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Number Talks with Mixed Numbers Addition

Students will practice mental math and harness their discussion skills through addition problems of like mixed numbers. This lesson may be used on its own or as support for the lesson Adding Mixed Numbers Using the Decomposition Strategy.
This lesson can be used as a pre-lesson for the Adding Mixed Numbers Using the Decomposition Strategy lesson plan.

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This lesson can be used as a pre-lesson for the Adding Mixed Numbers Using the Decomposition Strategy lesson plan.

Students will be able to solve addition problems with mixed numbers that have like denominators using the decomposition strategy.

Language

Students will be able to discuss and write out the strategy they used to add mixed numbers using target vocabulary with peer interaction as support.

(2 minutes)
• Tell students that today they will practice expressing their math thinking when it comes to adding mixed numbers with like denominators.
• Review the definitions of "mixed number" and "denominator" using students' home language (L1) and English (L2).
• Remind students that it is important for mathematicians like themselves to use key vocabulary to explain their reasoning and strategy for solving a problem. By communicating their ideas and strategies clearly, not only will their math skills improve, but their language skills will get better too.
(10 minutes)
• Model how to complete a Frayer Model for the word "strategy" on the document camera. Read aloud the definition, draw an image to represent the term, and write examples and non-examples.
• Place students into 7 groups. Assign each group one of the remaining vocabulary words. Hand out a Frayer Model to each student and instruct them to work as a team to become experts on the math term assigned to them. Encourage students to use models, symbols, pictures and words to complete their Frayer Model.
• Once students have collaborated and completed their own Frayer Model, have them decide on who will present their word.
• Call the representative from each word group up to the document camera to share the information on their assigned vocabulary term.
• Encourage students to ask questions to their peers about the word they are presenting.
(10 minutes)
• Display this problem and think aloud as you analyze it:
• In one week, the Pena family drank 2 1/4 gallons of orange juice and 1 1/4 gallons of apple juice. How much orange and apple juice did they drink that week?
• Say the following: "I notice that there are two mixed numbers in this problem. I can tell that I will need to add the two mixed numbers together because the questions asks for how much total orange and apple juice the family drank. I will write out the number sentence like this: 2 1/4 + 1 1/4 = ?. Now I must decide on a strategy to solve this addition problem mentally or in my head. I think I will add the whole numbers 2 and 1 first to make 3 wholes. Then I will add 1/4 and 1/4. Since they have the same denominator, I know that I only have to add the numerators together and I will get 2/4. I can simplify 2/4 to 1/2. The sum of 2 1/4 and 1 1/4 is 3 1/2. The Pena family drank 3 1/2 gallons of juice that week."
• Write or draw out your work on a piece of blank white paper. Keep your work organized and clearly demonstrate all the steps in your thinking process with words and pictures.
• Explain to students that you just solved a math problem by talking through it and using mental math. Tell students that only after you solved it in your head did you write and draw out the steps involved to explain your work.
• Tell students that knowing how to practice mental math and be able to talk through math problems and strategies is an important skill to master. Inform them that they will have the chance to practice solving a mixed number addition problem mentally before writing out the solution and sharing it with a partner.
• Display a problem for kids to solve mentally (e.g., "Ari ran 4 2/5 miles and Sam ran 5 1/5 miles today. What is the total distance these friends ran today?"). Display sentence stems to help students think through the problem:
• "I notice..."
• "I can tell that I will need to..."
• "I will use the strategy of..."
• "I know that..."
• Place students in effective partnerships and tell them to talk to their partner about the mental strategy they used to solve the problem. Students should also compare their answers to check if they are correct.
• Invite a few students to share the conversation they had with their partner as a whole group.
• As students share their strategies, create a chart paper with visuals and explanations of each person's strategies and thought processes. Label each strategy with the student's name and separate each solution strategy with a line to distinguish them from each other.
(10 minutes)
• Model how to compare the various strategies documented on the chart paper. (For example, Beth's strategy was to imagine the fraction models visually in her head and then add all the shaded in parts before checking her work by drawing the models she imagined. In comparison, Gavin's strategy was to count up by wholes first and then fractions.)
• Invite students to share their comparisons of the strategies written out on the chart paper.
• Distribute a sheet of plain white paper to each student and assign the following two problems for students to solve independently:
1. Dylan spent 1 1/2 hours on his science project on Monday and 3 1/2 hours on it on Tuesday. Find the total number of hours he spent on his science project in the two days.
2. My mom caught a fish that weighed 3 3/8 pounds and I caught a fish that weighed 2 2/8 pounds. What is the total weight of both fish?
• Remind students to solve the problems mentally and share their strategy with their partner before writing out in complete sentences the process they used.
• Tell students to fold their paper in half and write out the description of their solution to problem 1 on one half of the paper and the solution to problem 2 on the other half.
• Have students tape up their papers around the classroom once they are finished, and have them conduct a "gallery walk" around the room so they can read, compare, and contrast the various ways students solved the problems.
• Have them return to their seats before inviting small groups of students (3–4) to walk around the room while referring to their classmate's strategies and to verbally compare and contrast the work. Students are encouraged to notice any benefits or drawbacks of a particular strategy used.
• Display the following sentence frames and model a few to show students how to compare and contrast:
• "The strategy of ____ is useful because it ____."
• "This strategy is similar to that of ____ because they both __."
• "__'s strategy to solve the problem is ____ because ____."

Beginning

• Pair students with more advanced students or other ELs who speak the same home language (L1) for partner activities.
• Create and display a word/phrase bank with helpful terms from the lesson for students to refer to, with images if applicable.
• Provide students with vocabulary cards in English and students' home language (L1) if possible.
• Provide manipulatives such as fraction strips or linking cubes to help students solve the problems.

• Have students describe their math processes without relying on the sentence stems/frames.
• Encourage students to rephrase the directions and key learning points from the lesson.
• Tell students to create their own addition problems with mixed numbers to solve on their own.
(4 minutes)
• Ask students to verbally complete these sentence stems and share them with their partner:
• "Today I learned..."
• "The favorite strategy I observed in today's lesson was... I liked this strategy because..."
• "It is important to know multiple strategies to solve a problem because..."
• Invite a few students to share their partner's reflection.
(4 minutes)
• Write the mixed number 5 3/5 on the board and ask students to think of two mixed numbers that could be added to make the sum 5 3/5.
• Have students discuss briefly with a partner before sharing their responses with the whole class.
• Inform students that they have been working hard with addition of like mixed numbers and that they can even go backward and decompose or break apart a sum into two addends. They are truly skilled and flexible mathematicians!