Guided Lessons

# The Missing Numerator in Equivalent Fractions

Are these fractions really equal? Use this lesson to introduce the concept of equivalent fractions with your students. Teach this on its own or use it as support for the lesson Equivalent Fractions Using Area Models.
This lesson can be used as a pre-lesson for the Equivalent Fractions Using Area Models lesson plan.

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This lesson can be used as a pre-lesson for the Equivalent Fractions Using Area Models lesson plan.

Students will be able to create equivalent fractions by multiplying by different fraction forms of one whole and draft an accompanying area model.

##### Language

Students will be able to find the missing numerator in an equivalent fraction using visual aids and peer interaction.

(5 minutes)
• Draw a pizza on the board and tell students that you are very hungry today and would like to eat half of the pizza. Call on a student to come up and draw how much of the pizza you will eat (they should draw a line to divide the pizza in two halves and shade in one half of the pizza). Label it as 1/2 and emphasize that you plan on eating a fraction of the pizza known as one-half.
• Tell students that you decided to eat the same amount of pizza (one-half) but in slices that are more manageable to hold. Ask for students' ideas on what you could do to achieve the goal of eating half the pizza but in smaller pieces (e.g., cut the half in half or split the pizza into fourths). Jot down students' responses on the board and affirm that an excellent option would be to cut the pizza into 4 pieces and eat 2 of the pieces. Draw another pizza, ask a student to divide it into 4 pieces, and have them shade in 2 of the 4 pieces.
• Have students turn to a partner and state their observations of the two shaded in pizzas and how they are similar or different using these sentence stems: "The two pizzas are similar in that..." and "The two pizzas are different in that..."
• Invite a few students to share their responses and guide them to the understanding that the second pizza shows the same amount as the first pizza. Explain that the second pizza should be labeled 2/4 and that essentially 2/4 is the same or equivalent as 1/2. They are equivalent fractions. Tell students that today they will become familiar with equivalent fractions by practicing talking about these types of fractions.
(6 minutes)
• Read aloud the student-friendly objective for the lesson and have students restate or rephrase it in their own words.
• Display the glossary on the document camera and distribute a copy to students.
• Read aloud each vocabulary word and invite students to volunteer to read the definitions and describe the images. In the blank column on the right, model to students how you write "Example" as the title of this column.
• Place students in pairs and have them work together to draw or write an example to demonstrate understanding of each vocabulary term. Have students share their examples with the whole group, in whole sentences, using the sentence stem: "An example of ____ is ____." (For example, "An example of "part" is when someone eats part of a cookie.")
• Tell students to paste the Glossary in their math journals for future reference.
• Show another example of an equivalent fraction on the board by drawing a rectangle and dividing it into three equal sections. Shade in two of the three parts and ask students to name the fraction (2/3).
• Draw another rectangle of the same size and divide it into six equal parts. Ask students to talk to their partner about how many parts they would have to shade in to make an equivalent fraction to 2/3. Invite a few students to share their thinking with you and affirm their responses. Model how to shade in four parts. Write 2/3 = 4/6 and explain that to get an equivalent fraction, we can also multiply the numerator and denominator by the same number. For example, when we multiply the numerator 2 by 2 and the denominator 3 also by 2, we get the equivalent fraction 4/6, as shown by the two rectangles. The value or amount of the shaded parts is equal.
(10 minutes)
• Tell students that they will practice identifying equivalent fractions. Ask students to turn to a partner and do a think-pair-share on what they already know about equivalent fractions. Invite a few students to share their conversation with the whole group.
• Distribute the Equal Fractions worksheet to students. Read aloud the directions and model how to solve the first matching problem. Explain that students are to circle the two fraction visuals that are equivalent. In this case 1/2 = 2/4. Elaborate that even though the shape doesn't look the same, if we were to cut them out, we would realize that the value or amount is the same.
• Instruct students to complete the worksheet independently. Assist any struggling students.
• Form small groups of three or four students and have them share their responses to the questions. Remind them to use key vocabulary from this lesson in their conversations with their peers.
• Review and display the following sentence starters to help students as they discuss:
• "The equivalent fractions are ____ and ____."
• "I know that these are equivalent fractions because ____."
• "I shaded in ____ parts of the whole because ____."
• Call on a few students to share the main points from their discussions.
(10 minutes)
• Inform students that they will do an oral activity in which they will practice finding the missing numerator in an equivalent fraction independently. Then they will work with a partner and take turns discussing their responses to the problems using sentence stems.
• Distribute the Equivalent Fractions worksheet to students. Display a teacher copy and read aloud the directions.
• Place students into effective A-B partnerships and model how you think aloud as you solve for the missing numerator using the visual aid and sentence stems provided. Note: post the sentence stems in a visible location in the classroom.
• Partner A (Question): "The first fraction is ____. The second fraction has a denominator of ____. What should the numerator be for this to be an equivalent fraction?"
• Partner B (Answer): "The numerator should be ____ because I see ____. I can also check my answer by multiplying ____ by ____."
• Remind students to take turns playing the role of Partner A and Partner B.
• Tell students to solve for the missing numerator in the rest of the problems and then begin conversing with their partner.
• Circulate the room and listen in on students' conversations to check for understanding.
• Invite a few non-volunteers to identify their partner's work and mathematical reasoning and share it with the class orally.

Beginning

• Provide bilingual resources in students' home language to support them through the lesson.
• Give fraction manipulatives such as fraction strips to help students see fraction equivalence in multiple ways.
• Pair students with advanced ELs who are able to assist them in the partner activity.
• Preteach a lesson on fraction equivalence vocabulary to a small group of beginning ELs.
• Have students repeat and rephrase the directions in the lesson.

• Encourage students to converse with their partners without using the sentence stems for support.
• Have them be first to share their math processes during group sharing time.
• Invite students to further explore equivalent fractions by coming up with their own equivalent fraction sets and explaining how they came up with them.
(5 minutes)
• Distribute a whiteboard and marker to students.
• Write 3/5 on the board and have students find an equivalent fraction that has the denominator 10. Instruct students to write their answer on their whiteboards using drawings and hold them up all at once. Scan the room to gauge understanding and correct any errors. Call on a few students to share their thinking and notice if students use the key vocabulary from the lesson.
• Repeat with another fraction such as 6/8 and an equivalent fraction with a denominator of 4.
(4 minutes)
• Give each student a piece of scratch paper and have them answer two prompts:
• What did you learn from today's lesson?
• What is one question you have related to equivalent fractions?
• Have students crumple up their paper and throw it into the middle of the room. Then, ask students to each pick up one scratch paper and read the responses to the questions. Call on a few students to read the paper they picked up aloud.