Workshop: Problem Solving with Fractions
Est. Class Sessions: 2–3Developing the Lesson
Part 2. Workshop
Set Up the Workshop. Review the organization, menus, and problems of this Workshop by skimming the Workshop: Problem Solving with Fractions pages in the Student Guide. The Workshop is divided into two sections that address Expectations as shown in Figure 3. Minis not shown here are in the Answer Key.
Direct students to the Workshop: Problem Solving with Fractions pages in the Student Guide. Read through the brief vignette. Two students are sharing strategies after playing the Comparing and Ordering Fractions game.
Choose Targeted Practice. Students begin each section by first answering the Self-Check Questions, either individually or with a partner. 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 a problem or two from each of the questions with the whole class. Ask students to share their solutions and explain their reasoning. Facilitate a class discussion with students' solutions. Next, have students think about each “Can I Do This?” 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:
- 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. - Students who are “getting it” and just need more practice should circle the problem set marked with a circle (
). These problems provide opportunities to practice with some concept reinforcement and some opportunities for extension. - 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?” question.
There are many ways to vary a lesson to meet a wide variety of student needs. One way is to allow students to use different tools and processes. Some students will need to depend on the concrete models of fraction circle pieces and pictures, others can use these models more efficiently, and yet others may try to let go of the concrete models.
- Most students are expected to use concrete models like the fraction circle pieces to solve these problems. Encourage students to use fraction circles, refer to the Fractions on Number Lines Chart page in the Student Guide Reference section, draw pictures, and sketch number lines to support their solutions.
- Some students might be ready to find more efficient ways to use these models. Identify these students and encourage them to share their invented strategies with the class.
- Some students will use invented strategies. Encourage these students to use more than one strategy to solve a problem and compare their solutions. A few students may try to abandon the concrete models and use only symbolic models. Encourage these students to use the concrete models to check their solutions and ask them questions to ensure that they make connections between the models and the symbols. Continuing to use the concrete models gives students experiences that build number sense, estimation skills, and flexibility. To encourage deeper understanding of the concepts, ask students to solve a problem another way or to show another representation of the problem.
- Most problems in the Workshop involve fractions that relate to the fraction circle pieces. Some problems marked with involve fractions that do not relate directly to the fraction circle pieces. Encourage students to use any strategy for solving a problem that is not well supported by the circle pieces.
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 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 a partner or in a small group to solve the problems they chose.
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 Question, discuss solutions, and choose problems from the menu with your guidance.
Share Workshop Experience. Select a few problems from the Workshop to discuss as a class. You might choose these problems to represent common areas of difficulty for students or areas where students made significant progress over the course of the lesson. You may also choose to discuss problems all or most students would have solved. Questions 13, 17A–C, 18A–C, 29, and 35 in the Student Guide should have been completed by all students. Questions 17A–C and 18A–C are the same questions.
To stimulate discussion, ask questions such as:
