Lesson 6

Workshop: Addition

Est. Class Sessions: 2–3

Developing the Lesson

Part 2. Addition Practice

Compare Addition Strategies. Refer students to the Palindromes and Addition Practice section of the Palindrome Recording Chart pages in the Student Activity Book. Ask students to solve Questions A–F and to think about which strategy they choose to use for each problem. As students work, ask them to explain their thinking. It may be useful for students to make a table similar to the table in Figure 3.

When students have completed the problems, discuss their choice of strategies. Some strategies are better suited for addition with larger numbers, while some strategies become very cumbersome when adding larger numbers. It is sometimes more efficient to solve problems mentally and sometimes more efficient to use paper-and-pencil methods. Start to point these out in this discussion. See the Sample Dialog for a discussion using additional example problems.

Teacher: Can someone show us how they solve 58 + 27?

Nila: Yes. [Nila goes to the board and writes a solution to this problem using expanded form.] 58 + 27 = 85.

Teacher: Is this answer reasonable? How can we check?

Ming: Estimate. 58 + 27 is about 60 + 30. That's 90.

Teacher: You did a nice job of choosing friendly numbers, Ming. Can someone use another strategy to solve 58 + 27?

Jerome: I thought of a number line and did it in my head. 27 is close to 30. So I need to count on 30 from 58: 68, 78, 88. That is 3 too many so I count back 3 from 88 to 85. The answer is 85.

Teacher: I had a tough time following you. Can you show us this strategy on the class number line?

Jerome: [He shows his strategy on the class number line.]

Teacher: Compare your answer to Ming's and Nila's answer. Did you get the same answer?

Jerome: I got the same answer as Nila, and Ming got a close answer because he estimated.

Teacher: Can someone show us how to solve 284 + 297?

Maria: I can. I like the pencil-and-paper method. [Maria shows the All-Partials Method.] 284 + 297 = 400 + 170 + 11 = 581

Teacher: Can someone tell me if Maria's answer is reasonable?

Jerome: Well 284 and 297 are both close to 300. So, 300 + 300 = 600. That is close to 581. Yes, Maria's answer is reasonable.

Teacher: Can someone show us another strategy to solve 284 + 297?

Jack: I like to use base-ten pieces. 284 is 2 flats, 8 skinnies, and 4 bits and 297 is 2 flats, 9 skinnies, and 7 bits. [Jack grabs the base-ten pieces.] Let's see, I can trade 10 skinnies for 1 flat, and 10 bits for one skinny. I now have 5 flats, 8 skinnies, and 1 bit. That equals 500 + 80 + 1 = 581.

Teacher: Compare Maria's, Jerome's, and Jack's answers. Did you get the same answer?

Ming: Maria's and Jack's are the same and Jerome's is close. But I would not choose base-ten pieces.

Teacher: Why?

Ming: Too much work. The paper-and-pencil methods, compact, using expanded form, all-partials, are less work.

Teacher: What do you think, Jack?

Jack: I like the base-ten pieces, but they are a lot more work and time. Maybe I will try one of the paper-and-pencil methods. [Jack goes to the board and shows how to use the compact method to solve 284 + 297 and gets an answer of 571.]

Teacher: Did you get the same answer as you did with the base-ten pieces?

Jack: No.

Teacher: What do you think happened?

Jack: I forgot 10 somehow.

Maria: When you added the 80 + 90 you forgot one ten that you traded when you added the ones.

Jack: Oh, I see. That is why we check our answers.

Set Up the Workshop. Review the organization of the Workshop by skimming the Strategies to Add pages in the Student Activity Book. This Workshop is divided into three sections that address Expectations as shown in Figure 4. (Minis of the Student Activity Book pages not shown here are in the Answer Key.)

Choose Targeted Practice. Students begin each section by first answering the Self-Check Questions, either individually or with partners. These questions serve two purposes. First, they clearly communicate the content of the related targeted practice to students. Second, they help students quickly self-assess their progress with the Expectations to help them choose which problems to work on in the Workshop.

Use Self-Check : Questions 1, 10–11, and 16 on the Strategies to Add pages in the Student Activity Book to assess students' abilities to use place value concepts [E1], represent and solve addition problems using base-ten pieces and number lines [E2]; add using mental math strategies [E3]; and add multidigit numbers using paper-and-pencil methods [E4].

After students complete the Self-Check Questions in a section, discuss each of the questions with the whole class. Ask students to share their solutions and explain their reasoning. Facilitate a class discussion of students' solutions. Next, have students think about each question in the left-hand column of the menu following the Self-Check Questions. Ask students to review their work on the Self-Check Questions to decide which problems to choose from the following groups:

  1. Students who are “working on it” and need some extra help should circle the problem set marked with a triangle (). These problems provide scaffolded support for developing the essential underlying concepts as well as some opportunities for practice.
  2. Students who are “getting it” and just need more practice should circle the problem set marked with a circle (). These problems mainly provide opportunities to practice with some concept reinforcement and some opportunities for extension.
  3. Students who have “got it” and are ready for a challenge or extension should circle problems marked with a square (). These problems provide some practice and then move into opportunities for extension.

Note that students' self-assessment of their own abilities may vary between rows in a menu or between menus. For example, a student might circle the “” questions in one row and the “” or “” questions in another row or in a subsequent menu. A student's comfort and ability may vary by Expectation, and the Workshop allows each student to choose problems flexibly based on what type of practice he or she needs for each “Can I Do This?” task.

Check students' choices to see how well they match your own assessment of their progress on the related Expectations. Help students make selections that will provide the kind of practice they need.

Once students select questions to complete in a section of the Workshop, match groups of students who have chosen similar sets of problems from the menu. Have students work with their groups to solve the problems they choose. Again, flexibility is important. If problems seem either too easy or difficult for students, they should adjust their choices from the menu.

After the first few groups of students have completed their selected problems (but before all students have completed their problems), introduce the next section to the whole class. See the Meeting Individual Needs box. Again, have students try the Self-Check Questions, discuss solutions, and choose problems from the menu with your guidance. Follow this pattern through all three sections on the Strategies to Add pages in the Student Activity Book.

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A table for sorting strategies
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Expectations addressed in each section of the Workshop
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