Guided Lessons

# Explaining Equivalent Fractions

In order to build a strong foundation with fractions, students should be able to explain the concept and their thinking. Use this as a stand alone lesson or as a pre-lesson for *Let's Play Equivalent Fractions!*
This lesson can be used as a pre-lesson for theLet's Play Equivalent Fractions!Lesson plan.

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This lesson can be used as a pre-lesson for theLet's Play Equivalent Fractions!Lesson plan.

Students will be able to identify and represent equivalent fractions using visual fraction models.

##### Language

Students will be able to explain why fractions are equivalent using peer supports and sentence stems.

(4 minutes)
• Display a copy of the blank Concept Web graphic organizer on the document camera. Write the term Equivalent fractionIn the centre, and access students' prior knowledge by asking them what they know about the term or words. Encourage them to share examples or their knowledge of the independent word parts in the term.
• Support students as they share what they know by providing sentence stems:
• Equivalent fractions are ____.
• I know that ____.
• An example is ____.
• Share a real-world example of equivalent fractions. For example, "Maria has 1/3 of a cake, and Bruno has 2/6 of the same cake. Who has more?" Think aloud about the answer and how you know, and provide visuals to support your explanation.
• Go over the student-friendly Language Objective with the class and have them repeat it aloud.
(8 minutes)
• Explain that there are some important vocabulary terms that students will need to understand and use throughout the lesson today. Go through the Vocabulary Cards by displaying them on the document camera. Read each word and definition, and invite students to share what they notice about the images.
• Hand out a Glossary to each individual, and have them glue it into their maths journal or notebook to serve as a reference during the lesson.
• Show examples of equivalent fractions on the Matching Equivalent Fractions worksheet. First, label each of the pictures with a fraction. Then, match them. Explain that you can also look at the visuals to check that you correctly identified equivalent fractions.
• Cover up all images on the worksheet except #2, #3, and answer choice D.
• Think aloud as you look at #2, #3, and answer choice D. Ask students to imagine that these are pies that are sliced differently. Share that the same value of the pie is shaded in, but the pies look different because they are broken into a different amount of equal parts, or pieces. Say, "The pie on #2 is showing the fraction 2/4 and the pie on #3 is showing 4/8. I can see that these are equivalent fractions because the value of shaded area in each circle is the same even though the numerator and denominator in each fraction is different. If I look at answer choice D, I see it's also equivalent. The fraction is 1/2 and the value of the area shaded is the same."
• Write the following fractions on the board:
• 1/2
• 2/4
• 4/8
• Focus on the first two fractions, and model thinking aloud about the relationship between the two numerators and two denominators. Say, "The numerator in 2/4 is double the numerator in 1/2. The denominator in 2/4 is double the denominator in 1/2." Explain that if the relationship between the two numerators and the two denominators is the same, they are equivalent. Note that you could also work backwards and show the relationship with division as opposed to multiplication. Show students how both operations result in the same conclusion.
• Display the following steps for determining if two fractions are equivalent on an anchor chart or the board for students to reference during the Guided practise portion of the lesson:
• 1 - Write down the fractions from each of the pictures.
• 2 - Determine the relationship between the numerators by either multiplying or dividing.
• 3 - Determine the relationship between the denominators by either multiplying or dividing.
• 4 - Answer this question: Is the relationship between the numerators and denominators the same?
• Invite students to follow the steps to determine if 2/4 and 4/8 are equivalent. Support their discussion with sentence stems and frames.
(10 minutes)
• Give each student a copy of the How Do You Know They're Equivalent? worksheet, and display a copy on the document camera.
• Refer back to the step-by-step process of determining if the fractions are equivalent. Guide students through the first example on the worksheet and, before writing a response for the sentence stem, prompt students to turn and talk to a partner about how they know the fractions are equivalent.
• Ask the following questions to get students to create a more thorough explanation. Provide sentence stems/frames to support their conversation:
• What value is shown in each picture? (Sentence stem: This picture shows ____.)
• How are these two pictures similar? How are they different? (Sentence stem: These pictures are similar/different because ____.)
• What do you notice about the numerators/denominators? (Sentence stem: I notice that ____.)
• What is the relationship between the two fractions? (Sentence stem: The two fractions are ____.)
• Put students into effective partnerships and instruct them to complete the second problem on the worksheet. Circulate and provide feedback and clarification as needed.
• Gather the students' attention to go over the problem as a class. Call on nonvolunteers to answer the prompting questions, and be sure to display the sentence stems to support their oral language.
(10 minutes)
• Tell students that they are going to do a Numbered Heads Together activity to discuss the last example on the worksheet.
• Put students into small groups of four. Have each group of students count off by the number of students in the group so that every group has a one, two, three, and four. If the class is smaller, adjust the numbering for this activity.
• Present a question that requires explanation by the students. Point students' attention to #3 on the How Do You Know They're Equivalent? worksheet, and instruct them to discuss how they know the two fractions are equivalent.
• Give the groups a few minutes to make sure that everyone in the group can explain each step of how to determine the equivalency of the fractions. Allow them to create notes together. At this time, take down the reference chart of the steps that students should follow.
• Call a random number from 1-4 to be the reporter for the group, and tell the groups they are no longer allowed to talk or write to each other. Explain that the reporters are allowed to use the notes that have already been created. Invite the reporters, one at a time, to explain the next step of the problem, to agree/disagree with the previous reporter, or to justify the reasoning of their group in some way.
• Reveal the correct answer for the problem after every reporter shares.

BEGINNING

• 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.
• Invite students to label the last column on the Glossary as "Home Language" and give students time with reference materials in their home language to find the word for each vocabulary term.

• Allow learners to utilize glossaries and dictionaries for unfamiliar words.
• Choose advanced ELs to share their ideas first in group and class discussions.
• Encourage students to explain their process and answers without using the sentence stems/frames.
• Have learners repeat instructions and key vocabulary, summarizing important information for the class.
• Put students in mixed ability groups so they can offer academic and language support to beginning ELs.
(6 minutes)
• Give each student an index card for the Exit Ticket.
• Display the following word problem and provide visuals to support students' understanding of the context: "I had two pizzas at my house for dinner. The first one was divided into four equal parts, and I ate one slice. The second pizza was divided into eight equal parts, and I ate two slices. What of fraction of each pizza did I eat and are they equivalent?"
• Provide sentence supports for students, such as "The fraction for the first pizza is ____, and the fraction for the second pizza is ____. The fractions are/are not equivalent because ____."
(2 minutes)
• Ask students to consider other examples of things that are Equivalent. (e.g., amount of milk in two containers, size of two twin beds, etc.) Have students turn and talk to a partner about their ideas. Share out as a class.
• Remind learners that fractions are equivalent when they have the same, or equal value. It is important to understand equivalent fractions because it helps us to add, subtract, multiply, and divide fractions. It also helps us solve real world problems!