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Math in focus a, Singapore Math by Marshall Cavendish, Math in focus a, Singapore Math by Marshall Cavendish, Math in focus a, Singapore Math by Marshall Cavendish, Math in focus a, Singapore Math by Marshall Cavendish
!:1 I I I inga by re ath· Marshall Cavendish © 2013 Marshall Cavendish International (Singapore) Private Limited © 2014 Marshall Cavendish Education Pte Ltd Published by Marshall Cavendish Education Times Centre, New Industrial Road, Singapore 536196 Customer Service Hotline: (65) 6213 9444 US Office Tel: (1-914) 332 8888 I Fax: (1-914) 332 8882 E-mail: tmesales@mceducation.com Website: www.mceducation.com Distributed by Houghton Mifflin Harcourt 222 Berkeley Street Boston, MA 02116 Tel: 617-351-5000 Website: www.hmheducation.com/mathinfocus Cover: © Stephane Marechal/Photolibrary First published 2013 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 registered trademarks of Times Publishing Limited Singapore Math0 is a trademark of Singapore Math Inc and Marshall Cavendish Education Pte Ltd Math in Focus° Course Student Book A ISBN 978-0-547-55936-0 Printed in United States of America 13 14 15 4500703012 1401 20 19 18 BCD E CHAPTER Positive umbers ~ the mber Line Chap'il:eir Opell'lleli' How has the number system changed? Whole numbers, fractions, and decimals are numbers that can be represented in several ways ~li"fl@tl'fif.il'li@Wlle~qaie ° Finding factors of a whole number multiples of a whole number O Identifying prime numbers ~~11:©i~~ O ° Finding Using order of operations to simplify a numerical expression The INh.amlber lune 1.1 Represent numbers on a number line O Write statements of inequality comparing two whole numbers using the symbols > and < Represent fractions, mixed numbers, and decimals on a horizontal number line line O O Represent fractions, mixed numbers, and decimals on a vertical number 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 in every lesson Real-world and mathematical problems in every chapter o at the beginning of every chapter to assess chapter readiness assess readiness to continue lesson in every chapter e o Ma.:thJournal exercises Guided Practice after every Learn to Chapter Review/Test in every chapter to review or test chapter material :-;:.2,1ieHs four times during the year 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 .· 19 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 whole 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 Squares and Square Roots Learn • Find a square of a whole number ° Find a square root of a perfect 29 square Cubes and Cube Roots learn • Find a cube of a whole number • Find a cube root of a perfect cube 33 Evaluate numerical expressions that contain exponents 38 Ch@pterr Wli:'@p l!Jlp • Concept Map • Key Concepts 39 Chapierr Re'7iew/Tesi 40 CHAPTER u mber Ch@ptefi' Operrner How cold is an iceberg? 42 Negative numbers are the opposites of positive numbers For every positive number, there is a corresponding negative number 0 Representing positive numbers on a number line Writing statements of inequality for two given positive numbers using the symbols > and < 43 2.1 45 Negative Numbers situations Recognize the use of positive and negative numbers in real-world Represent negative numbers on a number line of inequality using the symbols > and < 0 Write statements 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 ·::2,;·: Write the absolute value of a number 54 Use absolute value to interpret real-world situations 58 ° Concept Map ° Key Concepts 59 CHAPTER ltiplyi Ch@pter Opell'ileli" How much you know about the construction of your home? 62 Whole number concepts can be extended to fractions and decimals when more precise calculations are needed ~ei!:©lU~ !Pirn@r Il\.rril@wied~e e Adding and subtracting decimals e Expressing improper fractions as mixed numbers e Expressing mixed numbers as improper fractions e Multiplying fractions by fractions 63 Dividing Fractions 65 3.1 Divide a whole number by a unit fraction e Divide a whole number by a proper fraction e Divide a fraction by a fraction e Divide a fraction by an improper fraction or a mixed number e Hands-On Activities Dividing Whole Numbers by a Fraction e Dividing Fractions e Dividing Fractions with a Remainder e Division Involving Whole Numbers and Fractions 3.2 e Multiplying Decimals Learn e Multiply tenths by a whole number e Multiply hundredths by a whole number e Multiply tenths by tenths e Multiply decimals by decimals with one decimal place e Multiply decimals with one or more decimal places Hands-On Activity Finding the Factors of a Decimal 78 3.3 Dividing Decimals 87 Divide a whole number by a decimal with one decimal place e Divide a whole number by hundredths O Divide tenths by tenths O Divide hundredths by hundredths O Divide hundredths by tenths :,ei'arT •.4 O Real-World !Problems: Fractions and Decimals 94 