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Math in focus b Singapore Math by Marshall Cavendish, Math in focus b Singapore Math by Marshall Cavendish, Math in focus b Singapore Math by Marshall Cavendish, Math in focus b Singapore Math by Marshall Cavendish, Math in focus b Singapore Math by Marshall Cavendish, Math in focus b Singapore Math by Marshall Cavendish,
~ / ~ ;' / ~ Si ga by re t · Marshall Cavendish © 2012 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 Moth in Focus' are registered trademarks of Times Publishing Limited Singapore Math€• is a trademark of Singapore Math lnc and Marshall Cavendish Education Pte Ltd Math in Focus·, Course Student Book B ISBN 978-0-547-56012-0 Printed in United States of America 13 14 15 4500703012 1401 20 19 18 BCDE CHAPTER Ch@!P)'il:e1r OpetrDell" Going on a vacation? Equations and inequalities can be used to describe situations and solve real-world problems e write algebraic expressions O Comparing numbers with symbols Evaluating algebraic expressions O O Using variables to Plotting points in a coordinate plane 8.1 Solving Algebraic Equations Use substitution to solve simple algebraic equations e Solve algebraic equations involving addition or subtraction ° Solve algebraic equations involving multiplication or division e Solve algebraic equations involving fractions In Student Book A and Student Book B, look for e Practice in every lesson Real-world and mathematical problems in every chapter e e chapter to assess chapter readiness o in every chapter Ma.:t:/-vJourn.td exercises Guided Practice after every Learn to assess readiness to continue lesson ° Chapter Review/Test in every chapter to review or test chapter material ° Cm uiative Reviews four times during the year 8.2 Writing Linear Equations 13 Learn • Write a linear equation to represent a given situation • Use tables and graphs to represent linear equations Solving Simple Inequalities :_ Learn ° Determine solutions of inequalities of the form x > c and x < c 22 Determine solutions of inequalities of the form x ~ c and x::;; c Hands-On Activity Writing Inequalities 8.4 Real-World Problems: Equations and Inequalities :.,,earn Write algebraic equations to solve real-world problems 29 Write algebraic inequalities to solve real-world problems 34 Key Concepts 35 Ch@pter Revuew /il'est 36 • Concept Map ° CHAPTER The ,,Jj El !fgffl ChE:!lp1i:ef1' Opell'llefl' Have you ever used a street directory? 38 Every point on the coordinate plane can be represented by a pair of coordinates Identifying and plotting coordinates negative numbers on the number line O Representing O Recognizing and writing the absolute value of a number ° Finding the perimeter of a polygon 39 9.1 42 Points cm the Coordinate Plane · cc, · ° Find the coordinates of points on a coordinate plane Draw and identify polygons on a coordinate plane Hands-On Activity Identifying Quadrilaterals Drawn on a Coordinate Plane 9.2 !Length of !Line Segments 50 ° Find the lengths of line segments on the x-axis and y-axis ° Find lengths of line segments parallel to the x-axis and y-axis Plot points on a coordinate plane for a real-world problem and solve it 9.3 Real-World Problems: Graphing i.,,ea;·~~£ 62 Graph an equation on a coordinate plane 66 ° Concept Map ° Key Concepts 67 C!hi@p'iteir iewiew!Test 68 CHAPTER Chapter Opener Have you ever made a quilt? 