Math Background

Lesson: Two-Digit Addition With Regrouping
Developing the Concept

Once children are comfortable using different strategies to do two-digit addition with regrouping, have them apply these strategies 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: 9 bundles of 10 craft sticks and single sticks, pencils, paper

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

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

  • Write30 + 30 on the chalkboard.
  • Ask: How many tens are in each group? (3) What addition fact helps you add the tens? (3 + 3 = 6)
  • Ask: What is the sum? (60) What should you think of when you add tens? (Think of the addition fact when you add tens.)
    Repeat the exercise with other tens. Have volunteers write the sums on the chalkboard while the rest of the class write the examples and sums on their papers.
  • Say: We can use a hundred chart to add tens to any number.
  • Write43 + 20 in vertical format on the chalkboard. Circle 43 on the hundred chart. Have a volunteer count down 20.
  • Ask: When you add tens to a number on the hundred chart, why doesn't the number in the ones column change?
    It doesn't change because tens are being added to the number, not ones. Repeat with other starting numbers and tens.
  • Write3 tens 17 ones on the chalkboard.
  • Ask: How can we write this number another way?
    We can regroup. We regroup the ones as 1 ten 7 ones. We can write the number as 47. Write several more examples on the chalkboard, including examples with ones less than 10. Have volunteers regroup the ones, if necessary, and write the number another way. Some children may need to use the craft sticks. Discuss when and why it was necessary to regroup or when it was unnecessary to regroup.
  • Say: We learned to use the Make a Ten strategy when we learned the addition facts to 20. Now as we add, we are going to use that strategy again.
  • Write27 + 6 on the chalkboard in vertical format.
  • Say: Look at the ones column. Can we regroup?
    Children should say that 7 + 6 = 13, so they can regroup to make 1 ten and 3 ones.
  • Ask: How can we show the 10 we regrouped? (We can make a little one over the tens column.) What do you think the sum will be? (33)
    Repeat with several more examples like the one above. Have a volunteer explain how to solve each example and write the sum while children at their seats solve the problem. Some children may need to use the craft sticks.
  • Write35 + 17 on the chalkboard in vertical format.
  • Ask: How is this problem different from the problems we just solved?
    Both numbers have two digits; there are two numbers in each of the tens and ones columns. Have a volunteer come to the board and solve the problem. Point out that there are 2 numbers plus the regrouped ten to add in this example.
  • Write several other examples on the chalkboard, including examples that don't require the ones to be regrouped and examples in which the ones add up to 10. Also include examples that use the cent sign (¢). Point out that this sign doesn't change how you add, but that when it is used, it must be written following the sum.
  • Ask: What should you decide first when you solve a two-digit problem?
    You must decide if the ones need to be regrouped.
  • Have volunteers solve the problems on the chalkboard and explain their thinking as they go along, while children at their seats solve the problems.
  • Say: Sometimes you don't need an exact answer, but you need a quick answer, so you can use estimation to round numbers to the nearest ten. That way you can add mentally and get an answer that is close.
  • Say: Look at the number line. I am going to circle the numbers 44 and 28.
  • Ask: What is the nearest ten to 44? (40) to 28? (30)
  • Ask: What is the sum of the two numbers? (70)
  • Ask: Is it quicker to add 40 and 30 or 44 and 28? Why?
    (40 + 30 is quicker, because you can add it in your head.)
  • Say: We have learned different ways to add two numbers. Now we are going to try adding 3 numbers and see some strategies we can use.
  • Write34 + 14 + 16 on the chalkboard in vertical format.
  • Ask: How many addends do we have? (3) In what order can we add them?
    Lead children to see that it doesn't matter in what order they add the numbers as long as they add the ones column first and then the tens column.
  • Ask: Would someone like to tell how he or she would add the ones and why? Remember, you can add the numbers in any order.
    Discuss the strategies that might be used—Make a Ten or Doubles. Remind children that the addends are still the same, even if they are added in a different order. Guide children to see that by using the associative rule, they can group the addends in any order to make adding easier. Repeat with other examples, discussing the strategies used in each. Have children write the examples and sums on their papers.

Wrap-Up and Assessment Hints
Children need practice with two-digit addition and the strategies used to do it. If the sum for a problem is not correct, ask the child how he or she might go about figuring out the correct answer. Find out what children are thinking and then select a strategy that builds on what they already know. Encourage children to use strategies and related addition facts.


Houghton Mifflin Math Grade 2