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 O problems Decide whether to round up or down to solve real-world problems e Divide a fraction by a whole number to solve real-world problems e Divide a fraction by a fraction to solve real-world problems O 107 e Concept Map e Key Concepts 108 CHAPTER Chapter Opener How can math help you cook? 114 You can use a ratio to compare two quantities, and you can use ratios to solve problems llte«:11:d; !Pwn@w ll{ll'il@\/'Jledge 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 .4.1 Comparing Two Ga.mntities i"earn ° Understand the meaning of ratio Use a part-part or a part-whole 115 118 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 RealaWorldl Problems: Ratios Learn ° Draw models to solve problems involving ratios • Draw models to 140 solve problems involving ratios of three quantities O Draw models to solve problems involving two sets of ratios • Draw models to solve before-and-after problems 150 ° Concept Map • Key Concepts 151 Ch c or x < c to represent a constraint or condition in a realworld or mathematical problem Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams SE: Course B: 2, 22-28, 31-34 Represent and analyze quantitative relationships between dependent and independent variables 6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation SE: Course B: 13-21, 62-65 Solve real-world and mathematical problems involving area, surface area, and volume 6.G.1 290 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems Common Core State Standards Correlations SE: Course 1B: 72, 75-87, 88-98, 99-103, 104-113 l : STANDARDS CITATIONS 6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism Apply the formulas V = fwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems SE: Course 1B: 168, 189-199, 200-208 6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate Apply these techniques in the context of solving real-world and mathematical problems SE: Course B: 42-49, 50-61, 66, 86, 98 6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures Apply these techniques in the context of solving real-world and mathematical problems SE:Course 1B: 168, 172-180, 181-188, 200-208 Develop understanding of statistical variability 6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers SE: Course 1B: 214, 217-218, 228-230 6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape SE: Course 1B: 214, 217-221, 223-225, 231-233, 244-248, 251, 253-255, 258, 260-261, 264-271 6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number SE: Course B: 242, 243, 244, 246-248, 251, 253-255, 258, 260-261, 264-270 Summarize and describe distributions 6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots SE: Course 1B: 215-216, 222-227, 228-237, 246, 253-254, 258, 266-268 6.SP.5 Summarize numerical data sets in relation to their context, such as by: SE: Course 18: 217-221, 223-225, 231-233, 244-250, 251-257, 258-263, 264-270 6.SP.5a Reporting the number of observations SE: Course 1B: 217-221, 248,255,261 6.SP.5b Describing the nature of the attribute under investigation, including how it was measured and its units of measurement SE: Course 1B: 217-221, 248,261 Common Core State Standards Correlations 291 STANDARDS CITATIONS 6.SP.5c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered SE: Course 1B: 223-225, 231-233, 244-250, 251-257, 258-263, 264-270 6.SP.Sd Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered SE: Course 1B: 254-255, 264-270 Math in Focus®, Course aligns to the Common Core State Standards for Mathematical Practice throughout CITATIONS How Math in Focus® Aligns: For example: Problem Solving is at the heart of the Math in Focus® curriculum Students use problem solving to build skills and solve routine and non-routine problems that include real-world and mathematical applications in proportionality, number sense, algebra, measurement, and data analysis SE: Course 1A: 58, 94-107, 118-126, 140-150, 159-167, 168-178, 198-203, 204-214, 246-252 SE: Course 18: 29-34, 62-66, 143-158, 200-208, 264-271 Students persevere in real-world problem solving through consistent prob/em-solving tools such as bar modeling For example: SE: Course 1A: 66, 68, 70, 72, 73, 88, 93, 97-98, 101-102, 117, 121-123, 142-147, 159-160, 164-165, 168-169, 193-198, 204-211, 219, 221-223, 229-231, 239-240, 246-250 SE: Course B: 13-14, 29-30 How Math in Focus® Aligns: For example: Math in Focus®'s concrete to pictorial to abstract progression helps students develop a deep mastery of concepts Students analyze and solve non-routine problems, formulate conjectures through explorations, hands-on activities, and observations, identify and explain mathematical situations and relationships, and relate symbols such as negative numbers and variables to real-world situations SE: Course 1A: 15, 18, 22, 29-31, 32, 33-35, 37,38,50,53,57,58,67, 70, 75,86, 107,126, 149, 150, 166, 167, 178, 188, 189, 192,197,213, 214,232,238,245,252 SE: Course