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Math Book A PDF

305 Pages·2011·14.58 MB·English
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M a t h i n Math in Focus™: Singapore Math by Marshall Cavendish F Courses 1–3 for grades 6 – 8 is a math program from Singapore o c created for U.S. classrooms, aligned with Common Core State u s Standards. Marshall Cavendish math programs have contributed to ™ : Singapore’s consistent top performance in international studies S i n since 1995. g a p o In the Student Book r e M • Learn introduces concepts through modeling in an engaging a and easy to understand format. t h b • Guided Practice allows the teacher to work through y exercises with students and assess understanding. M a • Practice provides independent opportunities for reinforcing rs h and enhancing concepts. a l l • Hands-On and Technology Activities reinforce ideas, C a concepts, and problem-solving strategies through interactive v e learning. n d i • Math Journal opportunities are found within the Practice to s h reflect, explain, construct arguments, and justify reasoning. • Brain @ Work provides opportunities at the end of each chapter for concept application and critical thinking. • Chapter Wrap Up provides a visual content map for each chapter. Connections between the key concepts are illustrated. • Chapter Review/Test offers cumulative practice on the concepts and skills instructed in each chapter in preparation for the assessment. 1453793 1453793-1A (M)MIF6A_SE_Cvr.indd 1 3/11/11 1:17 PM THIS BOOK IS THE PROPERTY OF: STATE Book No. PROVINCE Enter information COUNTY in spaces PARISH to the left as SCHOOL DISTRICT OTHER instructed. CONDITION ISSUED TO Year Used ISSUED RETURNED PUPILS to whom this textbook is issued must not write on any page or mark any part of it in any way, consumable textbooks excepted. 1. Teachers should see that the pupil’s name is clearly written in ink in the spaces above in every book issued. 2. The following terms should be used in recording the condition of the book: New; Good; Fair; Poor; Bad. Uniform label.indd 1 8/20/08 9:26:07 AM © 2012 Marshall Cavendish International (Singapore) Private Limited Published by Marshall Cavendish Education An imprint of Marshall Cavendish International (Singapore) Private Limited Times Centre, 1 New Industrial Road, Singapore 536196 Customer Service Hotline: (65) 6411 0820 E-mail: [email protected] Website: www.marshallcavendish.com/education Distributed by Houghton Mifflin Harcourt 222 Berkeley Street Boston, MA 02116 Tel: 617-351-5000 Website: www.hmheducation.com/mathinfocus First published 2012 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of Marshall Cavendish Education. If you have received these materials as examination copies free of charge, Marshall Cavendish retains title to the materials and they may not be resold. Resale of examination copies is strictly prohibited. Marshall Cavendish and Math in Focus™ are trademarks of Times Publishing Limited. Math in FocusTM Course 1 Student Book A ISBN 978-0-547-55936-0 Printed in United States of America 1 2 3 4 5 6 7 8 1401 17 16 15 14 13 12 11 4500291302 A B C D E (M)MIF6A_SE_copyright.indd 1 3/11/11 1:19 PM Course 1A Contents CHAPTER Positive Numbers 1 and the Number Line Chapter Opener How has the number system changed? . . . . . . . . . . . . . . . . . . . . . . 2 Big Idea Whole numbers, fractions, and decimals are numbers that can be represented in several ways . Recall Prior Knowledge • Finding factors of a whole number • Finding multiples of a whole number • Identifying prime numbers • Using order of 3 operations to simplify a numerical expression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 The Number Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Learn • Represent numbers on a number line • Write statements of inequality comparing two whole numbers using the symbols > and < • Represent fractions, mixed numbers, and decimals on a horizontal number line • Represent fractions, mixed numbers and decimals on a vertical number line • Write statements of inequality for two fractions or two decimals using the symbols > and < • Compare numbers in different forms In Student Book A and Student Book B, look for Practice and Problem Solving Assessment Opportunities • Practice in every lesson • Quick Check at the beginning of every • Real-world and mathematical problems in chapter to assess chapter readiness every chapter • Guided Practice after every Learn to assess readiness to continue lesson • in every chapter • Chapter Review/Test in every chapter to • exercises review or test chapter material • Cumulative Reviews four times during the year iii 1.2 Prime Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Learn • Identify composite numbers • Write a composite number as a product of its prime factors 1.3 Common Factors and Multiples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Learn • Identify the common factors of two whole numbers • Find the greatest common factor of two whole numbers • Use the greatest common factor with the distributive property • Find the common multiples of two numbers • Find the least common multiple of two whole numbers Hands-On Activity Find the Common Factors and the Greatest Common Factor of Two Numbers 1.4 Squares and Square Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Learn • Find a square of a whole number • Find a square root of a perfect square 1.5 Cubes and Cube Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Learn • Find a cube of a whole number • Find a cube root of a perfect cube • Evaluate numerical expressions that contain exponents Brain @ Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Chapter Wrap Up • Concept Map • Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Chapter Review/Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 iv CHAPTER Negative Numbers 2 and the Number Line Chapter Opener How cold is an iceberg? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Big Idea Negative numbers are the opposites of positive numbers. For every positive number, there is a corresponding negative number . Recall Prior Knowledge • Representing positive numbers on a number line • Writing statements of inequality for two given positive numbers using the 43 symbols > and < . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Negative Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Learn • Recognize the use of positive and negative numbers in real-world situations • Represent negative numbers on a number line • Write statements of inequality using the symbols > and < • Interpret and explain statements of order for positive and negative numbers in real-world situations Hands-On Activity Represent Negative Numbers on a Number Line and Compare Two Negative Numbers Using > and < 2.2 Absolute Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Learn • Write the absolute value of a number • Use absolute value to interpret real-world situations Brain @ Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Chapter Wrap Up • Concept Map • Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Chapter Review/Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 v CHAPTER Multiplying and Dividing 3 Fractions and Decimals Chapter Opener How much do you know about the construction of your home? . . . . 62 Big Idea Whole number concepts can be extended to fractions and decimals when more precise calculations are needed . Recall Prior Knowledge • Adding and subtracting decimals • Expressing improper fractions as mixed numbers • Expressing mixed numbers as improper 63 fractions • Multiplying fractions by fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Dividing Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Learn • Divide a whole number by a unit fraction • Dividing a whole number by a proper fraction • Divide a fraction by a fraction • Divide a fraction by an improper fraction or a mixed number Hands-On Activities • Dividing Whole Numbers by a Fraction • Dividing Fractions • Dividing Fractions with a Remainder • Division Involving Whole Numbers and Fractions 3.2 Multiplying Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Learn • Multiply tenths by a whole number • Multiply hundredths by a whole number • Multiply tenths by tenths • Multiply decimals by decimals with one decimal place • Multiply decimals with one or more decimal places Hands-On Activity Finding the Factors of a Decimal vi 3.3 Dividing Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Learn • Divide a whole number by a decimal with one decimal place • Divide a whole number by hundredths • Divide tenths by tenths • Divide hundredths by hundredths • Divide hundredths by tenths 3.4 Real-World Problems: Fractions and Decimals . . . . . . . . . . . . . . . . . . . . 94 Learn • Multiply decimals to solve real-world problems • Divide decimals to solve real-world problems • Divide a whole number by a fraction to solve two-step problems • Divide a whole number by a fraction to solve multi-step problems • Decide whether to round up or down to solve real-world problems • Divide a fraction by a whole number to solve real-world problems • Divide a fraction by a fraction to solve real-world problems Brain @ Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Chapter Wrap Up • Concept Map • Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 108 Chapter Review/Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Cumulative Review Chapters 1 – 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 vii CHAPTER 4 Ratio Chapter Opener How can math help you cook? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Big Idea You can use a ratio to compare two quantities, and you can use ratios to solve problems . Recall Prior Knowledge • Expressing fractions as equivalent fractions by multiplication • Expressing fractions as equivalent fractions by division • Writing equivalent fractions • Writing fractions in simplest form • Converting measurements given in one unit of measure to another • Interpreting a comparison bar model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 4.1 Comparing Two Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 Learn • Understand the meaning of ratio • Use a part-part or a part-whole model to show ratios • Write and interpret ratios as fractions • Use ratios to find how many times one number or quantity is as great as another 4.2 Equivalent Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Learn • Equivalent ratios show the same comparisons of numbers and quantities • Use the greatest common factor to write ratios in simplest form • Equivalent ratios have the same ratio in simplest form • Find equivalent ratios by multiplication • Find equivalent ratios by division • Find the missing term of a pair of equivalent ratios • Work with tables of ratios 4.3 Real-World Problems: Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 Learn • Draw models to solve problems involving ratios • Draw models to solve problems involving ratios of three quantities • Draw models to solve problems involving two sets of ratios • Draw models to solve before-and-after problems Brain @ Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 Chapter Wrap Up • Concept Map • Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Chapter Review/Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 viii CHAPTER 5 Rates Chapter Opener Who is the better goal scorer? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 Big Idea You can use a rate to compare one quantity to another quantity, and use rates to solve problems . Recall Prior Knowledge • Multiplying whole numbers • Multiplying fractions or mixed numbers by a whole number • Multiplying fractions • Dividing with fractions and whole numbers • Dividing fractions • Finding the quantity 155 represented by a number of units • Finding ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Rates and Unit Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Learn • Meaning of rates • Express and compute unit rates in terms of time and other quantities • Find a unit rate • Find and compare unit rates • Find the speed or rate of travel of a moving object 5.2 Real-World Problems: Rates and Unit Rates . . . . . . . . . . . . . . . . . . . . . . 168 Learn • Solve simple word problems involving rates and unit rates • Read a table to find the information to solve multi-step rate problems • Solve multi- step word problems involving comparison of unit rates • Find the distance given the speed and time • Find the time given the distance and speed • Find average speed to solve real-world problems Brain @ Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 Chapter Wrap Up • Concept Map • Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Chapter Review/Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 ix

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