ISBN Copyright 2015 The Continental Press, Inc.

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1 TABLE OF CONTENTS Introduction 3 Format of Books Suggestions for Use Annotated Answer Key and Extension Activities 9 Reproducible Tool Set 183 ISBN Copyright 01 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.

$equivalent fractions 1 Introduction Review the difference between rational and irrational, as well as the subcategories of rational : counting, whole, and integers.$

2 Understanding Rational and Irrational Numbers PAGES AND Objective To differentiate between rational and irrational and terminating and repeating decimals, and to write repeating decimals as equivalent fractions 1 Introduction Review the difference between rational and irrational, as well as the subcategories of rational : counting, whole, and integers. Discuss terminating and repeating decimals. Then work through the sample item to convert a repeating decimal to a fraction. Think About It Students should recognize that they use counting and whole most in everyday life. They should recognize that irrational will likely be used more in science and geometry. irrational rational integers whole counting rational PA Core Standard CC..1.8.E.1 Distinguish between rational and irrational using their properties. Eligible Content Determine whether a number is rational or irrational. For rational, show that the decimal expansion terminates or repeats (limit repeating decimals to thousandths). M08.A-N.1.1. Convert a terminating or repeating decimal to a rational number (limit repeating decimals to thousandths). The Continental Press, Inc. DUPLICATING THIS MATERIAL IS ILLEGAL. UNIT 9

3 LESSON UNDERSTANDING RATIONAL AND IRRATIONAL NUMBERS PAGES 6 AND Focused Instruction First, students will use a Venn diagram to organize and understand the categories of real. Next, students will change a repeating decimal into an equivalent fraction. Students must understand the difference between changing a terminating decimal into a fraction and changing a repeating decimal. They will work through a series of questions and use their knowledge of decimal place value. Conclude the Focused Instruction section by having students solving two problems involving converting decimals to fractions. whole, including 0, and their opposites a positive number without a fractional or decimal part whole, but without n n. 0. 9n n 9 Vocabulary irrational number: a real number that cannot be written in fraction form; a decimal that is non-terminating and non-repeating rational number: any number that can be written as a fraction, including whole, integers, fractions, and some decimals real : the set of rational and irrational repeating decimal: a decimal in which digits repeat in a pattern terminating decimal: a decimal whose digits end no 9 Connections to Standards for Mathematical Practice Make sense of problems and persevere in solving them. Attend to precision. Look for and make use of structure. UNIT The Continental Press, Inc. DUPLICATING THIS MATERIAL IS ILLEGAL.

4 PAGES 8 AND 9 LESSON Understanding RATIONAL AND IRRATIONAL repeat terminate DOK DOK M08.A-N 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. Independent Practice Answer Rationales 1 The, 16, and 6 represent terminating 1 decimals because their decimals end: 0.8, , and The fractions 11 and are equivalent to repeating decimals 1 because one or more digits continue forever: and Integers include negative, so not all integers are whole. The first statement is false. The second statement is true. Real are composed of all rational and all irrational. The third statement is false because non-terminating, non-repeating decimals are not rational. The fourth statement is true. The number 0 can be written as a fraction 0, so it is a 0 rational number. 3 Let n There are three repeating decimals places, so raise 10 to a power of 3: 10 3, or 1,000. Write the equation relating the difference between 1,000n and n and the decimals they represent: 1,000n n Combine like terms and solve for n: 999n 639; 639 n. Simplify by dividing the numerator and the denominator by 9: Extension Activity Make a number chart based off the Venn diagram in the Focused Instruction section. Work as a class to come up with examples of each type of number and post the chart in the classroom for future reference. The Continental Press, Inc. DUPLICATING THIS MATERIAL IS ILLEGAL. UNIT 31

5 LESSON UNDERSTANDING RATIONAL AND IRRATIONAL NUMBERS PAGE 0 Choices C and D are correct; and 0.00 are both irrational because they do not end and they do not repeat. The remaining choices are rational because they represent either terminating or repeating decimals. Choice A is a repeating decimal. Choice B is the ratio of two integers. Choice E is a terminating decimal. Choice F is the ratio of two integers. To change to a decimal, divide the numerator by the denominator. Continue dividing until the digits end or begin to repeat: DOK DOK So is equivalent to the decimal 0. 18, choice D. 6 The first, second, and fourth are rational. The first number,, is the ratio of two integers. 88 The second number, 3.01, is a repeating decimal. The fourth number, , is a repeating decimal. The third and fifth are irrational because the decimals do not end and do not repeat. The student should write out more decimal places to see that the repeating decimal is larger: UNIT The Continental Press, Inc. DUPLICATING THIS MATERIAL IS ILLEGAL.

ISBN Copyright 2015 The Continental Press, Inc.

ISBN Copyright 2015 The Continental Press, Inc. TABLE OF CONTENTS Introduction 3 Format of Books 4 Suggestions for Use 7 Annotated Answer Key and Extension Activities 9 Reproducible Tool Set 175 ISBN 978-0-8454-7911-7 Copyright 2015 The Continental