Guided Lessons

Compare Common Denominators Methods

Challenge your students to compare two methods for finding the least common multiple between two fractions. Use this lesson on its own or as support for the lesson Make It Work! Adding Fractions with Unlike Denominators.
This lesson can be used as a pre-lesson for theAdding Fractions on Number LinesLesson plan.

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This lesson can be used as a pre-lesson for theAdding Fractions on Number LinesLesson plan.

Students will be able to compare two strategies for finding common denominators.

Language

Students will be able to compare two strategies for finding common denominators using language frames and peer supports.

(5 minutes)
• Write the student-friendly language objective on the board and ask a volunteer read it: "I can compare two strategies for finding common denominators using colour-coding and peer supports." Have students choral read it again and raise their hand when they hear a vocabulary term they would like to define or have questions about (e.g., least common denominator (LCD), compare, strategies, colour-coding, etc.).
• Ask for volunteers to help you define the vocabulary terms in the language objective and draw visuals to accompany the terms.
• Gather more background information by asking students to talk to their partners about all the vocabulary terms that they may need to use when discussing the LCD (e.g., denominator, multiple, fractions, etc.).
• Tell students that today they will compare two strategies for finding common denominators in fractions:
1. Multiplying the denominators by each other
2. Finding the least common denominator
• Distribute the vocabulary cards and define Multiples, Factor, and Denominator. Choose volunteers to restate each of the meaning in their own words. (Tip: choose students who are familiar with the meanings or advanced ELs to restate the meanings first while others do so in their partnerships.)
(10 minutes)
• Show the vocabulary card for the word CompareAnd ask students to share some phrases they use when they compare two things. Use two everyday objects for them to compare if necessary. Write their responses on the board and allow students to correct each other when necessary (e.g., "____Is easier/harder than ____Because ____," or "They are alike/different because ____.").
• Display the colored pair of cards from the Two Methods for Finding Common Denominators worksheet and have students turn and talk about what they observe about the two cards (e.g., involve fractions, unlike denominators, finding the least common denominator, finding common denominators, etc.).
• Write down some of the student conversations you overhear from their partner conversations. Allow a student to share similarities and differences if you overheard the correct ideas. Label the list "Similarities and Differences" on the board.
• Redo both methods with the same addition problem from the cards (i.e., 38+ 25) on two separate chart papers using key vocabulary terms and numbering the steps as you complete the processes. Think aloud some of the steps, such as how to find the LCD on card B, "I need the denominators to equal the least common denominator, or 40, so I need to figure out ____X 5 = 40And multiply the numerator and the denominator by that Factor. I know 40 ÷ 5 = 8, and 40 is the eighth multiple in the list of multiples of 5, so I need to multiply the denominator and the numerator by 8."
• Ask students to look at the two anchor charts and rethink some of the ways the methods are the same or different. If necessary, model saying one difference, "The method on card A has fewer steps than the method on card B."
• Add more similarities and differences to "Similarities and Differences" list on the board and start creating separate sentence frames from the student discussions:
• "____Is the same in both methods because ____."
• "One difference/similariarity is ____."
• Make sure students understand that both of the cards displayed (i.e., cards A and B) show an addition problem involving fractions with unlike denominators and show how to find common denominators. Tell them that one card shows a method that only involves multiplying the denominators (i.e., 8 and 5) by each other to find a common multiple between the two numbers that can serve as a common denominator. Card B has a list of multiples for each of the denominators and then the lowest common denominator circled. Also, card B shows the multiplication of the numerator and denominator by the same factor that will change the denominator to the LCD (i.e., 40).
(8 minutes)
• Tell students they will now work in groups on a new addition problem. Distribute one set of precut cards from the Two Methods for Finding Common Denominators worksheet. Have groups look at the two methods depicted and talk about one similarity and one difference between the two methods they see. Encourage them to use the sentence frames written in the board as necessary.
• Pass out copy paper and have students redo the process that they see on the cards and talk aloud telling what they're writing and why as they copy the cards.
• Have groups share the mathematical processes they see on their cards.
(5 minutes)
• Have students help you create the list of the steps they followed as they copied the two methods down on their copy paper after all the cards are represented (only three groups need to present). Method 1 (from cards A, C, and E) should look like this:
1. Multiply each numerator and denominator by the other fraction's denominator.
2. Recreate the expression using the new fractions.
• Method 2 (from cards B, D, and F) should look like this:
1. Find the least common denominator by listing the multiples of the unlike denominators.
2. Multiply the numerator and denominator by the factor needed to get the least common denominator.
3. Recreate the expression using the new fractions.
• Model using sequencing words as you rephrase the steps and write them in a checklist form.
• Ask students to turn and talk to their partners to retell about the steps needed to find common denominators using both of the methods. Have partners take turns restating the steps for the methods.

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 students to use the vocabulary cards and terms in their conversations and writing. Allow them to draw pictures to support their understanding of the terms and represent their ideas with bar models or tape diagrams and orally explain their answers before writing them down.
• Remind them to refer to the anchor chart or their vocabulary cards when they ask questions or share information. Allow them to point, and assist them with their explanation.
• Provide them with their own copy of the pre-cut cards from the Two Methods for Finding Common Denominators worksheet so they can colour-code with highlighters the different parts of the fractions (refer to the pair A and B in the answer sheet) and use them in their discussions.

• Pair students with mixed-ability groups so they can offer explanations and provide feedback to beginning ELs when appropriate.
• Ask them to restate the explanations and to share sentence frames or stems they can use in their explanation (of how to add fractions when they have unlike denominators).
(7 minutes)
• Distribute a sheet of copy paper and have students fold it in half hamburger style. Write the following expression on the board: 35+ 79. Tell students you'd like to add the fractions together, but their denominators are different. Ask students to find common denominators using both of the strategies we compared today doing one strategy on each side.
• Have students write one thing that was the same and one thing that was different with each of the strategies. Tell them to refer to the board for sentence stems for comparative sentences and their vocabulary cards for assistance with the key terms.
(5 minutes)
• Have students consider both strategies for creating common denominators and ask them the following question: "What is the most important similarity between the two strategies?" (e.g., they're finding equivalent values, they're changing the denominator and the numerator but the value of the fraction stays the same, etc.)
• Have them talk in groups and choose students to share their ideas aloud. Correct misconceptions if necessary.
• Explain to students they can use both of the strategies for finding common denominators when they are adding or subtraction fractions.