Addition with Larger Numbers

Est. Class Sessions: 4

Developing the Lesson

Part 2: Using Base-Ten Pieces to Add

Show Trades with Base-Ten Pieces. Distribute sets of base-ten pieces to student pairs.

Display the following problem and ask:

Would you solve 678 + 267 using mental math or a different strategy? Explain. (Possible response: I wouldn't use mental math because there are too many numbers to keep straight in my head, and I think there are some trades. I'd use a different strategy.)

Direct students' attention to the Addition with Larger Numbers pages in the Student Guide. Read the opening vignette together as a class. Nikia and Maruta use base-ten pieces to solve the problem. Model the problem with a display set of base-ten pieces as students work with their own sets. Ask students to make connections between the base-ten pieces and the numbers Nikia recorded on the base-ten recording sheet.

Ask:

Why did Nikia put a 15 in the ones column? (It shows that 8 bits plus 7 bits make 15 bits.)
How did she show the sum of 7 skinnies and 6 skinnies? (She put a 13 in the tens column.)
Does she need to make any trades? (Yes, you can't have a 15 in the ones place or a 13 in the tens place.)
Is 81315 a reasonable sum for 678 + 267? (81315 is not reasonable. 678 is close to 700 and 267 is close to 250. 700 + 250 is 950, a reasonable estimate.)

Discuss Question 1 as a student shows how to use the Fewest Pieces Rule with the base-ten pieces and finds the answer in standard form: 945. One way of trading is shown in Figure 4. Students may develop other methods that work well for them, including some where they trade from the right. See Figure 5.

Ask:

What is the value of the 9 in 945? (900 or 9 hundreds)
Which base-ten pieces represent the 5? (5 bits)
What is the value of the 4 in the answer? (40, or 4 tens)

Practice Recording with Base-Ten Pieces. Direct students' attention to the Adding with Base-Ten Pieces pages in the Student Activity Book to continue practice. Read Nikia and Maruta's problem at the top of the page. Show how to represent and solve 196 + 232 with base-ten shorthand as students follow the text.

Ask:

What does the 12 in the skinnies column represent? (9 skinnies + 3 skinnies)
Explain the trades made for the fewest pieces. (12 skinnies were traded for 1 flat and 2 skinnies.)
Compare the number in standard form to the number shown with the fewest pieces. What do you notice? (When we use the fewest pieces, we see the number in standard form.)

Assign Questions 1–5. For these problems, students represent addition problems with base-ten shorthand, record their answers on base-ten recording sheets, and then make trades using the Fewest Pieces Rule to find the number in standard form. Have base-ten pieces available for students who choose to use them.

Some students may need or prefer to continue using the base-ten pieces longer than others. It is also not unusual for a student to sporadically return to using the manipulatives. Sometimes, when a child becomes confused using a paper-and-pencil algorithm, it can suffice to say, “Think of the base-ten pieces.” Using base-ten shorthand should also help in developing images of the pieces.

Consider the needs of your students when deciding the amount of practice necessary in class and at home. It is best to let the algorithm sink in slowly. Assigning a few problems a day over a long period of time is better than assigning many at once and expecting immediate fluency.

Decide when your students are ready to move on. Students may need to do additional problems together, in groups, or individually. See Figure 6 for examples of problems with one regrouping and Figure 7 for problems with multiple regroupings. Have base-ten pieces available for students who choose to use them. Ask students to explain their trades and to check to see whether their answers are reasonable.

Student Guide: 140

Answers