72 The area of a polygon can be found by dividing it into smaller shapes, and then adding the areas of those shapes Reitali! IF»rri@rr !K!rft@'l?JSed(gle e Finding the area of a rectangle using a formula ° Finding the area of a square using a formula O Identifying parallelograms, trapezoids, and rhombuses 73 10.1 75 Arrea of Triangles Learn • Derive the formula for the area of a triangle e Find the area of a triangle ° Find the height of a triangle given its area and base e Find the base of a triangle given its area and height Hands-On Activity Prove the Formula for Finding the Area of a Triangle 10.2 Area of Parallelograms and Trapezoids Learn e Derive the formula for the area of a parallelogram ° Find the area of a parallelogram O Derive the formula for the area of a trapezoid ° Find the area of a trapezoid O 88 Apply the formula for the area of a trapezoid 10.3 Area of Other Polygons team ° Find the areas of regular polygons 99 10.4 Area of Composite Figures 104 Recognize that a plane figure can be divided into other polygons Solve problems involving rectangles and triangles e Solve problems involving parallelograms, triangles, and rectangles e 113 ° Concept Map ° Key Concepts 114 Chapter Reviewfifes'll: 115 CHAPTER Chti:llpler Ope!i'iler Have you ever seen a rainbow? 118 A circle is a geometric figure that has many useful applications in the real world decimals c Dividing decimals Adding decimals a Subtracting decimals Multiplying Rounding numbers to the nearest whole number Rounding numbers to the nearest tenth 11.1 Rcu:llius, Diameter, and Circumference of a Cirde Identify the center and radius of a circle e a circle circle a Identify the circumference of a circle 119 122 Identify the diameter of ° Find the circumference of a Recognize that half of a circle is a semicircle and a quarter of a circle is a quadrant c Find the lengths of a semicircular arc and the arc of a quadrant Hands-On Activities Drawing Circles Using a Compass a Investigating the Relationship Between the Circumference and Diameter of a Circle Drawing Semicircles and Quadrants 11.2 Area of a Cirde e c Derive the formula for the area of a circle Find the area of a semicircle a Find the area of a circle 136 11.3 Real-World Problems: Cirdes 143 e Use the formula for circumference to solve real-world problems e Use the formula for area of a circle to solve real-world problems e Solve real-world problems involving rates and circles 158 e Concept Map e Key Concepts 160 METRIC CUSTOMARY Length N mile (mi) = 1,760 yards (yd) kilometer (km) = 1,000 meters (m) meter = 10 decimeters (dm) mile meter = 100 centimeters (cm) yard = feet meter = 1,000 millimeters (mm) yard = 36 inches (in.) 5,280 feet (ft) w c.n centimeter= 10 millimeters foot= 12 inches ~~~ liter (L) = 1,000 milliliters (ml) ~ gallon (gal) = quarts (qt) .J gallon = 16 cups (c) gallon = 128 fluid ounces (fl oz) quart = pints (pt) 0:, -0 quart = cups " pint = cups cup fluid ounces 0- " ,._ Mass and Weight kilogram (kg) 1,000 grams (g) gram = 1,000 milligrams (mg) ton (T) = 2,000 pounds (lb) pound 16 ounces (oz) TIME " tn- year (yr) = 365 days week = days " ~1 year 12 months (mo) year = 52 weeks (wk) leap year = 366 days day = 24 hours (h) hour 60 minutes (min) minute = 60 seconds (s) " .J_ " CO- .CONVERTING MEASUREMENTS You can use the information below to convert measurements from one unit to another - co To convert from a smaller unit to a larger unit, divide Example: 48 in = To convert from a larger unit to a smaller unit, multiply _J_ ft _J_ cm Example: 0.3 m = -r = ft 12 = Recall: 12 in 48-;- = 100 cm X 100 = 30 0.3 m = 30 cm Recall: m 0.3 48 in.= ft -0 - lf) PERIMETER, CIRCUMFERENCE, AND AREA Square Rectangle I I leogth (I) length (C) - Perimeter = 4£' Area = C2 (Y) Triangle Circle ow;dth(wl length (C) Perimeter = 2£' 2(C Area = Cw + 2w + w) Parallelogram /2< -,/'~height (h) )~) II base (b) Area - ~ s:: u f: base (b) , Area= bh - Circumference = nd 2nr Area = nr = Trapezoid base (b 1) ))IJ -N G radius(r) uhe;ght(h) base (b2 ) SURFACE AREAAND VOLUME Rectangular Prism Cube ·· height (h) Rledge(e) I ) ~dge(e) edge (e) "-✓ Y· width (w) length (C) N Surface Area = 6e2 Volume= e ' Surface Area = 2(Cw + wh + Ch) , Volume = Cwh = Bh* Prism w Pyramid bases height (h) U1 0- base Surface Area = Sum of the areas of the faces Surface Area = Sum of the areas of the faces = Perimeter of base x height+ Area of two bases Volume= Bh* Cylinder Volume = ~3 Bh* '° i Sphere Cone 0- I I radius (r) CXl ., .,._ radius (r) height (h) ., N- height (h) ., radius (r) Surface Area = 2rcr + 2:rcrh Volume = rcr h Surface Area = rcr(t + r), where C is the slant height Volume = rcr h W- Surface Area = 4:rcr Vo Iume = :rcr ., Ul- *B represents the area of the base of a solid figure ., CXl- N 0- PROBABILITY PYTHAGOREAN THEOREM Probability of an event, A happening Right Triangle - Number of favorable outcomes Number of equally likely outcomes I C Probability of an event not happening = - P(A) a - = P(A) co I'- LINEAR GRAPHS The slope, m, of a line segment joining points P (x1, y 1) and O (x2 , y ) is given by m= Y2-Y1 arm x2 x1 y,-Y2 x -x Given the slope, m, the equation of a line intercepting the y-axis at b is given by y = mx + b -l!) The distance, d, between two points P (x1, y 1) and O (x2 , y ) is given by d = ,/(x - x,}2 + (y - y ) or d = ,/(x - RATE Distance = Speed A - M verage spee Interest - x Time d _ Total distance traveled Total time = Principal x Rate x Time N TEMPERATURE Celsius ( C) Fahrenheit (°F) C = -95 x (F- 32) x2 ) + (y - y2) • SYMBOLS lal absolute value of the number a is greater than (x, y) ordered pair is less than or equal to 1:2 ratio of to < is less than > :5 no- = - ro :::J d" is greater than or equal to 2::: ~ · - - is not equal to -:j: I per % percent ~ · ~ ul - N = is approximately equal to J_ is perpendicular to - is congruent to II is parallel to is similar to AB line AB ten squared AB ray AB ten cubed AB line segment AB two to the sixth power LABC angle repeating decimal 2.66666 mLA measure of angle A - - - 10 10 2.6 w_ - Ul - ABC °''-l positive D.ABC triangle -7 negative degree Ja positive square root of the number a Va positive cube root of the number a 7f P(A) ABC pi; rr = 3.14 or rr = - 00 22 the probability of the event A happening -0 o-= N ~ Ul- ~ 00- N 0- Cover: © Stephane Marechal/Photolibrary Chapter 8: (c), © Image Source; (b), © Tetra Images/Getty Images; 6, © Annworthy/Dreamstime com; 8, © Kris Timken/Getty Images; 10, © Comstock Images/Getty Images; 14, © Image Source; 15, © Barbara Penoyar/Getty Images; 16, © Plush Studios/Bill Reitzel/Getty Images; 17, © Tetra Images/Getty Images; 18, © Image Source; 22, © Kris Timken/Getty Images; 25, © Annworthy/Dreamstime.com; 29, © Tetra Images/Getty Images; 30, © Plush Studios/Bill Reitzel/Getty Images; 34, © Marshall Cavendish International (S) Pte Ltd Chapter 9: 43, © Kris Timken/Getty Images; 45, © Image Source; 47, © Barbara Penoyar/Getty Images; 51, © Annworthy/ Dreamstime.com; 52, © Kris Timken/Getty Images; 53 (t), © Comstock Images/Getty Images; 53 (c), © Barbara Penoyar/Getty Images Chapter 10: 72, © Jim Jurica/iStockphoto; 73 (t), © Image Source; 73 (b), © lofoto/Dreamstime.com; 77, © Blend lmages/Alamy; 88, © Annworthy/ Dreamstime.com; 92, © Kris Timken/Getty Images; 94, © Comstock Images/Getty Images; 99, © Jose Luis Pelaez, Inc/Getty Images; 100, © Tetra Images/Getty Images; 105, © Blend Images/Ala my Chapter 11: 122, © Image Source; 123, © lofoto/Dreamstime.com; 124, © Marshall Cavendish International (S) Pte Ltd; 125, © Barbara Penoyar/Getty Images; 126, © Blend Images/Alamy; 127, © Marshall Cavendish International (S) Pte Ltd; 128 (c), © Comstock Images/Getty Images; 128 (b), © Kris Timken/ Getty Images; 134 © Yong Hian Lim/iStockphoto; 137 (t), © Comstock Images/Getty Images; 137 (b), © Tetra Images/Getty Images; 143, © Blend lmages/Alamy; 149, © Marshall Cavendish International (S) Pte Ltd; 153, © Tetra Images/Getty Images; 154, © Marshall Cavendish International (S) Pte Ltd; 155, © Marshall Cavendish International (S) Pte Ltd; 159, © Yong Hian Lim/iStockphoto Chapter 12: 172, © Image Source; 174 (t), ©Tetra Images/Getty Images; 174 (b), © Annworthy/Dreamstime.com; 177 (t), © Image Source; 177 (b), © Jose Luis Pelaez/Getty Images; 181, © Barbara Penoyar/Getty Images; 182 (t), © Jose Luis Pelaez/Getty Images; 182 (b), © lofoto/Dreamstime.com; 189, © Tetra Images/Getty Images; 191 (t), © Blend lmages/Alamy; 191 (b), © Image Source; 193, © Image Source; 201, © lofoto/Dreamstime.com; 203, © Annworthy/Dreamstime.com Chapter 13: 217, © Plush Studios/Bill Reitzel/Getty Images; 222, © Tetra Images/Getty Images; 230, © Flying Colours Ltd/Getty Images Chapter 14: 247, © Annworthy/Dreamstime.com; 248, © Marshall Cavendish International (S) Pte Ltd; 253, © Tetra Images/Getty Images; 254, © Blend lmages/Alamy; 258, © Image Source; 259, © Barbara Penoyar/Getty Images; 266, © Comstock Images/Getty Images; 267, © Flying Colours Ltd/ Getty Images Pages listed in black type refer to Book A Pages listed in blue type refer to Book B Pages in boldface type show where a term is introduced substituting into formulas, 78-81, 89, 92, 94, Absolute value, 54-56 recognizing and writing, 40 using, to find distances in the coordinate plane, 50-53 Activities, See Hands-On Activities Addition algebraic equations involving, 7-8 bar model for, 219 decimals, 119 expressions, 221 with decimals, 63 with like terms, 233 Algebra equation(s), 5-11 addition, 7-8 coordinate graphing and, 15-18, 62-64 dependent and independent variable, 13 division, 9-10 involving fractions, 11 multiplication, 9-10 Real-World Problems, 29-30 solution, substitution method to solving, 5-6 subtraction, 7-8 writing, 13-19 inequalities, 22 solutions of, 22-23, 25-26 Algebraic expression(s) arising from formulas, 78-81; 89, 92, 94, 105, 107, 127, 129-130, 137-139, 143-144, 146, 147, 149-151, 190, 192-193, 200-201, 203-204 bar models, 221-223, 226, 229-231, 233-234, 239-240, 246-250; 13-14, 29-30 coefficients and, 229 and distributive property, 239-240 equivalent, 233 evaluating, 226-227; expanding, 239-243 factoring, 242-243 involving addition and subtraction, 246; 7-8 involving fractions, 11 involving multiplication and division, 247-248; 9-10 simplifying, 229-236 solution, solving, 5-11 substitutes, 227 105,107,127, 129-130, 137-139, 143-144, 146,147, 149-151, 190, 192-193, 200-201, 203-204 terms of, 222 using variables to write, variables, 221-222 writing, 221-223, 226, 229-231, 233-234, 239-240,246-250 Approximation of circumference using pi, 127 Area, See also Surface area of circle, 136-140, 146-147 of composite figures, 104-108 of figures in the coordinate plane, 54, 73, 86, 98 of parallelograms, 74, 88-95 of polygon(s), 99-101 of rectangle, 54, 73, 75, 170 of semicircle, 139 of square, 27-29; 73 of trapezoids, 4, 88-95, 170 of triangle, 5-82, 170 Assessment Chapter Review/Test, 40-41, 60-61, 109-11 O, 152-153, 180-181, 216-217, 254-255; 36-37, 68-71, 115-117, 161-163, 210-213, 239-241, 273-274 Cumulative Review, 111-113, 256-259; 164-167, 275-279 Quick Check, 3-4, 44, 63-64, 115-117, 155-158, 183-184, 219-220; 3-4,39-41, 73-74, 119-121, 169-171, 216,243 Average speed, 175 Bar models, algebraic expressions and, 221-223, 226, 229-231, 233-234, 239-240, 246-250; 13-11, 29-30 before and after comparison models, 146-147, 204-211 comparison, 117,119,120,124,125, 143-147, 157, 159-160, 164-165, 168-169, 173, 204-211, 226; 13, 30 division, 66, 68, 70, 71, 73, 76, 88, 89, 95,219, 247-249 part-whole, 70, 72, 73, 88, 93, 97-98, 101, 102, 121-123, 193-198,219,221-223, 229-231, 233-234, 239-240,246-250; 14, 29 unitary method, 97,101,117, 143-147, 157 Base, 29, 193 of a prism, 192-193 of a trapezoid, 91 of a triangle, 76, 81-82 Big Idea, In every chapter Some examples are: 2, 182;39,242 Brain at Work, Throughout See for example, 38, 178,214,252; 34, 158-159, 271 unit rates, 161-162, 171 whole numbers, 6-7 Compass, drawing with a, 124 Composite figures, area of, 104-108 Composite number, 16 as product of prime factors, 16-17 Concept Maps, In every chapter Some examples are:39, 179,253; 35, 60,209,272 Concepts, See Big Idea; Key Concepts Cautions, Throughout See for example, 36, 119; 43, 251 Converting measurements, 116-117, 119-120, 129,142 Center of a circle, 122 Coordinate plane, 42 coordinates of the origin, 39 draw polygons on, 45, 47, 54, 73, 86, 98 finding area of figures on, 54, 73, 86, 98 graphing an equations on, 62-64 ordered pairs as coordinates, 4, 15-18, 39 plotting points on, 4, 54-55 points in, 42-47 quadrants, 42 reflections across the x-axis, 43-44 segment length in, 50-57 x-axis, 42 y-axis, 42 Chapter Introduction, In every chapter Some examples are: 2, 62, 218; 2, 118, 242 Chapter Review/Test, See Assessment Chapter Wrap Up See Review Circle(s} area of, 136-140, 146-147 center of, 122 circumference of, 124-125 finding, 127 diameter of, 123, 125 drawing with a compass, 124 radius of, 122 Real-World Problems, 143-153 Circumference, 124-125, 127 formula for, 143-144 Coefficient, 229 Commission, 201 Common factor, 19 greatest, 20 using, to factor algebraic expressions, 242-243 using, to simplify fractions, 64, 115-116, 155-156, 183-184 Coordinates, 42 identifying and plotting, 39 Cross section, 191 of prism, 191 Cube,33; 172 surface area of, 181 volume of, 33-55; 171 Cube root, 34 of perfect cube, 34-35 Cumulative Review, 111-113, 256-259; 164-167, 275-279 Common multiples, 24 least, 25-26 Communication, Math Journal, See Math Journal Commutative properties, 31, 35, 235 Comparison bar models, See Bar models circumference and diameter of a circle, 125-126 fractions and decimals, 7-14 measures of central tendency, 254-255 negative numbers, 50 numbers with symbols, quantities, 118-124 ratios, 118-119 Data, See also Equation(s}; Graphs choosing an appropriate display of, 229-231 collect and tabulate, 217-219 from a frequency table, 218 displaying and analyzing extremes, 224 outliers, 231 range, 224 using dot plot, 222-225 using histogram, 228-233 frequency tables, 218,219,225,261 identifying shape of, 223 interpreting from dot plot, 224 from histogram, 232 frequency tables, 218,219,225,261 in line plot, 215-216 representing numerical data using dot plot, 222-223 using histogram, 228 Pages listed in black type refer to Book A Pages listed in blue type refer to Book B Pages in boldface type show where a term is introduced Data set, finding average, 243 Decimal(s), 189-191 adding, 63; 119 comparing, using a number line, 7-10 dividing, 87-92, 95; 120, 243 expressing, percent as, 187 multiplying, 82-84, 94; 120 Real-World Problems, 94 104 subtracting, 119 visual models, 7-10, 43-44, 78-80, 85, 87-90 Denominators of fraction, 184 Dependent variable, 13 Diagonal of a rectangle, 75 Diameter of circle, 123 circumference and, 125 Discount, 208 Distributive property, 22-23 and expanding algebraic expressions, 239-240 Division algebraic equations involving, 9-1 bar models, See Bar models decimals, 87-92, 95; 120, 243 expressing fractions as equivalent fractions by, 115 finding equivalent ratios by, 132 fractions, 65-75, 101,103,156 mixed numbers, 74 75 simplifying fraction using, 183 with whole numbers, 156 Dot plot displaying and analyzing data using, 222-225 finding mean, using, 246 finding median, using, 253 interpreting data from, 224 representing numerical data using, 222-223 symmetrical or skewed, 223 Draw models to solve before-and-after problems, 146-147 to solve problems involving decimals, 85, 93 rates and unit rates, 168 ratios, 140-145 Equation(s), addition, 7-8 algebraic, 5-11 checking solutions, 7-10 dependent and independent variable, 13 division, 9-10 graphing, 62-63 linear, 13-19 multiplication, 9-10 on a balance scale, 5-10 solution, subtraction, 7-8 tables of value pairs, 15-18 writing, 13-19 Equivalent expressions, 233 Equivalent fractions expressing fractions as, 115 multiplication to find, 183 writing, 116 Equivalent ratios, 127-137 