
Sense Check: 77 is close to 80. Adding 2 should make it 79, which is still close to 80 but not there yet. This makes sense.
Checking your work is not about finding mistakes; it's about proving to yourself that you are confident and correct. It turns "I think it's right" into "I know it's right."
Real-world problems using this skill
We use this math every day without even thinking about it. It helps us count forward, keep score in a game, see how much we have, or figure out how many we need. Recognizing these situations helps you see why math is important and useful.
- You have 15 stickers. Your friend gives you 3 more. How many do you have now? (15 + 3 = 18)
- You are on page 42 of your book. You read 5 more pages. What page are you on now? (42 + 5 = 47)
- There are 60 minutes in an hour. A TV show starts in 8 minutes. What time will it start? (60 + 8 = 68, which we understand as "8 after the hour").
- You have 29 cents. You find 2 more cents on the floor. How many cents do you have? (29 + 2 = 31)
When you see a problem, first find the two-digit number and the small number being added. Ask yourself: "Am I adding ones to the ones place?" If yes, you can use the strategies you have learned.
Common Core alignment: CCSS.MATH.CONTENT.1.NBT.C.4 – Add within 100, including adding a two-digit number and a one-digit number, using concrete models or drawings and strategies based on place value...Understand that in adding two-digit numbers, one adds tens and tens, ones and ones.
Notes for teachers
This lesson is aligned with CCSS.MATH.CONTENT.1.NBT.C.4. Use it for whole-class instruction, independent practice, or homework. The sequence builds from concrete (number chart as a visual model) to abstract (mental math), emphasizing the constant role of the tens place when adding without regrouping.
All content is 100% free, student-safe, and designed for classroom and home use. The "Real-world problems" section is designed to facilitate classroom discussion and connect math to students' daily experiences.