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Serving Lemonade: Dividing a Whole Number by a Decimal In this lesson, students explore contexts and models for dividing a decimal by a whole number.NC Mathematics Standard(s):NC.5.NBT.7Compute and solve real-world problems with multi-digit whole numbers and decimal numbers.Add and subtract decimals to thousandths using models, drawings or strategies based on place value. Multiply decimals with a product to thousandths using models, drawings, or strategies based on place value. Divide a whole number by a decimal and divide a decimal by a whole number, using repeated subtraction or area models. Decimals should be limited to hundredths. Use estimation strategies to assess reasonableness of answers. Standards for Mathematical Practice:Make sense of problems and persevere in solving them.4. Model with mathematics.7. Look for and make use of structure.Student Outcomes: I can represent and solve problems involving dividing whole number by a decimal. Math Language:What words or phrases do I expect students to talk about during this lesson? Story context, whole number, decimal, equal groups, quotient, represent Materials: Base ten blocksPlay moneyDecimal gridsDividing a Whole Number by a Decimal sheetAdvance Preparation: Copy student sheetsLaunch:Review structure of a division situation (5 minutes)Say: There are 24 students the math club. The club is going to separate into teams with 4 members on each team? How many teams will the club have? How can we represent this with an expression? (24 ÷ 4) What does the 24 represent? What does the 4 represent? What is the quotient? What does the quotient represent? What makes this a division situation? (Students should understand that a total quantity is being separated into same-size groups. Note that some division situations involve separating total quantities into a given number of equal groups. If a student mentions that here, acknowledge it, but emphasize division as subtracting out same-size groups because it will support students in thinking about division of decimals in this lesson.)2. Introduce the following problem (5 minutes): The host at a cookout has 2 Liters of lemonade. He is serving lemonade in glasses that hold 0.08 Liters. How many glasses of lemonade can he serve? Use a visual image to represent this situation. Make sure students understand the problem by discussing questions such as the following:What does the host at the cookout want to do?What is the total amount of lemonade? What are some tools that could be used to represent the total lemonade? (decimal grids, base ten blocks, number line, money) How much lemonade is the host putting in each glass? How could we show the glasses in the visual image? (labels such as A, B, C…; different colors; a circle or box to represent each group)Explore:3. Representing and solving a division of a decimal by a whole number (15 minutes) Students work in small groups or with a partner to represent and solve the problem. As students work pose questions such as these:What is the total amount of lemonade? How does your representation show the total lemonade?How much lemonade is the host putting in each glass? How does your representation show each glass?How many glasses are there? How does your representation show the length of each piece?How could you represent this problem with an equation?Carefully select students to present to the class. Look for students who modeled the problem and kept track of their thinking. Also look for strategies that will generate discussion to help others move toward a deeper understanding of the mathematical goal.Some possible representations: Discuss:How Did You Represent the Problem? (10 minutes)Bring the group back together and have selected students share their strategies for solving the task. In addition to questions asked during the explore part of the lesson, ask the following questions:Possible points to address and questions to ask:Which part of the representation shows the total lemonade that the host has? Which part of the representation shows each glass of lemonade? (And/or ask about specific parts of the representation: What does the letters/numbers represent? What does this grid represent?)How does this representation show the action of division? (Extend if needed: How do you see the lemonade being separated into glasses with 0.04 in each glass?) How are these two representations the same? How are they different?Additional Activities: Extending Practice with Division of Decimals (20-25 minutes)A. Present the following problem in context: Leona ran 4 miles on a track that is 0.5 miles long. How many laps did Leona run on the track? Use a visual representation model this situation. Represent this situation with an equation.B. Write a story to match the expression: 3 ÷ 0.15C. Complete division of decimals problems using decimals grids.Evaluation of Student UnderstandingInformal Evaluation: Observe students as they work. Are students able to represent problems with a visual representation? Do representations model the action of division? Are students able to identify what each part of the model represents? Are students able to identify the quotient? Are students able to create a context that matches a division expression?Formal Evaluation/Exit Ticket:Dividing a Whole Number by a Decimal Meeting the Needs of the Range of LearnersIntervention:Use base ten blocks (flat represents one whole) to represent quantities such as 0.24. Have students separate blocks into groups with 0.02, 0.03, 0.04, 0.06, 0.08, or 0.12. Have students practice until they are confidently separating into groups that are the same size. Then work with students on transferring their thinking with the base ten blocks to decimal grids. Continue to use contexts to help students make sense of division of decimals. Extension: Between how many people can $3 be shared equally? Use visual models to show all of the ways that $3 can be shared equally. How do you know that you have identified all of the ways? Explain your thinking. Possible Misconceptions/Suggestions:Possible MisconceptionsSuggestionsStudents may confuse tenths and hundredths.Have students represent 1 tenth and 1 hundredth on a decimal grid. Repeat with other quantities such as .4 and 0.04.Students may struggle with the ideas that the quotient can be larger than the dividend or divisor.Use a story context to help students visualize what is happening in the problem. Ask students about what each of the numbers represents. Students need to see that the quantities refer to two different things. For example, in the lemonade problem (2 ÷ 0.08 = 25), the two refers to whole liters of lemonade, whereas the 25 refers to groups of 0.08 Liters of lemonade. In other words, when there are 2 Liters of lemonade, there are 25 glasses of 0.08 lemonade.Possible Solutions: Possible strategies for Part A of the student sheet:Leona ran 4 miles on a track that is 0.5 miles long. How many laps did Leona run on the track? Use a visual representation model this situation. Represent this situation with an equation.Serving Lemonade: Diving a Whole Number by a DecimalA. Leona ran 4 miles on a track that is 0.5 miles long. How many laps did Leona run on the track? Use a visual representation to model this situation. Represent this situation with an equation.B. Write a story to match the expression: 3 ÷ 0.15C. Complete division of decimals problems using decimals grids.172212063500001. 3 ÷ 0.5 = ____ 2. 3 ÷ 0.12 = ____3.?Logan has 1 liter of orange juice. If he puts 0.1 Liters of juice in each cup, how many cups of juice can he make??Equation: ___________________________293497015875000????4. 2.?A litter of puppies weighed a total of 4 kilograms. Each puppy weighed 0.4 kilogram. How many puppies were in the litter??Equation: ___________________________3009900117475002044709334500?Serving Lemonade: Diving a Whole Number by a Decimal Exit Ticket1.?Rasheem is creating a banner that is 3 meters long. He is putting a football sticker every 0.06 meters on the edge of the banner. How many football stickers will he need??418455324716005503545889000 28498813683000Equation: ____________________??????2.?Write a story problem to match 2 ÷ 0.25. Use the grids below to solve the problem. Story:?18288063500000 ................
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