G6 m2-a-lesson 4-t

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G6 m2-a-lesson 4-t

  1. 1. Lesson 4 NYS COMMON CORE MATHEMATICS CURRICULUM 6•2 Lesson 4: Interpreting and Computing Division of a Fraction by a Fraction—More Models Student Outcomes  Students use visual models such as fraction bars and area models to dividefractions by fractions with different denominators.  Students make connections between visual models and multiplication of fractions. Classwork Opening Exercise (2 minutes) Begin class with a review of equivalent fractions. Ask each student for a new example of an equivalent fraction. Students need to share how they know that the new fraction is equivalent to the old fraction. Opening Exercise Write at least three equivalent fractions for each fraction below. Be sure to show how the two fractions are related. a. Sample solutions include b. Sample solutions include Example 1 (3 minutes) For the first example, students will be asked to solve a word problem using the skills they used in Lesson 3 to divide fractions with the same denominator.  Molly purchased cups of strawberries. This can also be represented as . She eats cups in a serving. How many servings did Molly purchase? MP. 1  This question is really asking me how many are in two eighths. I can use a model to show that there are Lesson 4: Date: ©2013CommonCore,Inc. Some rights reserved.commoncore.org or, in other words, to divide eleven eighths by servings in the cups of strawberries. Interpreting and Computing Division of a Fraction by a Fraction— More Models 12/5/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 36
  2. 2. Lesson 4 NYS COMMON CORE MATHEMATICS CURRICULUM 6•2 Example 1 Molly purchased cups of strawberries. She eats in a serving. How many servings did Molly purchase? Use a model to prove your answer. MP. 1 Example 2 (3 minutes)  Now imagine that Molly’s friend Xavier purchased cups of strawberries and that he eats cup servings. How many servings has he purchased?  He has purchased servings or and servings. (This would be answered last after a brief discussion using the questions that follow.)  What is this question asking us to do?   How does the problem differ from the first example?   I am being asked to divide cups into cup servings. The denominators are different. What are some possible ways that we could divide these two fractions?  I could change to . These fractions are equivalent. I scaled up from by multiplying the top and bottom by . Lesson 4: Date: ©2013CommonCore,Inc. Some rights reserved.commoncore.org Interpreting and Computing Division of a Fraction by a Fraction— More Models 12/5/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 37
  3. 3. Lesson 4 NYS COMMON CORE MATHEMATICS CURRICULUM 6•2 Example 2 Now imagine that Molly’s friend Xavier purchased cups of strawberries and that he eats cup servings. How many servings has he purchased? Use a model to prove your answer. There are 1 and servings. Example 3 (3 minutes) MP. 1   What is this question asking us to do?  of what is or how many are in . Lead students through a brief discussion about this example:  Is your answer larger or smaller than one? Why?   Why is this question more difficult to model than the questions in Lesson 3?   Since is less than , we will have an answer that is larger than . The fractionsdo not have common denominators. How can we rewrite this question to make it easier to model?  We can create equivalent fractions with like denominators and then model and divide.  We can also think of this as r nine twelfths divided by eight twelfths. units ÷ units = or units. Lesson 4: Date: ©2013CommonCore,Inc. Some rights reserved.commoncore.org Interpreting and Computing Division of a Fraction by a Fraction— More Models 12/5/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 38
  4. 4. Lesson 4 NYS COMMON CORE MATHEMATICS CURRICULUM 6•2 Example 3 Find the quotient: .Use a model to show your answer. MP. 1 Exercises 1–5 (20 minutes) Students will work in pairs or alone to solve more questions about division of fractions with unlike denominators. Exercises 1–5 A model should be included in your solution. 1. We could rewrite this problem to ask . 0 Lesson 4: Date: ©2013CommonCore,Inc. Some rights reserved.commoncore.org Interpreting and Computing Division of a Fraction by a Fraction— More Models 12/5/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 39
  5. 5. Lesson 4 NYS COMMON CORE MATHEMATICS CURRICULUM 6•2 2. We could rewrite this problem to ask = or . 3. We could rewrite this as or . 4. This can be rewritten as Lesson 4: Date: ©2013CommonCore,Inc. Some rights reserved.commoncore.org . Interpreting and Computing Division of a Fraction by a Fraction— More Models 12/5/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 40
  6. 6. Lesson 4 NYS COMMON CORE MATHEMATICS CURRICULUM 6•2 5. We can rewrite this as fifteen twelfths four twelfths . Closing (10 minutes)  When dividing fractions, is it possible to get a whole number quotient?  When dividing fractions, is it possible to get an answer that is larger than the dividend?  When you are asked to divide two fractions with different denominators, what is one possible way to solve? Exit Ticket (5 minutes) Lesson 4: Date: ©2013CommonCore,Inc. Some rights reserved.commoncore.org Interpreting and Computing Division of a Fraction by a Fraction— More Models 12/5/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 41
  7. 7. Lesson 4 NYS COMMON CORE MATHEMATICS CURRICULUM Name ___________________________________________________ 6•2 Date____________________ Lesson 4: Interpreting and Computing Division of a Fraction by a Fraction—More Models Exit Ticket Draw a model to support your answer to the division questions. 1. 2. Lesson 4: Date: ©2013CommonCore,Inc. Some rights reserved.commoncore.org Interpreting and Computing Division of a Fraction by a Fraction— More Models 12/5/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 42
  8. 8. Lesson 4 NYS COMMON CORE MATHEMATICS CURRICULUM 6•2 Exit Ticket Sample Solutions Draw a model to support your answer to the division questions. 1. This can be rewritten as eighteen eighths divided by three eighths . 2. This can be rewritten as So this is equal to nine fifteenths divided by ten fifteenths or units ÷ units. . units 0 units Lesson 4: Date: ©2013CommonCore,Inc. Some rights reserved.commoncore.org Interpreting and Computing Division of a Fraction by a Fraction— More Models 12/5/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 43
  9. 9. Lesson 4 NYS COMMON CORE MATHEMATICS CURRICULUM 6•2 Problem Set Sample Solutions The following problems can be used as extra practice or a homework assignment. 1. Eight ninths ÷four ninths = . 2. Nine tenths ÷ fourtenths . 3. nine fifteenths ÷ five fifteenths . 4. Lesson 4: Date: ©2013CommonCore,Inc. Some rights reserved.commoncore.org Interpreting and Computing Division of a Fraction by a Fraction— More Models 12/5/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 44
  10. 10. Lesson 4 NYS COMMON CORE MATHEMATICS CURRICULUM fifteen twentieths ÷ four twentieths = Lesson 4: Date: ©2013CommonCore,Inc. Some rights reserved.commoncore.org 6•2 . Interpreting and Computing Division of a Fraction by a Fraction— More Models 12/5/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 45

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