Expanding algebraic expressions, 239-243 Exponent(s), 29 evaluating expressions with, 35-36 Expressions, See Algebraic expression(s) Factor(s), 3, 16 greatest common, 20, 129 prime, 16 Factoring algebraic expressions, 242-243 Factor trees, 20, 25, 31, 35 Formula(s), 75-76 area of circle, 136-137, 146-·i 47 area of parallelogram, 88 area of rectangle, 54, 73, 75 area of square, 73 area of trapezoid, 88, 91, 94 area of triangle, 75, 81, 94 circumference of circle, 127, 143-144 distance, 172-175, 62-63 interest, 202 perimeter of a polygon, 41, 55 surface area of prisms, 181-186, 200-206 volume of non-rectangular prisms, 201 volume of prisms, 189-195 volume of rectangular prism, 171, 189-190 Fraction(s), 189-191 algebraic equations involving, 11 common factors and, 64 comparing, using a number line, 7-10 denominators of, 184 dividing, 65-75, 101, 103, 157 equivalent, 115-116 expressing, 115 as equivalent fractions, 115 percent as, 187, 191 improper, 74 mixed number, 74 multiplying, 155-156, 184 on a number line, 7-10, 43-44 percent and, 185-187 ratios as, 122-123 Real-World Problems, 94 104 in simplest form, 116 visual models, 7-10, 43-44, 65-73, 76, 103 whole number as, 96, 101 Horizontal number line representing fractions, mixed numbers and decimals on, 7-8, 43-44 representing negative numbers, 46-48, 50 Improper fraction(s), 7-10, and mixed numbers, 63-64 Independent variable, 13 Inequality (Inequalities), 6; 22 on a balance scale, 24 real-world constraints, 23-28, 31 Real-World Problems, 31 solutions of, 22-23, 25-26 solving, 22-26 statements of, 6-7, 10, 44; Interest, 202 Isosceles triangle, perimeter of, 41 Frequency, 218 Frequency tables, 218,219,225,261 Graphing in the coordinate plane, 42-47 geometric figures in, 45, 50-57, 73, 86, 98 linear relationships, 62-64 Graphs, to representing linear equations, 15-18 Greatest common factor (GCF), 20 with distributive property, 22-23 to write ratios, 129 Guided Practice, exercises, Throughout See for example, 7-8, 80-84, 173-174, 199-202; 6-8, 44, 127-128, 186, 223-225, 267-268 Key Concepts, 39, 59, 108,179,215,253; 35, 67, 114,160,209,238,272 Least common multiples, 25-26 Length of line segments, 50-57 Like terms adding, 233 subtracting, 234 Linear equation(s), 13 dependent and independent variables, 13 tables and graphs to representing, 15-18 writing, 13-19 Linear graph, 62-63 Line plot, 215-216 Hands-On Activities, Throughout See for example, 22, 189,241;76-78, 195,219,268 Line segments, length of, 50-57 Height of triangle, 76, 80 Histogram, 228 choosing appropriate intervals, 229-231 displaying and analyzing data, 228-233 interpreting data from, 232 representing numerical data using, 228 Manipulatives compass, 124, 131 connecting cubes, 195 drawing triangles, 131 fraction strips, 67, 70, 72 graph paper, 85; 47, 76, 86, 98 nets, 173, 175,178,261 number cards, 21, 50 number cubes, 225 protractor, 131 ruler, 85; 131,219,248,261 variable paper strips, 232 Pages listed in black type refer to Book A Pages listed in blue type refer to Book B Pages in boldface type show where a term is introduced Markup, 204 Math Journal, Throughout See for example, 18, 149, 245; 110,248,250 Math Notes, Throughout See for example, 16-17, 172,234-235; 7-10, 126-127,258 Mean, 244 comparing, 254-255 concept of, 244 finding, using dot plot, 246 finding total and missing number from, 247 Real-World Problems, 264-268 Measurements circumference of circle, 127 comparing, circumference and diameter of a circle, 125-126 converting, 116-117, 119-120, 129,142 protractor, 131 ruler, 131,219,248,261 Measures of central tendency, See also Mean; Median; Mode comparing, 254-255 Problem Solving, 273-274 related to skewed distribution, 266 related to symmetrical distribution, 267-268 Median, 251 comparing, 254-255 concept of, 251 finding, using dot plot, 253 Real-World Problems, 264-268 Missing