ISBN Copyright 2015 The Continental Press, Inc.

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1 TABLE OF CONTENTS Introduction Format of Books Suggestions for Use 7 Annotated Answer Key and Extension Activities 9 Reproducible Tool Set 8 ISBN Copyright 0 The Continental Press, Inc. Excepting the designated reproducible blackline masters, no part of this publication may be reproduced in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. All rights reserved. Printed in the United States of America.

2 Dividing Fractions PAGES 00 AND 0 Objective To divide with fractions Introduction Review how to find the reciprocal of a fraction (flip the numerator and the denominator) and how to multiply fractions (multiply the numerators, then multiply the denominators). Then explain to students that to divide fractions, multiply the dividend by the reciprocal of the divisor. Use the examples on the page to review how to change a mixed number to an improper fraction and how to cross out common factors when multiplying fractions. Think About It Students may relate a situation such as dividing a measurement of cups by because they only have a -cup measuring cup. Whatever situation they describe, they should show understanding of when division of fractions is needed. It divides 0 times and 6 times. 0 yes 6 Common Core State Standard 6.NS. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. no Vocabulary reciprocal: the number by which another number is multiplied to equal a product of The Continental Press, Inc. DUPLICATING THIS MATERIAL IS ILLEGAL. UNIT 9

3 LESSON Dividing FrACTIONS PAGES 0 AND 0 Focused Instruction First, students work through a division problem that presents the opportunity to cancel common factors, making it easier to perform the multiplication. Students should recognize that by canceling common factors, they simplify the computation process because they compute with smaller numbers and they do not have to simplify the answer. Next, students use a fraction model to help them divide. The fraction bar represents whole, so first students divide it in half. Then they divide each half into parts to represent the friends. Since there are a total of 0 parts in the pound and each friend gets, each friend gets of a pound. This is the same 0 result as using division. Conclude the Focused Instruction section by having students solve two division problems. Guided Practice Students should complete the Guided Practice section on their own. Offer assistance as needed, pointing out the reminder and hint boxes along the right side of the page. 8 When I cancel common factors, I do not have to put the answer in lowest terms. It is already in lowest terms. Also, it lets me work with smaller numbers that are easier to multiply Connections to Standards for Mathematical Practice Make sense of problems and persevere in solving them. Model with mathematics. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. The model shows that there are sections in all, which is represented in the solution to the equation. 60 UNIT The Continental Press, Inc. DUPLICATING THIS MATERIAL IS ILLEGAL.

4 PAGE 0 LESSON Dividing FrACTIONS 0 6 Yes, Manuel did order enough, because NS. DOK 6.NS. 6 Independent Practice Answer Rationales To find the answer, divide 8 by : Choice C is correct. Choice A results when 8 is multiplied by. Choice B results when the dividend and the divisor are combined as a mixed number. Choice D results when the quotient is incorrectly simplified. A The number line should be divided into 6 sections to represent the 6 sandwiches. Each section should be divided into thirds, because each of a sandwich is serving. B The equation should show the total sandwiches divided by amount of serving: 6. C Calculate the total number of people Manuel can feed and compare it with the people coming to the party: Since the sandwiches will feed 8 people and there are 6 people coming, each person will be able to have at least one serving. Extension Activity Divide the class into four or five groups. Give each group a container with a fractional amount of a snack (e.g., pound of pretzels, cups of raisins, etc.). The groups must first divide to find how much each person will get. Then they will use measuring cups or scales to divide the amount evenly and check their answer. The Continental Press, Inc. DUPLICATING THIS MATERIAL IS ILLEGAL. UNIT 6

5 LESSON Dividing FrACTIONS PAGES 0 AND 06 A Area of a rectangle equals length times width, so dividing the area by the width will give the length. To change each mixed number to an improper fraction, multiply the whole number and the denominator, then add the numerator. The denominator stays the same:,0 9,0 9,7 ; The equation to find the width is 9,7 9. B Find the reciprocal of the divisor and then multiply: 9,7 9, The width is 0 feet. The fraction model shows. To find the quotient, multiply by the reciprocal of. The whole number is written as a fraction by giving it a denominator of. Multiply and cancel common factors: 6. Divide the perimeter of the square by : So each side of the square is 0 feet long. 6 Speed is found by dividing distance by time (speed d t ): 0 99, miles per hour. 6 7 The first statement is true, because the reciprocal of a whole number is over the whole number. The second statement is false, because the reciprocal of is. The third statement is false. The quotient of is, not. The fourth statement is false. The quotient of 8 is 8 9, not. 8 To find the size of each piece of land, divide by :. Choice B is correct. Choice 9 A is the result of dividing by, not. Choices C and D do not make sense since they show numbers larger than the initial piece of land. 0 d s t 0 s 0 99, ,7 9 h 9,7 9 9, s 0 8 s DOK 6.NS. 6.NS. 6.NS. 6.NS. 6.NS. 6.NS. 6 UNIT The Continental Press, Inc. DUPLICATING THIS MATERIAL IS ILLEGAL.