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# Subtracting Fractions Justifications

Continue to build on your students' understanding of unlike denominators by asking students to justify their answers of fraction subtraction. Use this lesson with the Subtracting Fractions with Different Denominators lesson.
This lesson can be used as a pre-lesson for the Subtracting Fractions with Different Denominators lesson plan.

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This lesson can be used as a pre-lesson for the Subtracting Fractions with Different Denominators lesson plan.

Students will be able to subtract fractions with unlike denominators.

##### Language

Students will be able to describe how to subtract fractions with unlike denominators using repeated explanations and peer input.

(5 minutes)
• Write four subtraction expressions on the board where one expression has like denominators and the other expressions have unlike denominators (e.g., 27 − ⅚, 912512, 610410, and ⅕ − 911) . Ask students to think about which one of the four expressions does not belong. Allow them to think on their own for 30 seconds before sharing their thoughts with their partners.
• Have some partnerships share their ideas aloud and write some of the ideas on the board that focus on key vocabulary terms (i.e., "denominator," "unlike," "subtraction," "common denominator," etc.).
• Have a volunteer read the student-friendly language objective that is written on the board: "I can describe how to subtract fractions with unlike denominators using repeated explanations and peer input." Define the key terms, such as "describe," "unlike," "denominators," "explanations," and "peer conversations."
• Ask students for examples of each of the vocabulary terms and write them around the terms in the language objective.
(6 minutes)
• Model the importance of changing denominators so they are alike, using bar models or a number line. Use the fraction from the board that does not belong with the other problems to model finding the least common denominator and then subtracting the fraction.
• Show students what the answer would be if you not found the common denominator, using bar models or number lines to represent the fractions.
• Use sequencing terms while you model explaining the process you used to subtract the fractions (i.e., explain your answer) and write the process on the board. Some phrases may include:
• "First, I ____."
• "After I ____, I ____."
• "Then, I ____."
• "My next step was ____."
• Have an advanced EL with a good understanding of the academic content restate the process you used to solve the subtraction problem to help explain their answer.
(8 minutes)
• Assign students a new subtraction problem they can complete in pairs (e.g., 5738) on the back of the Refine Your Justifications! worksheet. After they've finished the problem, have the same partners explain their answers to each other using whichever vocabulary and phrases they choose and write their explanations down in their the 1st Explanation section of the front page.
• Listen for student conversations and write their explanations on the Formative Assessment: Peer Persuasion Checklist.
• Share two student explanations: one that needs improvement and another one that has good sequence words and key vocabulary (e.g., "common denominator," etc.).
• Ask students to share aloud which explanation is more convincing. Based on the students ideas about the two example explanations, write some of the improvements students will make to their explanations to guide their next conversation.
• Lead them to understand that they may need more examples and that they may need to explain their thinking more than in their first explanation.
(11 minutes)
• Use the example from the explicit teaching section to model explaining what you know and how you know it. For example, "I know that the two denominators need to be the same because we need to have the same size piece to take away the right portion during a subtraction problem. I know this because of the bar models I drew to show the correct sizes of the fractional pieces."
• Tell students they will now refine their explanations with more evidence to support their answers in the Refine Your Justifications! worksheet in the 2nd Explanation section. Explain they will answer the following question: "What do you know about the problem and how do you know it?" Possible sentence frames can include, "I know that ____," and "I know this because ____."
• Have advanced ELs with a good understanding of the academic content restate what they know and how they know it about their subtraction problem. Model asking questions about a student's answer. For example, "Why wouldn't you do ____?" or "How can you know ____?" or "What else do you know that makes you sure you know the answer?"
• Assign students the 3rd Explanation section where they rewrite their explanation of their answer for the last time. Remind them to consider the necessary evidence (e.g., bar models, number lines, non-examples, etc.) to support questioning from their peers.

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.
• Allow them to focus on either explaining their answers or asking questions so they can perfect their answers throughout the lesson.
• Pre-teach a lesson on asking questions and explaining answers before this lesson.

• Pair students with mixed-ability groups so they can offer explanations and provide feedback to beginning ELs when appropriate.
• Have students share their answers, and encourage them to use proper phrases and vocabulary terms in their explanations to serve as a model for their peers.
• Ask them to share some of the sentence stems they can use in their justifications and questioning to make the supports more student-centered.
(5 minutes)
• Assign students to explain their answers to their new partners for the third and last time. Allow them to use the notes they've written in the 3rd Explanation section.
• Have their partners ask follow-up questions to act as skeptical listeners and prompt presenters to support their answers with visuals and correct sentence frames (e.g., "Why wouldn't you do ____?" or "How can you know ____?").
• Provide the following sentence frames for assistance with student justifications after their partner's questions:
• "I know this is true because ____."
• "My bar model/number line shows ____."
• "I know there is no other answer because ____."
• Continue to use the Formative Assessment: Peer Persuasion Checklist to take notes on student phrases and explanations. This can serve as a formative assessment of their understanding of subtracting fractions as well as their ability to justify their answer orally.
(5 minutes)
• Ask students to use what they learned to answer the following question: "Why do you need to find common denominators to get the right answer in a subtraction problem?"
• Encourage partners to discuss their answers.
• Share an example you overheard and write it on the board. Ask students to ask follow-up questions, such as, "How come the numerators can be different but the denominators need to be the same?"