Lesson 7

Workshop: Addition and Subtraction

Est. Class Sessions: 1

Developing the Lesson

Part 2. Workshop

Set Up the Workshop. The menus and problems for this Workshop are in the Strategies to Add and Subtract pages in the Student Activity Book. The Workshop is divided into four sections that address Expectations as shown in Figure 2. 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.

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.

Use Self-Check: Questions below to assess student flexibility with addition and subtraction strategies. All these opportunities are on the Strategies to Add and Subtract pages in the Student Activity Book.

Self-Check: Question 1
E1.
Show that different partitions of the same number are equal using base-ten pieces, number lines, and number sentences (e.g., 200 + 30 + 7 = 200 + 20 + 17).
E2.
Represent and solve addition problems using base-ten pieces and number lines.
E3.
Represent and solve subtraction problems using base-ten pieces and number lines.
Self-Check:
Questions 11–12
E4.
Solve addition and subtraction problems using mental math strategies (e.g., composing and decomposing numbers, counting up, and counting back).
Self-Check:
Questions 17–18
E6.
Add multidigit numbers using paper-and-pencil methods (expanded form, all-partials, and compact).
E7.
Subtract multidigit numbers using paper-and-pencil methods (expanded form and compact).
Self-Check:
Questions 26–28
E9.
Choose appropriately from among mental math, estimation, and paper-and-pencil methods to add and subtract whole numbers.

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?” question.

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

Once students select the 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 chose. Again, flexibility is important. If problems seem either too easy or difficult for students, they should adjust their choices from the menu.

By Grade 4, many, if not most, students will be proficient and express confidence with representing addition and subtraction with base-ten pieces.

You may find, however, that some students, although professing confidence with the base-ten representation, are in fact still shaky about what is actually happening as they make trades using a paper-and-pencil method—particularly the compact method for either operation. As students work on solving problems using paper-and-pencil methods, listen to their conversations and ask questions to make sure they understand the notations they are using.

Ask questions like:

  • What does the little “1” you wrote here mean?
  • When you take one from this [pointing to the tens] column to make 14 (for example) in this [pointing to the ones] column, does it change what the number is? What is actually happening?

If students are unclear about the mathematical underpinnings of the steps they are doing when performing a paper-and-pencil computation, have them work with the base-ten pieces alongside their paper-and-pencil computations. Students having trouble with trades might find the expanded form method helpful as well.

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 four of the sections on the Strategies to Add and Subtract pages in the Student Activity Book.

Some students may not have completed all of their selected questions in a section before you introduce the next section with the whole class. While this may mean interrupting students' flow of work, it is also important that students who complete problems more quickly are able to continue working. For students who need more time, unfinished problems can be completed at the end of the Workshop lesson as needed, or else for homework. For students who finish all of their selected problems before the rest of the class, encourage them to work on more advanced problems from the menus or to play variations of the Digit Game as suggested in Part 1 of the lesson.

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Expectations addressed in each section of the Workshop: Addition and Subtraction
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