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Multiplying Fractions: Cassandra’s Master MixIn this lesson students consider how multiplying a number by a fraction less than one, equivalent to one, and greater than one impact the product. NC Mathematics Standard(s):Measurement and DataNC.5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction, including mixed numbers. ? Use area and length models to multiply two fractions, with the denominators 2, 3, 4. ? Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number and when multiplying a given number by a fraction less than 1 results in a product smaller than the given number. ? Solve one-step word problems involving multiplication of fractions using models to develop the algorithm.Standards for Mathematical Practice:2. Reason abstractly and quantitatively.Students are given the context involving making a recipe multiple times. Students decontextualize as they consider what happens to the product when the quantity of the fraction is less than one, equivalent to 1, and greater than 1. Students are also encouraged to reason quantitatively about how they could determine if the product will be less than, equal to, or greater than the whole number by which it is multiplied. 3. Construct viable arguments and critique the reasoning of others.Students calculate how much of each item will be needed if the recipe will be made five times and make an argument concerning how the original quantity needed changes when the recipe must be made 5 times. 7. Look for and make sense of structure.Students look for and make sense of patterns in how the product is impacted based on the fraction or mixed number it is being multiplied by. Student Outcomes: I can explain why the product of a whole number is more or less than the number that I am multiplying by.Math Language:What words or phrases do I expect students to talk about during this lesson? Multiplication, equivalent, greater than, less thanMaterials: Cassandra’s Master Mix TaskFraction bars or circlesGraph paperBlank paperAdvance Preparation: Print student copies of task (see below).Provide availability to fractions manipulatives, graph paper, and blank paper.Launch:Introduce Cassandra’s Master Mix Task (5-10 minutes): Give students a few moments to read the task below. This lesson builds on students understanding of comparing fractions to one whole and multiplying fractions. Cassandra is quite famous for her master snack mix at the lunch table. She has figured out the perfect blend for a snack mix. Each week Cassandra makes the recipe, and sometimes she shares with her friends. They love it too! Cassandra decided to surprise her four friends by making the recipe for each of them as well as herself. Cassandra checked the cabinet and found that she had 5 cups available for each of the ingredients. Which ingredients will Cassandra need to buy more of before making the recipe for herself and her four friends? Cassandra’s Master Snack Mix 34 cups pretzel sticks 112cups apple flavored oat cereal 32 cups of peanuts 13 cup chocolate candies 1 cup of raisins 213cups rice chex cerealDirections:Put all ingredients in a large bowl. Stir. Pose the following questions:What is Cassandra planning to do?What does she need to find out?What math tools might you use to help you think about the problem?Explore:Students collaborate with a partner to develop a strategy for figuring out which ingredients Cassandra will need to buy more of to make the recipe five times. (30 minutes) Pose questions similar to the ones above, and extend with these questions:How did you represent the amount of pretzels Cassandra will need?Are there any ingredients that you can tell whether or not Cassandra needs more without calculating the total needed? Explain your thinking.Do you notice any patterns that might help Cassandra figure out which ingredients she needs to buy?Which tools are you using to think about the task?Discuss:Which ingredients will Cassandra need to buy more of to make the recipe for her friends? How do you know? (20 minutes) Ask students how they could represent the amount needed for each ingredient with an equation. If students share repeated addition equations, ask if there is another equation that could be used to represent this situation. Ask students what they notice about all of the ingredients that Cassandra does not need to buy more of. Are there any ingredients that Cassandra has exactly enough of? What do you notice about that ingredient? Ask students what they notice about the ingredients that Cassandra will need to buy more of before making the recipe. What is true about those ingredients? Could we use this information to predict whether or not Cassandra would need more of each of the following ingredients if she also had 5 cups of them in her cabinet? How do you know? 44cups of cashews 134 cups of pistachios 12cup of chocolate morsels.Evaluation of Student UnderstandingInformal Evaluation: Use questions such as the ones suggested in the explore to informally evaluate student understanding of the following concepts:If you multiply a whole number times a fraction less than 1, the product will be less than the whole number.If you multiply a whole number times a fraction more than 1, the product will be more than the whole number.If you multiply a whole number times a fraction equivalent to 1, the product will be equal to the whole number.Formal Evaluation/Exit Ticket: 45720106680020000Cassandra’s Master Mix Exit Ticket Name: ______________Cassandra also has a famous recipe for strawberry citrus lemonade. She is planning to make her lemonade recipe for her four friends and herself. Which ingredients will she need more than 5 cups of to make the recipe. Can you tell without finding the exact amount needed? Explain how you know. Cassandra’s Strawberry Citrus Lemonade 23 cups fresh lemon juice 54 cups of orange juice 12 cup grapefruit juice 1 cup of strawberries 314cups waterDirections:Add all ingredients to blender. Blend in several 4-5 second rounds. Meeting the Needs of the Range of LearnersIntervention:Students may benefit from visually seeing five wholes compared to five sets of ? and five sets a 1 ? to make sense of why the fraction’s relationship to 1 whole can be used to determine if the product will be more or less than the whole number. Extension: Possible Misconceptions/Suggestions:Possible MisconceptionsSuggestionsStudents may think that the only way to know if the product will be greater than the whole number or not is to actually multiply. Special Notes: NonePossible Solutions: Name: ______________________Cassandra’s Master MixCassandra is quite famous for her master snack mix at the lunch table. She has figured out the perfect blend for a snack mix. Each week Cassandra makes the recipe, and sometimes she shares with her friends. They love it too! Cassandra decided to surprise her four friends by making the recipe for each of them as well as herself. Cassandra checked the cabinet and found that she had 5 cups available for each of the ingredients. Which ingredients will Cassandra need to buy more of before making the recipe for herself and her four friends? Cassandra’s Master Snack Mix 34 cups pretzel sticks 112cups apple flavored oat cereal 32 cups of peanuts 13 cup chocolate candies 1 cup of raisins 213cups rice chex cerealDirections:Put all ingredients in a large bowl. Stir.Cassandra’s Master Mix Exit Ticket Name: _________________________Cassandra also has a famous recipe for strawberry citrus lemonade. She is planning to make her lemonade recipe for her four friends and herself. Which ingredients will she need more than 5 cups of to make the recipe. Can you tell without finding the exact amount needed? Explain how you know. Cassandra’s Strawberry Citrus Lemonade 23 cups fresh lemon juice 54 cups of orange juice 12 cup grapefruit juice 1 cup of strawberries 314cups waterDirections:Add all ingredients to blender. Blend in several 4-5 second rounds. ................
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