Y.4 Add ones to two-digit numbers using a number chart – with regrouping
What is adding ones to two-digit numbers?
Adding ones to two-digit numbers means combining a number from 1 to 9 with a two-digit number like 24 or 57. We focus on the ones place first. When the total of the ones column is 10 or more, a special step called regrouping (or carrying) is needed.
- Adding 24 + 5 combines the ones: 4 ones + 5 ones = 9 ones. The number is 29.
- Adding 24 + 7 combines the ones: 4 ones + 7 ones = 11 ones. Since 11 ones is the same as 1 ten and 1 one, we must regroup.
The words regrouping and carrying mean the same thing. "Regrouping" helps us understand that we are changing 10 ones into 1 group of ten.
Understanding place value: tens and ones
Every two-digit number is made of tens and ones. The tens digit tells how many groups of ten are in the number. The ones digit tells how many single units are left over. Regrouping happens when we have 10 or more single units in the ones place.
- The number 36 means 3 tens and 6 ones. We can draw it as 3 sticks of ten beads and 6 single beads.
- The number 50 means 5 tens and 0 ones.
- 10 ones are always equal to 1 ten. This is the most important rule for regrouping.
If you can visualize or draw tens as groups and ones as singles, regrouping becomes a clear and logical step, not just a memorized rule.
What is regrouping?
Regrouping is the process of exchanging 10 ones from the ones place for 1 ten, which is then added to the tens place. We do this because our number system only allows a single digit (0-9) in the ones place. When we get 10 or more ones, we must "trade them in" for a ten.
- If you have 13 ones, you can trade 10 of them for 1 ten. You are left with 1 ten and 3 ones, which we write as the number 13.
- Adding 28 + 4 gives you 12 ones (8+4). You regroup 10 ones into 1 ten. That 1 ten is added to the 2 tens from 28, making 3 tens. The leftover 2 ones go in the ones place, for a total of 32.
Regrouping is like making change: ten pennies are always worth one dime. You trade many small coins for one bigger coin to make counting easier.
Using a number chart to add with regrouping
A number chart (like a 100s chart) is a powerful tool for adding with regrouping. It shows all numbers in rows of ten. To add a one-digit number, you move down the chart. When your move takes you past the end of a row (like from 39 to 40), you have just regrouped by moving to the next ten.
- Start at 48 on the number chart.
- Adding 5 means moving down 5 squares: 49, 50, 51, 52, 53.
- Notice the important jump from 49 to 50. You left a row that started with 40 and entered a row that starts with 50. This jump is the regrouping event.
- You added 1 one to get from 48 to 49. Then, to get to 50, you used the next 1 of your 5, but it created a new ten, resetting the ones column to 0. The final answer is 53.
On a number chart, regrouping is visually clear as moving down to the start of a new row. This helps students see that the number is getting one ten larger while the ones start over.
The step-by-step process for regrouping on a chart
Follow these clear, repeatable steps to solve any problem of adding ones to a two-digit number with regrouping using a number chart.
- Find the Start: Locate the two-digit number (37) on your number chart.
- Plan the Move: The one-digit number (6) tells you how many squares to move down.
- Move and Count: Move down one square at a time, saying each number aloud: 38, 39...
- Regroup at the Row's End: When you move from 39 to 40, you have reached a new ten. This is regrouping. Remember, you have used some of your "moves" to get here.
- Continue to the Final Number: Finish your moves: ...40, 41, 42, 43. You have moved 6 squares total: 38(1), 39(2), 40(3), 41(4), 42(5), 43(6).
- State the Answer: The number you land on is the sum. 37 + 6 = 43.
The key is to move slowly and recognize the moment you cross from one row (the 30s row) into the next (the 40s row). That crossing is the act of regrouping.
Recognizing when regrouping is needed
You can predict if a problem needs regrouping before you solve it. Look at the ones digit of the two-digit number and the one-digit number you are adding. If these two digits add up to 10 or more, you will need to regroup.
- 42 + 3: 2 ones + 3 ones = 5 ones. This is less than 10. No regrouping needed. Answer: 45.
- 42 + 9: 2 ones + 9 ones = 11 ones. This is 10 or more. Regrouping is needed. The answer will be in the 50s.
- 68 + 5: 8 ones + 5 ones = 13 ones. This is 10 or more. Regrouping is needed. The answer will be in the 70s.
This prediction skill is powerful. It tells your brain, "The tens digit is going to change on this problem." It moves you from counting to calculating.
Common patterns and shortcuts on the number chart
With practice, you will see helpful patterns when using the number chart to add with regrouping. These patterns make solving faster and build a stronger number sense.
- The Nine Pattern: Adding to a number with a 9 in the ones place almost always means regrouping. (e.g., 29 + 2, 59 + 4). The answer's tens digit will be one more than the original.
- The Zero Rule: After regrouping, if you use up all the ones that made the ten, the new ones digit will be zero. (e.g., 50 + 10, but for our case, 34 + 6 = 40, because 4+6=10 exactly).
- Row Jumps: The answer to a regrouping problem is always in the next row of ten on the chart. If you start in the 20s row, your answer will be in the 30s row.
Seeing these patterns means you are thinking mathematically. You are not just finding answers; you are understanding how numbers are organized.
Solving problems without the chart: mental math strategies
Once you are confident with the chart, you can begin to solve regrouping problems in your head. The goal is to use the same logic of making a ten, but without visual aids.
- Look at the Ones: 6 + 8 = 14 ones.
- Regroup the Ones: 14 ones = 1 ten and 4 ones.
- Add the New Ten: Take the 1 ten and add it to the 2 tens in 26. 2 tens + 1 ten = 3 tens.
- Combine Tens and Ones: 3 tens and 4 ones = 34.
Another Strategy (Making a Friendly Number):
For 26 + 8, you could think: "26 needs 4 more to make 30." Take 4 from the 8 to make 30. You have 4 left from the 8. 30 + 4 = 34.
Mental math is built on a foundation of understanding. The number chart builds that foundation by making the concept of regrouping visible and concrete.
Checking your work for accuracy
A good mathematician always checks their answer. For addition with regrouping, you can check your work by using a related subtraction problem or by using the number chart in reverse.
- Subtraction Check: If 45 + 7 = 52, then 52 - 7 should equal 45. On the number chart, start at 52 and move up 7 spaces: 51, 50, 49, 48, 47, 46, 45. You land on 45, so the answer is correct.
- Estimation Check: Before solving, you knew 5+7=12, so regrouping was needed and the answer should be in the 50s. Your answer of 52 fits this prediction, giving you confidence it is reasonable.
Checking your work is not about finding mistakes; it's about proving to yourself that your answer makes sense. It is a essential habit for learning.
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, specifically targeting the skill of composing a ten when adding a two-digit and a one-digit number. Use it for whole-class instruction with a projected number chart, for small-group guided practice, or as independent review.
The progression from concrete (visualizing the chart) to abstract (mental math) is designed to build deep conceptual understanding. The "Note" boxes provide meta-cognitive prompts to develop students' mathematical thinking and communication skills.
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