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# Strategies for Comparing Fractions

This lesson can be used as a pre-lesson for the Fraction Wars lesson plan.

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This lesson can be used as a pre-lesson for the Fraction Wars lesson plan.

Students will be able to compare fractions with different numerators and denominators.

##### Language

Students will be able to explain and compare their strategies for comparing fractions using sentence starters.

(5 minutes)
• Write "Comparing Fractions" in the middle of a piece of chart paper. Lead students in a think-pair-share about numbers, symbols, or words they associate with this term. Provide the sentence stem, "When I think of comparing fractions, I think of..." to students as they think and talk with a partner. Invite students to share their word/number/symbol associations and record them in the area surrounding the word on the chart paper.
• Validate students' responses as you record them.
• Read aloud the content and language objective of the lesson and have students repeat them chorally.
• Tell students that today they will practice comparing and contrasting strategies to compare fractions.
(8 minutes)
• Inform students that they will first review some important vocabulary needed to succeed in this lesson.
• Introduce each tiered word by displaying the vocabulary card on the document camera. Distribute a Glossary to each student and have them glue it in their math journals for reference throughout the lesson.
• Invite a student to read the word and its definition aloud. Have another student explain the image (if there is one) and how it connects to the word. As you review all the vocabulary terms, encourage students to add symbols, pictures, or words to their Glossary to help them understand the meaning of the words.
• Have students orally use each key term in a sentence and share their sentence with a table partner. Invite a few non-volunteers to share their sentences with the whole group.
(10 minutes)
• Tell students that their focus for today's lesson is on strategies to compare fractions.
• Write 2/3 and 3/4 on the board. Tell students that today they will focus on three strategies:
1. Draw a model (pie, bar).
2. Draw a number line with benchmark fractions.
3. Find a common denominator (or equivalent fraction).
• Create an anchor chart on a piece of chart paper with the strategies, an explanation, and an example.
• Explain that drawing a model or picture of the fractions gives a clear visual understanding to help us see which one is greater. Drawing a number line is another strategy that helps us see where the fractions are in comparison to each other and to benchmark fractions. Explain that benchmark fractions are those that are easy for us to visualize mentally, such as 1/4, 1/2, or 3/4.
• Tell students that finding a common denominator is another effective strategy to compare fractions that have different denominators. This sometimes means that you convert or change one fraction into an equivalent fraction. If you can change the fractions so that they have the same denominator, you can easily compare the fractions.
• Distribute the Fraction Equivalency Chart to students and display a teacher copy on the document camera. Explain to students how they can use this chart as an additional support in strategies 1 ("Draw a model") and 2 ("Using benchmark fractions").
• Model how to use each strategy to compare 2/3 and 3/4. Use the Fraction Equivalency Chart as a guide. Remind students to use the Glossary as a reference to remember the meaning of each symbol (>, <) as they compare the fraction.
• Explain to students that it is important as mathematicians to be flexible thinkers and be able to try different strategies to solve the same problem. By knowing multiple strategies, students will be able to confirm if their answer is right and be able to think it different ways about math operations.
• Distribute whiteboards and markers to students.
• Place students into partnerships and have them compare the following fractions, using a different strategy each time, on their whiteboards: 5/8 and 1/8, 2/3 and 7/8, 6/10 and 1/4, 12/30 and 6/15, 5/9 and 17/20
• Circulate to offer assistance as needed.
(10 minutes)
• Tell students to discuss their strategy with their partner, using the following paragraph frame: "To compare ____ (fraction) and ____ (fraction), we chose the ____ strategy because... First, we... Then, we... Therefore, we could see that ____ (fraction) is greater than/less than/equal to ____ (fraction)."
• Have a few pairs of students share their strategy and explain their reasoning with the whole class.
• Facilitate a discussion about the various strategies they used in their fraction comparisons. Provide the following questions and sentence stems/frames for students to use as they compare and contrast the strategies they used:
• What worked well in the strategy you used? ("____ worked will in this strategy because...")
• What did not work well for the strategy you used? ("____ did not work well for the strategy we used because..." or "Everything went well in the strategy we used.")

Beginning

• Provide a paragraph frame for students to use (see example) as they demonstrate and justify their assessment.
• Give students access to bilingual glossaries and online dictionaries for them to look up unfamiliar words throughout the lesson.
• Place students with more advanced ELs for partner work.
• Pull aside a small group of students as they work on the group work and guide them through the process.
• Have students repeat the directions in their home language (L1) or in English (L2) before beginning their work.
• Allow students to work on the formative assessment piece with a helpful partner.

• Encourage students to speak and write their answers without using the sentence frames/stems.
• Allow students to be the first to share their ideas or rephrase their classmates' contributions to class discussions.
• Have students create and display a word/phrase bank with helpful terms from the lesson for reference purposes, with images if applicable.
(5 minutes)
• Give each student an index card and make sure they still have their whiteboards and markers with them. Have them write one fraction on the card. Place students in a new partnership and have them work together using one of the four strategies of their choice to compare the fractions on the two cards.
• Have students verbally state to the whole group the answer to their fraction comparison. Then have them explain the strategy they used to figure it out and why they chose that strategy. For example, "Kaya and I compared 3/9 and 1/2. We decided to use the 'draw a model' strategy and we drew bar models for each fraction so we could see which was greater. We chose this strategy because we both like having the picture to see how the fraction would actually look. We could see that 3/9 is less than 1/2 because there is less shaded in parts in the 3/9 bar model than the 1/2 bar model."
(2 minutes)
• Remind students that it is essential to be flexible math problem-solvers. By knowing multiple methods or strategies to solve the same problem, they are growing their math thinking skills along with their brain flexibility.
• Quickly go around the class and ask students to complete this sentence: "My favorite strategy for comparing fractions is the ____ strategy because..."

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