Y.9 Add two-digit numbers without regrouping - sums up to 100
What are two-digit numbers?
Two-digit numbers are numbers that have two digits: a tens place and a ones place. The tens digit tells how many groups of ten. The ones digit tells how many leftovers.
- In 38, the 3 means 3 tens (30) and the 8 means 8 ones. 3 tens + 8 ones = 38
- In 21, the 2 means 2 tens (20) and the 1 means 1 one. 2 tens + 1 one = 21
Picture it:
The largest two-digit number is 99 (9 tens and 9 ones). In this lesson, we will work with sums up to 100, so our answers will stay at 100 or less.
What does "no regrouping" mean?
No regrouping (also called "no carrying") means that when we add the ones, the total is less than 10. When we add the tens, the total is less than 10. We do not need to move a group of ten to the next column.
- Ones: 8 + 1 = 9 (less than 10, so we write 9 in the ones place).
- Tens: 3 + 2 = 5 (less than 10, so we write 5 in the tens place).
- The answer is 5 tens and 9 ones = 59.
If the ones add up to 10 or more, we would need to regroup. But in this lesson, we practice only problems where the ones are 9 or less, so regrouping is not needed.
Understanding tens and ones place value
Every two-digit number has a tens place (on the left) and a ones place (on the right). When we add vertically, we must line up the digits carefully: tens under tens, ones under ones.
If we wrote 38 + 21 in a messy way, we might get the wrong answer. Always keep the columns straight.
Wrong way: 38 + 21 written as 3821 (that would be a huge number!).
Using grid paper or lining up numbers in columns helps us see the tens and ones clearly.
Step-by-step: adding the ones first
When we add two-digit numbers, we always start with the ones column on the right. Then we move to the tens column on the left. This order works for all addition, even when we regroup.
- Step 1: Add the ones. 4 (ones) + 5 (ones) = 9. Write 9 under the ones column.
- Step 2: Add the tens. 2 (tens) + 3 (tens) = 5. Write 5 under the tens column.
- Step 3: Read the answer. The number is 59.
Always start with the ones. If you start with the tens, you might still get the right answer, but it is easier to make mistakes. Form the habit: ones first!
Adding tens after the ones
After we finish the ones, we look at the tens column. The tens digits are added together. Because we are not regrouping, the sum of the tens will be 9 or less, so the total number will be less than 100.
Check: ones: 6+3=9 ; tens: 4+2=6 → 69. No regrouping because 9 is less than 10 and 6 is less than 10.
Ones: 1+8=9. Tens: 5+2=7. Sum = 79.
What if the ones add to 9? That is fine, we just write 9. No regrouping. In later grades, you will add ones that make 10 or more.
What happens when we add a number with zero ones?
Sometimes a two-digit number ends with 0, like 20, 30, 40. Zero is still a digit. Adding zero ones is easy: it does not change the ones.
Ones: 7 + 0 = 7. Tens: 2 + 4 = 6. So 67.
Ones: 0 + 9 = 9. Tens: 5 + 2 = 7. Sum = 79.
Remember: 0 + any number = that number. That makes adding easy!
Adding when the tens digits are the same
If the tens digits are equal, we still add them. The total tens will be twice that digit. But it must stay 9 or less. For example, 3 tens + 3 tens = 6 tens (which is fine).
Ones: 2+4=6. Tens: 3+3=6. Answer 66.
Ones: 1+2=3. Tens: 4+4=8. Sum = 83.
Even when tens are the same, the sum of the ones could be any number from 0 to 9. Still no regrouping.
Using expanded form to understand addition
Expanded form means writing a number as the sum of its tens and ones. For example, 38 = 30 + 8. This helps us see why adding column by column works.
Write each number in expanded form:
- 25 = 20 + 5
- 43 = 40 + 3
Now add the tens: 20 + 40 = 60. Add the ones: 5 + 3 = 8. Then combine: 60 + 8 = 68.
Now see it in the math-stack:
Expanded form shows why we add tens to tens and ones to ones. They are like units: you add apples to apples.
Checking your work
It is always smart to check your addition. One way is to add the numbers in a different order (addition is commutative, meaning 23+46 is the same as 46+23). Another way is to use subtraction later.
Reverse the order: 42 + 37. Add ones: 2+7=9. Add tens: 4+3=7. Same answer, 79. So it checks out!
You can also estimate: 37 is almost 40, 42 is about 40, so 40+40=80. Our answer 79 is close to 80, so it makes sense.
Word problems: putting it together
Sometimes math is in a story. We need to find the numbers and add them. Look for key words like "in all," "total," "altogether."
Maria has 24 stickers. Her brother gives her 35 more stickers. How many stickers does Maria have now?
We add 24 + 35.
Maria has 59 stickers in all.
A farmer has 46 apples and 23 oranges. How many pieces of fruit does he have?
The farmer has 69 pieces of fruit.
Read the problem carefully. Underline the numbers and the question. Then correctly line up the tens and ones vertically.
Practice with a helper
Try these on your own, then check with a friend or teacher. Remember to line up the tens and ones.
- 1. 32 + 47 = ?
- 2. 51 + 28 = ?
- 3. 63 + 24 = ?
- 4. 70 + 29 = ?
- 5. 85 + 14 = ?
Answers: 1. 79, 2. 79, 3. 87, 4. 99, 5. 99 (all without regrouping).
Did you notice that 99 is the highest sum you can get without regrouping? Because 9+9=18 would need regrouping. So our sums stop at 99.
Common mistakes to avoid
Even careful mathematicians make errors. Here are some common ones and how to avoid them.
Wrong: 23 + 4 written as 23 + 40 (the 4 should be under the ones place).
Right: 23 + 04 (but we usually just write 23 + 4, but know that 4 is 04 when we line up the tens and ones vertically).
In two-digit addition, both numbers should have two digits. If one has only one digit, think of it as 0 tens.
If you add tens first and get distracted, you might forget to add the ones. Always do ones first, or at least check both.
Example: 32 + 51. If you add 3+5=8 and write 8 in the ones place by accident, you'd get 38 instead of 83! So always keep the tens and ones columns separate.
Take your time. Double-check your columns. Practice makes perfect.
Why learn addition without regrouping?
This is the first step to understanding bigger addition. Once you master no regrouping, you will be ready for regrouping (carrying). It builds a strong foundation.
If you have 45 pennies and your sister has 32 pennies, you can add to find out you and your sister have 77 pennies together.
Math is everywhere. Adding two-digit numbers helps with money, scores, measurements, and more.
Common Core alignment: CCSS.MATH.CONTENT.1.NBT.C.4 – Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
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.
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