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What’s in the PunchIn this lesson, students explore situations that involve dividing a unit fraction by a whole number.NC Mathematics Standard(s):Emphasized Standard: Apply and extend previous understandings of multiplication and division to multiply and divide fractions.NC.5.NF.7 Solve one-step word problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions using area and length models, and equations to represent the problem.Supporting Standard:NC.5.NF.3 Use fractions to model and solve division problems. Interpret a fraction as an equal sharing context, where a quantity is divided into equal parts. Model and interpret a fraction as the division of the numerator by the denominator. Solve one-step word problems involving division of whole numbers leading to answers in the form of fractions and mixed numbers, with denominators of 2, 3, 4, 5, 6, 8, 10, and 12, using area, length, and set models or equations.Emphasized Standards for Mathematical Practice2. Reason abstractly and quantitativelyAttend to precisionLook for make use of structureStudent Outcomes: I can explain the two problem types for division situationsI can interpret, represent, and solve division situationsI can use the relationship between multiplication and division to solve division problemsMath Language:What words or phrases do I expect students to talk about during this lesson? sharing, grouping, remainder, divisor, dividend, quotientMaterials: What Do You See imagesWhat’s in the Punch? Activity sheetMore Punch Problems activity sheetDice and number cards for additional activities (centers) Advance Preparation: Gather materials LaunchWhat Do You See? (8-10 minutes)Use the images on the What do you see? Activity sheet and display them one at a time.For each image ask students to work as individuals then in small groups to think about and discuss:What do you notice about the image?How many wholes are there? What is the size of each small region inside a whole?How many small regions are there?What multiplication equations could be used to describe the picture?What division equations could be used to describe the picture?Explore Exploring What’s in the Punch? (15 minutes) Distribute the What’s in the Punch? Activity sheet to students. Have students read OR read directions to students.Have students retell the task to each other and brainstorm ways to get started on the task. Have students share their ideas on how to get started with the class.Allow students to work on the task. As they are working here are possible questions to ask: ObservationPossible QuestionsStudents are unable to get started on the task.What is the task asking?What fraction do you see?How could you represent that fraction as a picture?Students do not partition correctly or in equal sections.How can you prove that you have made (halves, fourths, etc.)?Can you draw another rectangle and show me what (one-half, one-third, etc.) is?Students do not know what to do when considering the number of serving bowls.If we are sharing the punch between these (two) serving bowls how could we show that in our picture? Would our fraction be getting larger or smaller if I am sharing the amount in different serving bowls? Discuss:Discussing Strategies for What’s in the Punch (10 minutes) Facilitate a class discussion in which students share their strategies and talk about mathematics concepts embedded in the What’s in the Punch task. Feel free to use turn and talks, have students get up and move to find other classmates to make this discussion as active as possible. QuestionPossible Response(s)How did you get started on Bowl A?“I divided a rectangle into 2 equal parts to represent the 2 ingredients. Then since we were sharing the punch between 2 mixing bowls I divided each half into 2 equal pieces so I had 4 equal sections.” “I split it in half twice to get 4 equal pieces.” What was being divided or shared in Bowl A?“We were dividing an ingredient by 2.” “We were dividing half of a gallon of an ingredient into 2 different serving bowls.”What was an equation that we could write to represent Bowl A?“One-half divided into 2 parts.”“One-half split into 2 parts.”“One-half divided by 2.” Why is the equation for Bowl A ? divided by 2 and not 2 divided by ??“Our starting amount is ? of a gallon and we are putting that into 2 groups.”