Paper-and-Pencil Subtraction

Recording Trades on the Base-Ten Recording Sheet. The work with base-ten pieces in the last lesson laid the foundation for understanding a standard subtraction algorithm. This lesson makes connections between the trades made with the pieces and the marks typically written above the columns in this algorithm.

Explain that you will use paper and pencil to record the trades done with base-ten pieces. Demonstrate a few problems with base-ten pieces and simultaneously write down marks in a table on a display of the Base-Ten Recording Sheet to represent the work with pieces.

Begin with a problem that requires one trade, such as 46 – 27.

Display 4 skinnies and 6 bits. Then show 46 using the tens and ones column in the table as in Figure 1.

On the next line of the table, write “ – 27” to indicate that you will subtract 27 from 46.

Show the trade with base-ten pieces by removing 1 skinny and replacing it with 10 bits as in Figure 2.

Show how this trade can be recorded in the table: cross out the 4 and write a 3 above it. Then cross out the 6 and write a 16 above it. See Figure 2. As you discuss the steps, ask questions that will check students' understanding of the connection between the trades you made with the pieces and the marks you made in the table.

After making and recording the trades, ask students to help you complete the subtraction problem, and write the answer 19 below it.

Pose a few more problems for students to solve. Ask students to record their work on the first page of the Subtraction on Recording Sheets pages in the Student Activity Book. See Figure 3 for examples. Have base-ten pieces available for students who choose to use them.

As students work, circulate about the room and ask questions to make sure they understand the notations they are making on the recording sheets.

After students have practiced solving a few problems, assign Questions 1–6.

Suggest that students think of base-ten pieces as they solve the problems—they do not need to use the pieces unless they choose to. As students solve the problems at their desks, ask them to explain what each of the steps means.

Assign the Recording Your Subtraction Homework pages in the Student Activity Book.

Recording Trades Using the Compact Method. Ask students to turn to the Paper-and-Pencil Subtraction pages of the Student Guide. Question 1 asks them to compare Kathy's recorded work and her work with base-ten pieces as shown in the Lesson 3 pages of the Student Guide. See Figure 4. Ask them to discuss Question 1 with a partner and then with the class.

Then ask students whether they agree with Sara's comment that you don't need a table to record subtraction problems—the columns tell the place value. Ask them to examine Sara's work and discuss Question 2. Then have them solve the subtraction problems in Question 3 using Sara's compact method.

Assign the Johnny's Paper-and-Pencil Subtraction Homework pages in the Student Activity Book.