number, finding, 247 Mixed number(s), 74 dividing, 74-75 and improper fractions, 63-64 multiplying, 155 on a number line, 7-10, 43-44 Mode, 258 concept of, 258 Real-World Problems, 264-268 summarizing data set, 260 Multiple(s), 24 least common, 25-26 of whole number, Multiplication algebraic equations involving, 9-10 bar model, 219 decimals, 94; 120 expressing fractions as equivalent fractions by, 115 to find equivalent fractions, 183 find equivalent ratios by, 131 of fractions, 155-156 fractions by whole numbers, 184 whole numbers and mixed numbers, 155 Negative numbers, 45-51 absolute value of, 54-56; 40 in the coordinate plane, 42-44 on a number line, 46-48, 50; 40 opposites, 47 Net, 172 of cube, 172 of rectangular prism, 173 of solids, 172-178 of square pyramid, 177 of triangular prism, 17 Non-rectangular prisms with missing dimensions, 203 surface area and volume of, 201 Number line, 5-13 to compare numbers, 5-10 horizontal, 7-8, 46 inequalities on, 25-26 representing data in dot and line plots, 215-216, 222-225 negative numbers, 46-48, 50; 40 positive numbers, 5-10, 43 solutions of inequalities on, 22-28, 31 the distance formula, 172, 175-176, 178 vertical, 9, 47-48 Numbers absolute value of, 54-55 factors, 3, 16, 20, 129, 220 negative, 45-51 positive, 45 prime or composite, 16-17 Numerical expression(s), 35 with exponents, 35-36 order of operations and, Opposite, 47 Order of operations and numerical expressions, exponents and, 35-36 simplifying algebraic expressions, 235 Ordered pairs, 4, 15-18, 39 Origin, 39, 42-43 Outliers, 231 Parallelograms area of, 4, 88-95 identifying, 74 perimeter, 41 Part-part model ratios, 121-123 Part-whole model bar models, See Bar models ratios, 121-123 Per, 159 Percent, 185-187, 189-191 of change, 204-211 discount, 208 markup, 204 expressing decimal as, 190 fraction as, 189 mixed number as, 189 finding fraction by multiplying, 190 quantity represented by, 193 to solve problem, 204, 206, 208-210 fraction and, 185-187 meaning of, 185 of a quantity, 193-195 Real-World Problems, 198-202 commission, 201 interest, 202 sales tax, 199 visual models, 185, 193-198, 204-211 Periectcube,33-35 Periect square, 29-31 Pi(rr), 125-126 Polygon(s) area of, 99-101 in coordinate plane, 45, 47, 54, 98 perimeter of, 45 Positive number, 5, 43 Practice Guided Practice, Throughout See for example, 7-8, 173-174, 207-211;6-8, 138-140, 267-268 Practice exercises, In every lesson See for example, 14-15, 18, 27-28, 32, 37-38; 12, 20-21,27-28, 33-34 Prerequisite Skills Quick Check, See Assessment Recall Prior Knowledge, In every chapter Some examples are: 3, 115-117, 219-220; 3-4, 119-121, 215-216 Prime factorization, 16-17 and finding roots, 35 Prime factors, 16 Prime number(s), 16 See a/so Prime factorization identifying, Prism cross section of, 191 identifying, 169 with missing dimensions, 202 non-rectangular, suriace area and volume of, 201 rectangular net of, 173 suriace area of, 182 volume of, 171, 189-190, 200 triangular net of, 174 suriace area of, 184 volume of, 189-195 Problem Solving, Throughout See for example, 41, 180-181; 240-241 algebraic equations, 29-30, 37 algebraic expressions, 246-250 Brain at Work, In every chapter Some examples are: 38, 178, 214, 252; 34, 113, 158-159 circumference and area of circle, 162-163 graphing, 70-71 inequalities, 31, 37 measures of central tendency, 273-27 parallelograms, 107 percent, 198-202, 204-211 rates and unit rates, 168-17 ratio, 152-153 Real-World Problems, In most lessons Some examples are: 94-104, 246-250; 29-32, 264-268 rectangles, 105, 107 suriace area and volume, 211-213 triangles, 105, 107 Proper fraction, dividing whole number by, 68 Pyramid net of square, 177 suriace area of, 185 Pages listed in black type refer to Book A Pages listed in blue type refer to Book B Pages in boldface type show where a term is introduced Quadrants, 42, 