Math Background

Lesson: Two-Digit Subtraction With Regrouping
Developing the Concept

Once children are comfortable with using the different strategies in solving two-digit subtraction with regrouping, have them apply them to paper-and-pencil activities. The use of manipulatives, such as tens and ones blocks, craft sticks, and beans will be helpful. Children will use many of the same strategies that they used in Addition and Subtraction Facts to 20. Encourage children to share their thinking as they work through the examples.

Materials: tens and ones blocks or bundles of ten craft sticks and single craft sticks, pencils, paper

Preparation: Have the large hundred chart and number line you used for “Introducing the Concept” available.

Prerequisite Skills and Concepts: Children should know the subtraction facts to 20 and the strategies used in learning them.

  • Write the problem70 − 20 on the chalkboard.
  • Ask: How many tens are in each group? (7 and 2) What subtraction fact helps you subtract the tens? (7 − 2 = 5)
  • Ask: What is the difference? (50) What should you think of when you subtract tens? (Think of the subtraction fact when you subtract tens.)
    Show children the example with the craft sticks: first show the fact and then show subtraction using the tens bundles. Repeat the exercise with other tens. Have volunteers write the differences on the chalkboard while children write the examples and differences on their papers.
  • Say: We can use a hundred chart to subtract tens from any number.
  • Write87 − 30 in vertical format on the chalkboard. Circle 87 on the hundred chart. Have a volunteer count back 30.
  • Ask: When you subtract tens from a number on the hundred chart, why doesn't the number in the ones column change?
    It doesn't change because you are subtracting tens from the number, not ones. Repeat with other starting numbers and tens.
  • Write5 tens 7 ones on the chalkboard.
  • Ask: How can we show this number another way?
    You can regroup a ten to make 10 ones. Then you can add the 10 ones to the 7, making 4 tens and 17 ones. Write several more examples on the chalkboard. Have volunteers regroup the tens and write the number another way. Some children may need to use the sticks.
  • Say: We learned to regroup a ten to make 10 ones. Now we are going to decide when to regroup.
  • Write27 − 6 on the chalkboard in vertical format.
  • Ask: Look at the ones column. Do we need to regroup?
    Children should say that they can take 6 ones from 7 ones, so they do not need to regroup. Repeat with other examples that show both regrouping and no regrouping.
  • Write24 − 7 on the chalkboard in vertical format.
  • Ask: How can we show the 10 and ones we regrouped? What do you think the difference will be?
    Demonstrate how to cross out the ten and write the new number above. Then show how to cross out the ones and write the new number of ones. Repeat with several more examples like the one above. Have a volunteer explain how to solve each example and write the difference while children at their seats solve the problem. Some children may need to use craft sticks.
  • Write62 − 37 on the chalkboard in vertical format.
  • Ask: How is this different from the examples we just solved?
    Both numbers have two digits; there are numbers in both the tens and ones columns. Have a volunteer come to the chalkboard and solve the problem. Remind children that they must check the ones column first to decide if they must regroup, and then do the regrouping, if necessary. Then they subtract the ones column first, followed by the tens column.
  • Write several other examples on the chalkboard, including examples that don't require the tens to be regrouped. Also include examples that use the cent sign (¢). Point out that the cent sign doesn't change how you subtract, or the difference, but that when it is used, the cent sign must be written following the difference. Have volunteers solve the problems on the chalkboard and explain their thinking as they go along, while children at their seats solve the problems.
  • Ask: What should you decide first when you solve a two-digit problem?
    You should look at the ones column and decide if you need to regroup.
  • Say: Sometimes we don't need an exact answer, but we need a quick answer, so we use estimation to round our numbers to the nearest ten. That way we can subtract in our heads and get an answer that is close.
  • Say: Look at the number line. I am going to circle the numbers 62 and 39.
  • Ask: What is the nearest ten to 62? (60)  to 39?(40)
  • Ask: What is the difference of the two numbers? (20)
    We estimate the difference of 62 and 39 as 20.
  • Ask: Is it quicker to subtract 60 − 40 or 62 − 39? Why?
    (60 − 40 is quicker because you can subtract it in your head.)
    Repeat with other numbers and have children use mental math and estimation to solve the problems.
  • Say: We have learned different ways to subtract. Now we are going to learn how to check our subtraction problems by adding to see if we have the correct answer.
  • Write83 − 49 in vertical format on the chalkboard. Work through the problem and find the difference as children solve it on their papers.
  • Say: Now we should check our subtraction to make sure we have the correct answer.
  • Write34 + 49 in vertical format beside 83 − 49 = 34 on the chalkboard.
  • Ask: Can you tell me how this problem is related to the subtraction problem we just solved?
    Elicit that two of the numbers are the same: 34 and 49. Walk children through the example, regrouping the ones and finding the answer. Then elicit from children that all three of the numbers are the same.
  • Say: The sum equals the number we started with. We have used addition to check our answer in subtraction by adding.
  • Draw a line from the sum in the addition problem to the number you started with in the subtraction problem as shown below. Remind children to use their answer (the difference) and the number they subtracted as the two numbers to add when they check their subtraction.
    add to check subtraction
  • Write several subtraction problems on the chalkboard. Have volunteers solve them on the board as children in their seats solve them on their papers. Then have children check their answers by adding. Allow time for children to explain what they have done.

Wrap-Up and Assessment Hints
Children need practice with two-digit subtraction and the strategies used. If the answer to a problem is not correct, ask the child to explain how he or she went about solving the problem. Find out what they are thinking and then select a strategy that builds on what they already know. Encourage children to check their subtraction by adding.

Houghton Mifflin Math Grade 2