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# Compare Visuals for Equal Fractions

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This lesson can be used as a pre-lesson for the Show Me Equivalent Fractions! lesson plan.

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This lesson can be used as a pre-lesson for the Show Me Equivalent Fractions! lesson plan.

Students will be able to find equivalent fractions using number lines or bar models.

##### Language

Students will be able to explain how to find equivalent fractions using number lines or bar models.

(5 minutes)
• Display a number line and a bar model of the same fraction (e.g., 5/11) and ask students to think about what is the same or different in the two visuals.
• Allow students to think for one minute on their own and then share their ideas with their partners. (Note: they should understand that the visuals represent the same fractions but one is on a line while the other is in a box.) Gather information about students' background knowledge by listening to their discussions and writing down some of the phrases they used to compare the bar model and number line.
• Challenge students to represent these two fractions using a visual of their choice (i.e., number lines or bar models) on their whiteboards: 3/4 and 6/8.
• Ask students to share their visuals and lead the students to understand that the fractions have the same amount shaded in the bar model, or have the same placement on a number line, even though the fractions are different. Tell them the fractions are equivalent because the values are the same, even though the numbers are different. (Note: it's helpful to draw the bar models and number lines vertically so students can see the equivalency.)
• Tell students that today they'll compare equivalent fractions on number lines and bar models. They'll become experts on creating equivalent fractions using one of the visual examples (i.e,. bar models or number lines) and present their information.
• Share some of the phrases students used to compare the two visuals aids and tell them they will be able to converse about the similarities and differences at length by the end of the lesson.
(6 minutes)
• Model creating bar models and number lines for two benchmark fractions (see the Fraction Equivalency Chart) and a third larger fraction (e.g., 10/20 and 1/2). (Tip: make sure the boxes for the bar models and the lines for the number lines are proportional so students can visually see the equivalency.) Have students copy your teacher markings on their whiteboards.
• Model comparing the number line to the bar model. For example, say, "I notice the bar model has rectangles to separate the piece of the whole, while the number line separates pieces of the whole on a line."
• Ask students to turn and talk to each other about one thing that is the same and one thing that is different between bar models and number lines. Write on the board some of their thoughts and create sentence frames for future use in the lesson.
• Present another fraction in real world examples, such as pies split into 12 pieces or 10 of 20 students wearing black, etc. Make sure to provide an example of two fractions that are not equivalent and show them in both the bar model and number line. Then, compare the two visual aids and write your comparison on the board.
(10 minutes)
• Explain that now that they understand how to represent equivalent fractions with two different visual models, they'll become experts at creating equivalent fractions for one of the models and present the information to their groups. Tell them they will eventually compare the two visual representations.
• Provide the following scenario for students to consider: "You want to buy a portion of a cake or a pie. The sign says 1/3 of the cake costs \$5 and 5/8 of the pie costs \$5. Which is a better value?"
• Have students participate in a jigsaw activity to solve this problem. Separate the class into groups of 3–5 students, where half of the groups will become experts at finding equivalent fractions with bar models and the other half of the groups will use number lines. Tell the students to draw their information on chart paper because they will present the information as experts in front of the class.
• Provide the following sentence frames to assist in their explanations:
• "First, I ____."
• "After I ____, I ____."
• "Then, I ____."
• "My next step was ____."
• Alternate between number line experts and bar model experts for the group presentations. Tell students that while the groups present their visuals, they need to think about how the groups solved their problems and what evidence they included in their chart paper. After each presentation, have the students answer the following questions:
1. How did the group solve their problem?
2. What drawings or visuals did they use?
• Have the audience take notes on a T-chart they draw on their whiteboards. Have them label one side "bar models" and the other side "number lines."
(7 minutes)
• Have students share some of their notes after the presentations while you write down the notes on a T-chart on the board that focuses on the use of the bar models or number lines.
• Display two exemplary group chart papers, one with a bar model and the other with a number line, from the jigsaw activity. Model synthesizing the T-chart notes into comparisons between number lines and bar models in relation to the equivalent fractions. (Even though both methods compare two different fractions to see equivalencing, the number line has a line separated into groups to represent a fraction, while the bar model has a rectangle separated into sections to represent a fraction.)
• Have students turn and talk to their elbow partners restating some of your comparisons, but also creating their own. Write down some of the common phrases students use as they compare the bar model method to the number line method on the Formative Assessment: Presenting Summaries worksheet. Some of the phrases may include the following:
• "The bar model and number line are similar because ____."
• "The bar model ____, but the number line ____."
• Share some good examples you heard during their conversations.

Beginning

• Allow students to use their home language (L1) or their new language (L2) in all discussions. Provide bilingual reference materials to assist in their vocabulary word acquisition.
• Encourage them to use the vocabulary cards and terms in their conversations and writing. Allow them to draw pictures to support their understanding of the terms on the vocabulary cards.
• Have them use the Fraction Equivalency Chart while they explain how to create equivalent fractions on the chart itself.

• Pair students with mixed-ability groups so they can offer explanations and provide feedback to beginning ELs when appropriate.
• Have them share their group's information with support from their other group members.
(9 minutes)
• Have students write on an index card the difference between using a bar model and number line for finding equivalent fractions.
• Provide the following sentence frames for students who need additional support with their written explanations: "The bar model and number line are similar because ____. The bar model ____, but the number line ____. I prefer the ____ because ____."
• Ask students to present their information in partners or groups and continue to use the Formative Assessment: Presenting Summaries worksheet to write notes about their answers.
(3 minutes)
• Choose students to present their sentences to the class and allow students to give input and critique the responses respectfully.
• Display the Fraction Equivalency Chart and choose volunteers to shade in two equivalent fractions using the bar models and another student to write the fractions represented in the shaded bar models. Then, have a third student explain why the two fractions are equivalent.

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