Guided Lessons

# Explain Fraction Conversions

Encourage students to explain their processes when converting from a mixed number to an improper fraction, and back again. Use this lesson on its own or as support to the lesson Single Strategy for Adding and Subtracting Mixed Numbers.
This lesson can be used as a pre-lesson for theSingle Strategy for Adding and Subtracting Mixed NumbersLesson plan.

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This lesson can be used as a pre-lesson for theSingle Strategy for Adding and Subtracting Mixed NumbersLesson plan.

Students will be able to convert mixed numbers into improper fractions and back again.

##### Language

Students will be able to explain how to convert between mixed numbers and improper fractions.

(3 minutes)
• Conduct a "Which One Doesn't Belong?" conversation activity with four different fractional numbers written on the board, such as improper fractions, mixed numbers, and regular fractions (e.g., 1 23Subscript, 13, 53, 116). Ask students, "What do you notice about the numbers? What things are the same or different about the numbers?"
• Discuss different categories or groups they can create (e.g., greater than one or less than one, all fractions or whole numbers and fractions, common denominators or unlike denominators, two terms are the same value (1 23And 53), etc.)
• Choose a volunteer to read the language objective: "I can explain how to convert between mixed numbers to improper fractions."
(7 minutes)
• Review the vocabulary terms with the students and have them choral read the meanings.
• Distribute the cut vocabulary cards and ask students to find their partner without telling their partner about their card. Their partners have to ask questions about the card to see if they're a match.
• Pass out whiteboards and ask them to write down an example of what you say and hold up the whiteboard.
• Ask students to write the vocabulary terms, such as "whole numbers," "fractions," "mixed numbers,"and "improper fractions," based on the numbers you say aloud and hold them up. When they hold them up, have them say a complete sentence, such as, "You said 34, which is a regular fraction."
• Ask them to draw bar models to represent each of the numbers, whether they are improper fractions or regular fractions.
• Say the different numbers and have them write them on their whiteboards. For example, say, "Write five and seven-eigths (i.e., 5 78)".
• Use one of the examples you already discussed with the class to model converting an improper fraction into a mixed number. Say the steps using sequencing terms and then write the steps on the board. For example, say, "I have 76. I know 7 is one more than 6, so I will write 6 + 1Over the denominator 6. I know 66Equals one (draw out the bar model to represent 66), so I can make two fractions 66And 16. Next, I change 66To one, and now I have 1 16."
• Explain that today they will use their understanding of their vocabulary terms to explain the process needed to convert an improper fraction into a mixed number and vice versa.
(8 minutes)
• Solicit students' understanding of converting from a mixed number to an improper fraction and model that process as well. Use the same vocabulary and sequencing terms shown above. For example, say "I have 1 16. I know 6 is in the denominator for the fraction, so I can write 66To replace the number one. Then, I can add the numerators one and six together when both fractions have common or like denominators. My answer is 76."
• Ask an advanced student with a clear understanding of how to convert from mixed numbers to improper fractions to model the conversion with a different number, such as 5 34. (Tip: you can have students write 44Five times and then add them, or they can reason that 5 x 4 = 20So the new fraction to replace the number five is 204. Then they can add 204+ 34.)
• Ask another student to model converting the same number back to an improper fraction. Take notes on the students' language and phrases they use during their explanations.
• Read some of the phrases aloud to the students and talk about ways to improve the explanations (e.g., add more sequencing words, use vocabulary words, have examples, etc.).
• Have students turn and talk to their partners and practise restating a process of their choice (i.e., converting between 5 34And 234) using the new sequencing word and vocabulary. Some of the language frames may include:
• "First, I ____."
• "After I ____, I ____."
• "Then, I ____."
• "My next step was ____."
(12 minutes)
• Have students work in groups of four where each member is a number from 1–4. Assign half the groups as Group A and the other half as Group B.
• Have Group A members work together to convert the improper fraction 73Into a mixed number (i.e., 2 13). Tell Group B to work together to convert the mixed number 2 13Into an improper fraction.
• Distribute chart paper to each group and have them draw visuals and show their work. Then, ask them to write out a step-by-step explanation of their process. Encourage them to use the sequencing words written on the board.
• Provide sentence frames or a paragraph frame to those students who may need additional support.
• Challenge students to make sure they can all explain their process for converting between an improper fraction and a mixed number. Tell students you will choose a number 1–4 and the student who has that number will explain the process aloud. The student presenters can use any notes the group created to solve the problem in their explanations.
• Choose a student from each group to present. If you're short on time, make sure an equal number between Group As and Group Bs have presented. (Tip: select groups with advanced ELs first so they can model the explanation process for the class first and the other students can refine their answers.)

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.
• Provide a paragraph frame for their assessment explanation:
• "First, I ____. Then, I __. Next, I ____. My answer is ____. I know this is correct because ____."
• Allow students to use the Fraction Equivalency Chart in their explanations and to check their conversions.
• Preteach lessons on improper fractions, mixed numbers, and fraction equivalency.

• Pair students with mixed-ability groups so they can offer explanations and provide feedback to beginning ELs when appropriate.
• Have students share their answers aloud first.
• Ask them to provide examples of transition words and sentence frames that they can use in their explanations.
(5 minutes)
• Write the mixed number 3 37And ask students to convert it to an improper fraction.Then, distribute lined paper and have them explain the process they followed to complete the problem of their choice.
• Have students refer to the board for sequencing sentence stems and their vocabulary cards for assistance with the key terms.
(5 minutes)
• Conduct a 3-2-1Activity. Ask students to label their lined paper from 3 to 1 and write about:
• ThreeKey vocabulary terms they need to explain how to convert between improper fractions and mixed numbers,
• TwoSequencing terms they used in their explanations,
• OneQuestion they still have about improper fractions or mixed numbers.
• Choose volunteers to share their question and ask other students to answer the questions. Correct misconceptions as necessary.