Math Background

Lesson: Two-Digit Addition With Regrouping
Introducing the Concept

Children will use the Make a Ten strategy in this lesson, along with other strategies. Remind children that if they are adding two numbers such as 8 + 5, they can regroup the numbers to make adding easier. Tell children that they can take 2 from the 5 and add the 2 to 8 to make a ten. Also remind them that they must remember to subtract the 2 from the 5, leaving a 3, so they add 10 and 3 and get 13. Tell children that they will use this strategy to add two-digit numbers.

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

Preparation: Prepare a tens and ones workmat and a ten frame for use on the overhead. Make 9 bundles of craft sticks, 10 per bundle, using rubber bands to hold them together. Or use tens and ones blocks. Make a large number line and hundred chart for the classroom.

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

  • On the chalkboard, write 20 + 50.
  • Ask: How can you add these numbers?
    Allow time for suggestions from the children. Lead children to see that they can use the fact 2 + 5 to discover the answer. They know that 2 + 5 = 7, so they should see that 20 + 50 = 70.
  • Demonstrate making the facts with the single craft sticks and then the tens using the bundles of sticks.
  • Now point to the hundred chart. Circle 37.
  • Say: A hundred chart can help you add by tens. Today we are going to add 30 to 37.
  • Ask: How many tens are there in 30? (3) How can you add 30 to 37?
    Elicit from children that they can move down one row each time they count 10 more.
  • Have a volunteer point to the 37 and move down 3 rows as the class counts on 3 more tens.
  • Say: I need some volunteers to help me act out an addition story.
    Choose 8 children to come to the front of the room. Then ask 7 more children to come to the front and make a second group.
  • Ask: How can we easily find out how many children there are?
    Children might say, “Count them.” If so, ask them if there is a way to make counting easier. Elicit that 2 children can be added to the group of 8 from the group of 7, making 10, so that there are 10 and 5. Therefore, there are 15 children altogether.
    Explain to the class that they just regrouped the children to make it easier to add.
  • Review the process of making a ten on the overhead with craft sticks, bundling ten of them together, or with tens and ones blocks.
  • Say: Let's try adding numbers on the overhead.
  • Using the overhead, place a tens and ones mat with 2 bundles of sticks in the tens column and 6 sticks at the top of the ones column and 7 sticks at the bottom. Write 26 + 7 above the mat.
  • Ask: Can you regroup the sticks in the ones column? How?
    Children should say that yes, there are more than 10 sticks, so 10 of them can be regrouped as 1 ten bundle and the ten bundle moved to the tens column. Then there are 3 sticks left. The sum is 33. Repeat the activity, making sure that you use examples that show ones that add up to 10. Explain that when the number is said, it's expressed as a number of tens and 0 ones.
  • Say: Today we are going to add two-digit numbers.
  • Write 24 + 17 on the overhead. Place a tens and ones mat under the algorithm and arrange the tens bundles and sticks on the mat.
  • Ask: How many ones are there? Can the ones be regrouped?
    There are 11 ones. Yes, you can make 1 ten, and 1 stick, or one, is left.
  • Ask: How many tens are there now? What is the sum?
    There are 4 tens. The sum is 41. Repeat with other addends. Be sure to include ones that add up to a sum of 10.
  • Say: Sometimes I don't need to find an exact answer, so I estimate the answer. Suppose I decide to stop at the store on my way home and buy 2 oranges. I have 80¢. I look at the price of the oranges in the store and see that they are 37¢ each. How can I find out if I have enough money to buy 2 oranges?
    Elicit from children that they could round the amount to add quickly.
  • Display the large number line to the class.
  • Say: To round 37, I ask myself, “What is the nearest 10?”
    Point to the 37 on the number line and have children discover that 40 is the nearest 10.
  • Say: If round 37¢ to 40¢, I know that I have enough money and will have a few cents left.
    Repeat with several other numbers, asking volunteers to point to the number and then find the nearest 10.
  • Ask: How will you decide if the nearest ten is greater than or less than the number?
    Look for the ten that is closest to the number. Remind children that sometimes it is quicker and easier to round to the nearest ten, or estimate, when an exact sum isn't necessary.
  • Finally, write the following problem, in vertical format, on the chalkboard: 18 + 22 + 38.
  • Ask: How many addends have I written on the chalkboard? (3)
  • Ask: Which column should we add first?
    Elicit that the ones should be added first, no matter how many addends they are adding.
  • Tell children that when they add more than two numbers in a column, they can use different strategies to make it easier to add. They can look for doubles, they can make a ten, or they can use the associative rule and group the addends in any order to make adding mentally easier.
  • Ask: Which two numbers in the ones column will you add first?
    Accept reasonable answers, but lead children to see that they can use doubles to add the two 8s first and then the 2, or they can use the Make a Ten strategy and add the 8 and 2, making 10, and then add the remaining 8. Encourage children to use the associative rule to check their results. Provide several more examples with 3 addends. Have volunteers tell how they would solve the problems. Ask why they chose the numbers they added first in each column.

Houghton Mifflin Math Grade 2