“We have ? of a gallon and know the number of groups which is 2 and we have to find the size of the group.” As the discussion wraps up if time permits give the following extension problem to check students’ understanding: A punch bowl has ? a gallon of orange sherbet and ? a gallon of Sprite. If the punch is put into 4 serving bowls how much orange sherbet is in one serving bowl?Additional Activities The following activities could be done as a whole group or as centers.More Punch Ingredients Activity Sheet Students complete the activity sheet. The teacher may want students to complete this in a teacher-facilitated small group. Practice Modeling Division ProblemsStudents roll two dice. The first dice represents the denominator in a unit fraction (e.g., a 3 means you would start with the fraction 1/3. The second dice represents the number of groups to share the fractional amount in (e.g., a 5 means you would be dividing 1/3 by 5). Students draw a picture and determine the answer. Multiplying FractionsStudents need 1 dice and a set of number cards. Students draw one number card to represent a whole number. Students make a fraction (1 in the numerator) and roll a dice to get the denominator for a fraction. For example, if the number card has a 6 and the dice has a 4 students would multiply 6 x ?. Evaluation of Student UnderstandingInformal Evaluation: Use the questions suggested above to assess student understanding as they interact with the problems and the models. Student responses on the activity sheets will allow for assessing understanding of the ideas in the lesson.Formal Evaluation/Exit Ticket: Students’ work from the Explore phase or Follow-up activities can be used as a formal evaluation. If you would like to pose an additional exit ticket consider posing: There are 4 cups of flour on the counter. I need ? a cup of flour to make a cake. How many cakes can I make with the flour that I have? Draw a picture, write an equation, and find the answer. Meeting the Needs of Different Learners Intervention: If students are struggling with the idea of dividing fractions, using manipulatives such as pattern blocks or graph paper may help. Extension: If students need an extension, use a mixed number for the starting amount.?Possible Misconceptions/Suggestions:ObservationPossible QuestionsStudents are unable to get started on the task.What is the task asking?What fraction do you see?How could you represent that fraction as a picture?Students do not partition correctly or in equal sections.How can you prove that you have made (halves, fourths, etc.)?Can you draw another rectangle and show me what (one-half, one-third, etc.) is?Students do not know what to do when considering the number of serving bowls.If we are sharing the punch between these (two) serving bowls how could we show that in our picture? Would our fraction be getting larger or smaller if I am sharing the amount in different serving bowls? ?Special Notes: The activity sheet can also be reused by changing the numbers. Solutions: What’s in the Punch?Bowl A: ? of each ingredient will be in 1 containerBowl B: Sundrop: 1/6; Cheerwine and Orange Juice: 1/12; Sherbe: 1/4Bowl C: Sprite and Cheerwine: 1/12; Sherbet: 1/6 More Punch ProblemsSherbet: 1/6; Sprite: 1/4 Sundrop: 1/12Ice cream: 1/6, Cheerwine: 1/12, Sundrop: 1/12Sprite: 1/8; Sundrop: 1/16What Do You See? Image A 37507377470Image B254024680319397142468031951566901700076199017000Image C3847253484721944159478375651546990What’s in the Punch?The following types of punch were made at the party. The punch is made in the mixing bowls but served in smaller containers. Mixing BowlIngredientsContainersA? Gallon Cheerwine? Gallon Rainbow Sherbet2B1/3 Gallon Sundrop1/6 Gallon Cheerwine1/6 Gallon Orange Juice1/2 Gallon Orange Sherbet2C? Gallon Sprite? Gallon Cheerwine 1/2 Gallon Raspberry Sherbet3Bowl A Draw a picture of the bowl and label the amount that is Cheerwine. Use your picture to determine how much of each ingredient is one container. Bowl B Draw a picture of the bowl and label the amount that is Cheerwine. Use your picture to determine how much of each ingredient is one container. Bowl C Draw a picture of the bowl and label the amount that is Cheerwine. Use your picture to determine how much of each ingredient is one container. More Punch ProblemsA punch bowl has 1/3 of a gallon of Rainbow sherbet, 1/2 of a gallon of Sprite, and 1/6 of a gallon of Sundrop. After the punch is split equally among two serving bowls how much of each ingredient is in one serving bowl. A punch bowl has ? of a gallon of vanilla ice cream, ? a gallon of Cheerwine, and ? of a gallon of Sundrop. After the punch is divided into three serving bowls how much of each ingredient is in one bowl. A punch bowl has raspberry sherbet, Sprite, and Sundrop. There is 1/4 of a gallon of sprite. There is 1/8 of a gallon more of Sprite than Sundrop. The rest is Raspberry Sherbet. If the punch is split into two serving bowls how much Sundrop and Sprite is in one serving bowl? Number Cards012012345345678678901901234234567567890890123123456456789789 ................
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