B: 24, 34, 47, 66, 76- 78, 113, 124-126,131,158-159, 173,175,178,195, 208,219,224,237,248,250,255,261,268,271 292 Common Core State Standards Correlations How Math in Focus® Aligns: For example: In Math in Focus®, students communicate in Math Journals and demonstrate and explain mathematical steps using a variety of appropriate materials, models, properties, and skills They share and critique mathematical ideas with others during class in 5-minute Warm-Up and Hands-On and group activities, Guided Practice Exercises, Ticket Out the Door exercises, Projects, and other Differentiated Instruction activities SE: Course 1A: 5-11, 15,16118, 20-23, 26, 29, 31, 33, 35, 38, 45-48, 50, 53, 54, 56, 57-58, 65, 67, 70, 72, 75, 77, 78,80-86,87,90,93,94, 107, 118,126,127,140,149,159,166, 168-178, 185, 188-189, 192, 193, 198-203, 204,213,221, 223, 226, 229, 234-235, 238, 239-241, 245, 246,252 SE: Course 1B: 5-10, 12, 13, 22-28, 31, 34, 42-44,47,50,62,66, 75-81,88,89,92,94,99, 104,105,107,112,122, 124-128, 129-131, 136-139, 143-144, 146, 147, 149-151, 158, 172,173,178,181,186,189,190, 192-193, 195, 200-201,203-20~208,217,219,222-22~ 228,237,244,248,250,251,255,258,261,264, 267-268, 271 How Math in Focus® Aligns: For example: In Math in Focus®, students and teachers represent mathematical ideas, model and record quantities using multiple representations, such as concrete materials, manipulatives, number lines, bar models, drawings, tables, coordinate graphs, symbols, algebraic expressions, equations, inequalities, and formulas SE: Course 1A: 5-15, 23, 24, 34, 47-49, 55, 66, 68, 70-73, 77, 81, 83, 85, 88, 93, 97-99, 101, 102, 117, 121-123, 140, 143-147, 159-160, 164-165, 168-169, 172, 175-176, 178, 185, 193-198, 202, 204-211, 219, 221-223, 227, 229-232, 239-240, 246-250, 256 SE: Course 1B: 5-10, 13-18, 22-30, 31, 47, 62-64, 75-76, 86, 88, 91, 94, 98124, 131, 136-137, 146-147 181-186, 189-195, 200-206, 215-216, 219, 222-225, 248,261 How Math in Focus® Aligns: Math in Focus® helps students explore the different mathematical tools that are available to them, such as pencil and paper, concrete and visual models such as number lines and grids, or technology to model developing skills and interpret everyday situations that involve ratios, rates, percents, measurement, geometric formulas, and data collection and distribution For example: SE: Course 1A: 5-15, 16-19, 21, 50, 67, 70, 72, 85,124,140,142,144,146,185, 193-198, 204-211, 232 SE: Course 1B: 5-10, 22-28, 31, 45, 47, 50-57, 62-64, 75-78,86,88,91,98, 131,219,195, 215-216, 222-225, 248,261 Common Core State Standards Correlations 293 How Math in Focus® Aligns: For example: In Math in Focus®, students check answers, define, highlight, review, and use mathematical vocabulary, define and interpret symbols, label bar and geometric models correctly, and compute with appropriate formulas and units in solving problems and explaining reasoning SE: Course 1A: 5-8, 10, 17, 30, 39, il-4, 45, 47, 54, 59, 65-66, 68, 70-73, 76, 88-89, 94, 97, 99, 101,108, 116-120, 124-125, 129, 142-147, 151, 157-160, 168-178, 179,185, 198-211, 215, 221-223, 226, 229-231, 233-234, 239-240, 246-250, 253 SE: Course B: 3, 13-14, 29-30, 35, 42, 54, 67, 75, 78-81, 89, 92, 94, 105, 107, 114, 122, 126-127, 129-130, 137-139, 143-144, 146-147, 149-151, 160, 172, 190, 192-193, 200-201, 203-204, 209,218, 229-231, 238, 244 How Math in Focus® Aligns: For example: The inherent pedagogy of Math in Focus® allows students to look for and make use of structure Students recognize patterns and structure and make connections from one mathematical idea to another through, Best Practices, Big Ideas, Math Notes, and Cautions Also occurs as skills and concepts are interconnected in prior knowledge activities, concept traces, and chapter concept maps SE: Course 1A: 2-4,7, 16-17, 20, 22-23, 31, 35,36,39,42,46,51,59,62-64, 71, 78-79,90 97, 99,101,108,114, 115-117, 119, 122-123, 132, 143-147, 151, 154-158, 157, 172, 179, 182-187, 215, 218-220, 234-235, 242-243, 253 SE: Course 1B: 2-4, 13, 35, 38-40, 43, 45, 50-57, 62-63, 67, 72-74, 86, 98,114, 118-121, 125-127, 160, 168-171, 209, 214-216, 222-223, 238, 242-243, 251,258, 266-268, 272 How Math in Focus® Aligns: For example: In Math in Focus®, students are given consistent tools for solving problems, such as bar models, standard algorithms with fractions and decimals, numerical and geometric properties, and formulas so they see the similarities in how different problems are solved and understand efficient means for solving SE: Course 1A: 16-17, 20, 22-23, 25, 31, 35, 63, 66, 68, 70, 72-73, 78, 82-84, 87-104, 117, 121-123, 143-147, 155, 159-160, 164-165, 168-178, 193-198, 204-211, 219, 221-223, 229-231, 234-235, 239-240, 246-250 SE: Course 1B: 13-14, 29-30, 54, 78-81, 89, 92, 94,105,107, 119-120, 127, 129-130, 137-139, 143-144, 146- 147, 149-151, 190, 192-193, 200-201, 203-204, 243 294 Common Core State Standards Correlations BLANK