Guided Lessons

# Discussing Fraction Representations

Support your students as they utilize key academy language to speak about visual and numerical representations of fractions. Use this as a stand alone lesson or as a pre-lesson for *Fractions in Action*.
This lesson can be used as a pre-lesson for the Fractions in Action lesson plan.

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This lesson can be used as a pre-lesson for the Fractions in Action lesson plan.

Students will be able to write fractions in mathematical notation and words.

##### Language

Students will be able to explain specific information about fractions using key vocabulary and sentence frames.

(3 minutes)
• Elicit student answers to the following questions: What is something that you are a part of? How many people are in the whole group?
• Define the word part as one of the pieces that make or form something. Point out that each of us is a part of something, such as a team, class, or family. For example, each student is a part of the class because they are one of the pieces that forms the class.
• Define the word whole as something that is full or complete. Tell learners that the whole is a class, family, or team.
• Challenge them to think of any other examples of parts and the whole. Record student answers on the board to serve as a reference for the remainder of the lesson.
• Read the student-friendly Language Objective aloud and have students repeat it. Explain that they will learn some important vocabulary to talk about fractions today.
(8 minutes)
• Display each of the Vocabulary Cards on the document camera to provide additional visuals for the tiered vocabulary terms from the lesson. Read aloud each word and have the students repeat it aloud to practice pronunciation. Then, do the same for the definitions. Add any necessary explanation for the visuals on each card.
• Explain that a fraction represents a part of a whole or any number of equal parts. Share that we can look at a representation, which is something such as a picture that stands for something else, of a fraction to learn a lot of information.
• Tell the class that you have a table where four students can sit, but there is one empty seat because a student is absent. Add that you can represent this information with a fraction.
• Write the fraction 1/4 on the board and label each part with a key term. Review the definition of the key terms numerator (the number in a fraction that is above the division line, it shows how many equal parts of the whole that you have) and denominator (the number in a fraction that is below the division line, it shows the number of equal parts in the whole).
• Create a visual representation of 1/4, such as a square separated into four equal parts with one part shaded. Point out that these two representations show the same thing. Say, "The whole, or the larger square, is broken into four parts, which represents the four seats at the table. I can see that one part of the whole is shaded. The numerical representation is showing one part of the whole, as well. The numerator shows one part, and the whole is divided into four equal parts, so the denominator is four. Both fractions show one fourth. These fractions show one seat out of the four where a student does not sit."
• Provide another example by giving a scenario, such as "I know that in my class, there are 12 students. 8 students ride the bus. What fraction of my class rides the bus?"
• Model drawing the visual representation by creating a rectangle with twelve equal parts, eight of which are shaded. Then write 8/12. Model thinking aloud about how the fractions show the same thing, and be sure to use the tiered vocabulary words. Revisit the Vocabulary Cards as necessary.
• Distribute a copy of the Glossary to each student and have them put it into their Math Journals to serve as a reference for the remainder of the lesson.
(10 minutes)
• Have students take out a whiteboard and whiteboard marker and tell them that you have another example to share. Tell them that they can use the whiteboard to show work if needed. Say, "We ordered a pizza for our family on Friday night. It had twelves slices. We ate seven of them. What fraction of the pizza did we eat?"
• Show the visual representation of the fraction by drawing the pizza with twelve equal pieces, seven of which are shaded. Then, write 6/12 next to it. Ask students to discuss with a partner whether your visual and numerical representations are correct. Provide sentence starters for students to use in their discussion, such as "The numerator/denominator is right/wrong because ____." or "The visual representation is right/wrong because ____."
• Share out as a class and have students explain why your representations did not match. Listen for students to use tiered vocabulary in their explanations.
• Display a copy of the Identify the Fraction Errors worksheet on the document camera. Show only the pizza example at the top, modeling how to think aloud about the visual and numerical representations. Orally ask yourself, "Is the denominator correct? Is the numerator correct? Does the fraction represent the same value as the picture?"
• Show students the example representations without displaying the sentence frames. Ask the same prompting questions to engage them in the conversation about critiquing the flawed response. Allow them to talk to a partner before sharing with the whole group. Provide sentence frames, such as "The numerator/denominator is right/wrong because ____." or "The visual representation is right/wrong because ____."
(12 minutes)
• Distribute a copy of the Identify the Fraction Errors worksheet to each individual. Inform them that they will work with a partner to critique the wrong responses. Explain that being able to notice mistakes helps us become detail-oriented mathematicians who can analyze math problems and solutions with a critical eye.
• Instruct students to identify the errors in the four problems on the worksheet and discuss how they could fix the problem. Remind them to use the key vocabulary, relying on the Glossary as a reference, as they discuss the errors and new response.
• Have partners share out the completed sentence frames with their error analysis and suggested solution for each problem.
• Engage the rest of the class in sharing if they agree or disagree with the responses that are shared.

Beginning

• Provide a set of Vocabulary Cards to individuals to reference during the lesson.
• Have learners repeat instructions and key vocabulary to the teacher.
• Provide a word bank of key terms and phrases for students to use in group and class discussions.
• Group students intentionally based on academic and language needs.
• Provide sentence frames for students to use in the Assessment section, such as "My partner's numerical representation matches/doesn't match their visual representation of the fraction. I know this because ____."

• Allow learners to utilize glossaries and dictionaries for unfamiliar words.
• Choose advanced ELs to share their ideas first in group and class discussions.
• Have learners repeat instructions and key vocabulary, summarizing important information for the class.
(5 minutes)
• Give each student an index card and instruct them to draw a circle that is divided into eight equal parts. Have them shade five of the equal parts.
• Instruct them to write the numerical representation of the fraction to match the visual representation.
• Put learners into partnerships and pose the following question for discussion, "Does your partner's numerical representation match their visual representation of the fraction? How do you know?"
• Observe partner conversations and provide feedback and prompting questions as needed.
(2 minutes)
• Call on a nonvolunteer to explain what they talked about with their partner, and allow them to share their visual and numerical representations with the rest of the class.
• Remind students that a fraction shows a part of a whole or any number of equal parts, and that understanding fractions helps us better understand what parts of the whole we have. Point out that fractions are used in our everyday lives from telling time to cooking to measuring and building.