Math Background

Three-Digit Addition and Subtraction With Regrouping
Developing the Concept

Review the concepts taught in Introducing the Concept. Explain to children that in this lesson they will be learning to add and subtract three-digit numbers without using models.

Materials: place-value blocks, half-full jar or cup of approximately 100 paper clips (or any small object), paper, pencils

Preparation: Place the paper clips in the jar or cup. Make sure the jar or cup is about half full.

Prerequisite Skills and Concepts: Children should be familiar with basic addition and subtraction facts and with place-value concepts. Children should be able to add and subtract one- and two-digit numbers, with and without regrouping.

Group children in pairs. Give each pair hundreds, tens, and ones base-ten blocks, paper, and pencils. Write the number 151 on the board in large print. Leave enough space between each digit to make it clear where the place-value columns are.

  • Say: With your partner, use the base-ten blocks to model the number 151.
    Children should build the number 151 using 1 hundred, 5 tens, and 1 one.
  • Ask: How did you know how to build the number 151?
    Children should respond that they used place value to figure out that they needed 1 hundred, 5 tens, and 1 one to make 151.

    Write the number 329 on the board in large print under the number 151.

  • Say: Now use the base-ten blocks to model the number 329.
    Children should build the number 329 using 3 hundreds, 2 tens, and 9 ones. Have a volunteer explain how to use the blocks to show 329.
  • Say: Now we are going to add these numbers without using our blocks.
    On the board, write in a “+” sign to the left of 329 and put an equals line under the bottom number to create an addition exercise. Then draw a line between the ones and tens columns and the tens and hundreds columns of the numbers.
  • Ask: What kind of exercise is this?
    Children should answer that it is an addition exercise.
    What should we do with the numbers in the ones place? (add)
  • Ask: How many ones are there in each number? Look at the two numbers in the ones place. (1 in the top number and 9 in the bottom number)
  • Ask: What is the sum of the numbers in the ones place? (10)
  • Ask: Can we write “10” in the ones place? (no)
  • Say: Since we can't write 10 in the ones place, we must regroup the 10 ones as 1 ten and zero ones.
    Write the zero in the ones place of the sum.
  • Ask: What do we do with the ten we regrouped from ones?
    Children may answer that you add the ten to the other numbers in the tens place.

    Show children how to write a small “1” over the numbers in the tens place. Then challenge them to complete the addition on their own. Remind them to add together only the numbers that are in the same place-value column.

  • Ask: What is the sum?
    Children may answer 151 + 329 = 480. Have a volunteer explain how he or she got the sum.

    Repeat with an exercise in which it is necessary to regroup tens, such as 192 + 235.

  • Say: Now let's try a subtraction exercise.
  • Write237 − 143 = on the board in vertical form. Instruct children to write the exercise on a sheet of paper and to draw vertical lines between place-value columns.
  • Say: Let's subtract the ones first. Write your answers in the ones place on your paper.
    Allow children time to write their answers.

    Have a volunteer provide the answer and explain how to obtain it. Children may answer that they subtracted 3 ones from 7 ones and got 4 ones.

  • Say: Now let's look at the tens place. We have to subtract 4 tens from 3 tens, which we can't do. We will need to regroup a hundred as 10 tens.
  • Ask: How can we regroup 2 hundreds?
    Children should answer that you regroup the 2 hundreds as 1 hundred and 10 tens.
  • Say: Sometimes it helps to make notes to ourselves to remember what we have done.
    Show children how to cross out the 2 in 237, write a 1 above the 2, cross out the 3 and write 13 above the 3 to make 13 tens.
  • Ask: Now what do we subtract in the tens place?
    Children may answer that they need to subtract 4 tens from 13 tens. Have a child volunteer the answer. (9 tens)
  • Ask: What happens to the hundreds in this problem?
    Help children see that in the hundreds place, you subtract 1 hundred from 1 hundred, so there will be no hundreds in the answer. Make sure children understand that the answer is 94.

    Allow children to practice by having a member of each pair write two three-digit addition and subtraction exercises that require regrouping. Then have them complete each other's exercises. Allow pairs to share their results with the class. When children are comfortable with vertical addition and subtraction, present some horizontal addition and subtraction exercises. Show children how to rewrite the horizontal problem as a vertical problem. Have them practice writing the exercises vertically, using guidelines if necessary to keep the digits aligned properly.

  • Say: Now we're going to learn about estimating.
  • Say: Suppose I told you that there are about 100 paper clips in this jar (cup).
    Hold up the half-full jar of paper clips (or whatever other small object you chose).
  • Ask: About how many paper clips would it take to fill up the whole jar?
    Have a volunteer provide the answer. (about 200)
  • Say: If there are about 100 paper clips in the jar, and the jar is half full, then it would take about 100 more paper clips to fill the whole jar. You just used estimation to figure that out. When you estimate, you do not need to find exact numbers. Your answer can tell about how many.

    Write the problem310 + 380 = ? on the chalkboard. Draw a 300—400 number line with intervals of 10. Mark the numbers 310 and 380 on the number line.

  • Say: Let's estimate to find this sum. To estimate, decide to which hundred each number is nearest. You can do this by rounding to the nearest hundred. Look at the number line to see what I mean.
  • Ask: To which hundred is 310 nearest? (300) To which hundred is 380 nearest? (400)
  • Say: To estimate the sum of 310 and 380, round each number to the nearest hundred. Then add. 300 + 400 = 700, so 310 + 380 is about 700.

    Have children practice estimating using the following exercises: 460 + 280; 520 + 370; 290 − 110; 630 − 480. Write each exercise on the board and allow volunteers to estimate each sum or difference and explain how they got the answers. Encourage them to use the number line.

Wrap-Up and Assessment Hints
Provide children with many opportunities to practice adding and subtracting three-digit numbers with and without regrouping. Continually reinforce the importance of lining up numbers so that each numeral is in the correct place-value column. Include exercises that require children to use estimation. Observe children as they work through exercises and offer assistance as needed. Keep in mind that some children may prefer to have base-ten blocks available as they work through exercises. Finally, remind children to check subtraction using addition to be sure their work is correct.

Houghton Mifflin Math Grade 2