Lesson 7

Workshop: Many Ways to Show a Fraction

Est. Class Sessions: 2

Developing the Lesson

Part 2. Many Ways to Show a Fraction

Show Fractions with Words, Numbers, Models, and Number Lines. The Many Ways to Show a Fraction pages in the Student Guide depict a class discussion about different representations of fractions including circle pieces, fraction strips, number lines, and rectangular arrays.

Use the discussion questions to facilitate a similar discussion with your students. Have students discuss the questions for each representation with partners before discussing them as a whole class.

Questions 1–4 refer to John's drawing using circle pieces.

Questions 5–6 refer to Jackie's use of a fraction strip.

Question 7–8 refer to Jerome's use of a number line.

Questions 9–14 refer to Jessie's drawing of a rectangle divided into 12 pieces.

  • What is the unit whole for each way the students used to show 1/4? (The red circle, one fraction strip, from 0 to 1 on the number line, and a whole pan of lasagna.)
  • How is the denominator shown for the circle pieces, fraction strip, and number line? (Possible responses: For the circle pieces, four yellow pieces cover the whole. The fraction strip is divided into four equal parts. The number between zero and 1 is divided into four equal parts.)
  • If I covered the red circle with one pink and three aquas, would that show fourths? Why or why not? (No. There are four pieces, but they are not equal pieces.)
  • How did John, Jackie, Jerome, and Jessie show the numerator in the way they showed 1/4? (John shaded one of the four parts of the circle. Jackie shaded in one of the parts of the fraction strip. Jerome put a point 1/4 of the way from 0 to 1 on the number line. Jessie shaded in 1 of the 4 columns in her rectangle.)

Set Up the Workshop. The menus and problems for this Workshop are in the Student Activity Book on the Showing Fractions pages.

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. The Workshop is divided into five sections that address Expectations as shown in Figure 6. Minis of the Student Activity Book pages not shown here are in the Answer Key.

Use Self-Check: Questions 1, 16, 23, and 32 in the Student Activity Book to assess students' abilities with the following Expectations:

E1.
Represent fractions using area models (circle pieces, fraction strips, drawings) and number lines.
E2.
Use words and numbers to name fractions.
E3.
Recognize that the same fractional parts of different-sized unit wholes are not equal.
E4.
Identify the unit whole when given a fractional part of a whole.
E5.
Name and represent fractions greater than one as mixed numbers and improper fractions using models (fraction strips, circle pieces, number lines).
E6.
Write number sentences from area models of fractions (e.g., 1/2 = 3/6, 1/3 + 1/3 = 2/3, 1/3 + 1/3 + 1/3 = 1/3 × 3).
E7.
Make connections among representations of fractions including symbols, words, area models, and number lines.

Use the Menu for Fraction Fill to have students self-assess their ability to write number sentences to show a unit whole divided into fractions [E6].

Choose Targeted Practice. 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 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:

  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 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?” question.

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 together 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 Questions, discuss solutions, and choose problems from the menu with your guidance. Follow this pattern through each section of the Workshop.

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. They can also be sent home as 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 menu or to play one of the Fraction Fill games.

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 3, 8, 13, 15, 17, 18, 24, 28, 37–40 in the Student Activity Book should have been completed by all students.

Revisit Fraction Fill. Refer students to the menu after Question 40 on the Show Fractions pages in the Student Activity Book. Have students choose if they will play Fraction Fill 1 or Fraction Fill 2. Then organize students into groups based on their choices and ask students to play at least two rounds of the Fraction Fill game they selected.

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Expectations addressed in each section of Workshop: Many Ways to Show a Fraction
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