Math Background

Lesson: Two-Digit Subtraction With Regrouping
Introducing the Concept

Children will analyze and solve problems using skills and strategies. Remind children that they worked with subtraction last year, and earlier this year they subtracted facts and used different strategies, which they will now use to subtract two-digit numbers. Also remind children that addition and subtraction are related operations.

Materials: overhead projector, tens and ones workmat, bundles of 10 craft sticks and single craft sticks, large number line, and large hundred chart

Preparation: Prepare a tens and ones workmat for use on the overhead. Make nine bundles of ten craft sticks. Make a large number line and hundred chart for the classroom.

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

  • On the chalkboard, write 60 − 20.
  • Ask: How can you subtract these numbers?
    Allow time for suggestions from the children. Lead children to see that they can use the fact 6 − 2 to help them discover the answer, or difference. They know that 6 − 2 = 4 so they can use mental math and realize that 6 tens − 2 tens is the same as 60 − 20, so the difference is 4 tens, or 40.
  • Now point to the hundred chart. Circle 62.
  • Say: A hundred chart can help you subtract by tens. Today we are going to subtract tens from other numbers.
  • Ask: How many tens are there in 30? (3) How can you subtract 30 from 62?
    Elicit that you can count back one row each time you count back 10.
  • Have a volunteer point to 62 and move up three rows on the chart as the class counts back 3 tens. Repeat with other numbers, reminding children that they should think where they start on the chart and ask themselves how many tens they should count back.
  • Demonstrate regrouping a ten to make 10 ones. Using the overhead, place a tens and ones mat with 8 bundles of sticks in the tens column and 2 sticks in the ones column.
  • Say: I have put 8 bundles of ten craft sticks and 2 single craft sticks on the tens and ones mat.
  • Ask: How can we show this number another way?
    Elicit that you can unbundle, or regroup, 1 of the tens and make 10 ones. Then the 10 craft sticks can be put with the other 2.
  • Demonstrate the process of regrouping on the overhead. Point out to children that the number 82 can be shown as 8 tens and 2 ones or 7 tens and 12 ones. Repeat with other numbers, including numbers with zero in the ones place. Tell children that this is not unlike regrouping when they added, except that they are regrouping one of the tens to make more ones.
  • Say: Sometimes when you subtract, you will not have enough ones to subtract from. You will have to decide whether or not you need to regroup before you subtract. Let's try some examples on the overhead.
  • Using the overhead, place a tens and ones mat with 7 craft stick bundles in the tens column and 3 sticks in the ones column.
  • Ask: Can you take away 5 ones? (no) What can you do?
    You can regroup 1 ten as 10 ones to make 6 tens and 13 ones. Then you can take away 5. You have 6 tens and 8 ones left, or 68. Repeat with other combinations, including some that don't need regrouping and some that have zero in the ones column of the difference. Once children are comfortable with regrouping, write the algorithms for the models on the chalkboard.
  • Say: Today we are going to subtract two-digit numbers.
  • On the overhead, write 51 − 16. Place a tens and ones mat under the algorithm and arrange the bundles of tens and the ones on the mat to show 51.
  • Ask: Can you take away 6 ones? (no) Do you need to regroup?
    Yes, you need to regroup 1 ten as 10 ones so that you have 4 tens and 11 ones. Now you can subtract 6 from 11 and 1 from 4. The difference is 35. Repeat with other numbers. Include examples that don't need regrouping. Make sure that children understand that they should always look first at the ones column to see if they need to regroup.
  • Say: Sometimes I don't need to find an exact answer, so I estimate it. I can round the two numbers to the nearest ten before I subtract.
  • Display the large number line on the chalkboard.
  • Say: You can use the number line to round to the nearest 10. If I have the number 38, I think, “What is the nearest 10?”
  • Point to the 38 on the number line and show children that 40 is the nearest 10. Repeat with several other numbers, asking volunteers to point to the number and then find the nearest 10.
  • Ask: If we want to estimate the difference of 42 and 19, what should we do?
    Look for the ten that is closest to the numbers. Round 42 to 40 and 19 to 20. 40 − 20 = 20. Estimate the difference as 20. Remind children that sometimes it is quicker and easier to round to the nearest ten, or estimate, when an exact answer isn't necessary. Repeat with other numbers.
  • Demonstrate how to subtract money using two-digit numbers.
  • Ask: How many pennies equal 1 dime? (10)
    Point out that subtracting pennies and dimes is similar to subtracting tens and ones—the dimes are the tens; the pennies are the ones. Remind children that when they subtract, the cent sign is part of the answer, and they must remember to write it next to the answer.
  • Say: After you find a difference, you can use addition to check your work.
  • On the chalkboard, write the subtraction problem 53 − 34 in vertical form. Work through it with children.
  • Say: We have found the difference. (19) Now we can check our work to see if the answer is correct. We can start with the difference and add the number we subtracted.
  • On the chalkboard next to the subtraction problem, write 19 + 34 in vertical form. Have a volunteer write the sum.
  • Ask: Is the sum the same as the number we subtracted from?
    Yes. Repeat with other examples. Remind children to use addition to check their answers when they subtract. Tell children that they can do this because addition and subtraction are related operations.
Houghton Mifflin Math Grade 2