128 drawing, 131 lengths of semicircular arc and arc of, 129 Quantities absolute value of real-world, 55-56 compare two, in a ratio relationship, 118-124 opposite direction or values, 45-46, 50-51 percent of, 193-197 Quick Check, See Assessment Reciprocals, 65 Rectangle, area of, 54, 73, 170 diagonal of, 75 perimeter, 55 Rectangular prism net of, 173 surface area of, 182 volume of, 171, 189-190, 200 Reflections across the axes on a coordinate plane, 43-44 Regular polygon, 99-100 Radius, 122 of circle, 122 Range of data, 224 Rate(s), 159 problem solving, 168-176 Real-World Problems, 149-151 unit, See Unit rates Ratio(s), 118 compare, two quantities, 118-124 draw models, 140-147 equivalent, 127-137 finding, 124, 158 as fractions, 122-124 greatest common factor to write, 129 meaning of, 118-120 part-part and part-whole models, 121-123 Real-World Problems, 140-147 in simplest form, 129, 130 tables of, 134-137; 15-18 terms of, 118 Real-World Problems circles, 143-153 fractions and decimals, 94-104 graphing, 62-64 mean, median, and mode, 264-268 percent, 198-202 commission, 201 interest, 202 sales tax, 199 plotting points on coordinate plane for, 54-55 rates, 168-176; 149-151 ratios, 140-147 surface area and volume, 200-206 unit rates, 168-176 writing and solving algebraic equations for, 29-30 writing and solving inequalities for, 31 Recall Prior Knowledge, See Prerequisite Skills Review Chapter Review/Test, See Assessment Chapter Wrap Up, 39, 59, 108, 151, 179, 215, 253;35, 67,114,160,209,238,272 Cumulative Reviews, See Assessment Rhombuses identifying, perimeter of, 41, 45 Rounding tenth, 121 whole numbers, 121 Sales tax, 199 Semicircle, 128 area of, 139 drawing, 131 Simplest form fractions in, 116 ratios in, 129, 130 Skewed distribution, related measures of central tendency to, 266 Solid(s) net of, 172-178 surface area of, 181-186 Solution of equations, 5-6 of inequalities, 22-23, 25-26 Speed,163 average, 175 finding, 163-164 Square area of, 27-29; 73 of a number, 29 Square pyramid, net of, 177 Square root, 30 of perfect square, 30-31 Statements, inequality, 6-7, 10 compare, 161-162 express and compute, 160 problem solving, 168-17 Units of measure, converting, 116-117, 119-120, 129,142,158 Substitution method, to solving algebraic equations, 5-6 Subtraction algebraic equations involving, 7-8 bar model for, 219 like terms, 234 with decimals, 63, 119 Surface area, 181 of cube, 181 of non-rectangular prisms, 201 of pyramid, 185 Real-World Problems, 200-206 of rectangular prism, 182 of solids, 181-186 of triangular prism, 184 Symmetrical distribution, relating measures of central tendency to, 267-268 Symmetrical dot plot, 223 Table(s) frequency table, 218-219, 225, 261 graphing ordered pairs from, 62-63 of ratios, 134-137 to represent linear equations, 15-18 Tally, 218, 219, 225 Variables addition, 221-222 to represent numbers, 221-222 subtraction, 222 Vertical number line representing fractions, mixed numbers and decimals on, 9, 43-44 representing negative numbers on, 46-48, 50 Vocabulary, Throughout See for example, 5, 65, 239; 5,172,258 Volume of non-rectangular prisms, 201 of prisms, 189-195 Real-World Problems, 200-206 of rectangular prism, 171, 189-190 Whole number, dividing decimals by, 243 division, 65-66, 68, 75, 87, 96 finding factors and multiples of, multiplying fractions and, 155 on a number line, 5-7, 43 44 rounding, 121 Term(s) of an algebraic expression, 222 of a ratio, 118 Trapezoids area of, 74, 88-95, 170 perimeter, 41 Triangle area of, 75-82, 170 base and height of, 76, 80-82 Triangular prism net of, 174 surface area of, 184 Unit cost, 161 Unit price, 162 Unit rates, 159 x-axis, 42 lengths of line segments on, 50-53 x-coordinate, 42 y-axis, 42 lengths of line segments on, 50-53 y-coordinate, 42-43 Zero as a coordinate, 39 distance from, 54-55 meaning of, 45 neither positive nor negative, 47