Life Skills Math 2003

Life Skills Math 2003 correlated to California s Map for Mathematics 7 5910 Rice Creek Pkwy, Suite 1000 Shoreview, MN 55126 Copyright 2006 Pearson Education, Inc. publishing as Pearson AGS Globe. All rights reserved. CU.04.07

Publisher: American Guidance Service, Inc. Program Title: Life Skills Math 2003 Components: Level: Intended Audience: SE: Student Edition; TE: Teacher s Edition; ACT: Activity in Teacher s Resource Library (TRL); WB: Workbook Activity in TRL; CC: Community Connections; MJ: Math on the Job Seven High school and adult learners who are below grade level in comprehension skills or who need extra help grasping new concepts. California s Map Seven By the end of grade six, students have mastered the four arithmetic operations with whole numbers, positive fractions, positive decimals, and positive and negative integers; they accurately compute and solve problems. They apply their knowledge to statistics and probability. Students understand the concepts of mean, median, and mode of data sets and how to calculate the range. They analyze data and sampling processes for possible bias and misleading conclusions; they use addition and multiplication of fractions routinely to calculate the probabilities for compound events. Students conceptually understand and work with rations and proportions; they compute percentages (e.g., tax, tips, interest). Students know about π and the formulas for the circumference and area of a circle. They use letters for numbers in formulas involving geometric shapes and in ratios to represent an unknown part of an expression. They solve one-step linear equations. 1

(California s Map, 7: AGS Life Skills Math, Cont.) NUMBER SENSE 7 1.0 Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions, and percentages: 7 1.1 Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10) with approximate numbers using scientific notation. SE 344 SE 344 SE 344 7 1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers. SE 23-24; TE 23-24 Throughout. See the following examples: SE/TE 25, 27, 28, 76-80, 82, 89, 91, 92, 94-95, 104-105, 107-110, 112-114, 120-126, 132-134, 136-137, 139, 141, 143, 145-148; WB 9-10, 27, 31-33, 35-43; ACT 8-9, 22, 25-27, 29-38 Examples on SE/TE 24, 26, 74-75, 79, 93, 104, 106, 108, 111, 120, 132 2

(California s Map, 7: AGS Life Skills Math, Cont.) NUMBER SENSE 1.0, Cont. 7 1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications. SE 65, 195-196; TE 65, 195-196 SE 65, 138-139, 196, 198, 199,202-204, 212, 214, 216, 218, 221, 222, 346, 348; TE 65, 138-139, 196, 198, 199, 202-204, 212, 214, 216, 218, 221, 222, 346, 348; WB 60, 61, 62, 64, 66, 67, 68; ACT 55, 56, 57, 59, 63 SE 138, 195, 197, 199, 212, 213, 215, 217; TE 212, 215, 217 7 1.4 Differentiate between rational and irrational numbers. 7 1.5 Know that every rational number is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions. 7 1.6 Calculate the percentage of increases and decreases of a quantity. SE 65; TE 65 SE 65, 204, 230, 345; TE 65, 204, 230, 345 SE 213; TE 213 SE 214; TE 214; ACT 62 SE 65, 204, 230 SE 214 3

(California s Map, 7: AGS Life Skills Math, Cont.) NUMBER SENSE 1.0, Cont. 7 1.7 Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest. SE 213-214, 228, 231; TE 213-214, 228, 231 SE 214, 229-230, 232-235, 237-239, 240; TE 214, 229-230, 232-235, 237-239, 240; ACT 62, 66, 67, 68, 69; WB 72, 73, 74 SE 214, 229, 231, 236; TE 214, 229, 231, 236 7 2.0 Students use exponents, powers, and roots and use exponents in working with fractions: 7 2.1 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base. SE 320, 344 SE 320, 344; TE 320, 344 SE 320, 344 7 2.2 Add and subtract fractions by using factoring to find common denominators. SE 104-105, 106-107; TE 104-105, 106-107 SE 104-105, 106-107, 114, 333-334, 336, 338; TE 104-105, 106-107, 114, 333-334, 336, 338; WB 35, 36; ACT 29, 30 SE 104, 106; TE 104, 106 4

(California s Map, 7: AGS Life Skills Math, Cont.) NUMBER SENSE 2.0, Cont. 7 2.3 Multiply, divide, and simplify rational numbers by using exponent rules. SE 108-109, 132-135, 142; TE 108-109, 132-135, 142 SE 108-114, 132-137, 138-141, 142-147, 192-196, 198-204, 255, 257, 328-331, 343-345; TE 108-114, 132-137, 138-141, 142-147, 192-196, l98-204, 255, 257, 328-331, 343-345; ACT 31-32, 36-38, 55-59; WB 37-38, 41-43, 60-64 SE 132, 134-136, 140, 142, 144, 146, 192-196, 197-204, 254, 256; TE 132-137, 138-141, 142-147, 192-196, 197-204, 254, 256 7 2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and explain why. Not applicable to this program. 5

(California s Map, 7: AGS Life Skills Math, Cont.) NUMBER SENSE 2.0, Cont. 7 2.5 Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers. Not applicable to this program. ALGEBRA AND FUNCTIONS 7 1.0 Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs: 7 1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A). SE 303-304 SE 305; TE 305 SE 303-305; TE 303-305 7 1.2 Use the correct order of operations to SE 321 SE 321; TE 321 SE 321 6

evaluate algebraic expressions such as 3(2x + 5 2 ). 7 1.3 Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the process used. (California s Map, 7: AGS Life Skills Math, Cont.) ALGEBRA AND FUNCTIONS 1.0, Cont. 7 1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression, constant) correctly. 7 1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph. SE 10-11; TE 10-11 SE 11, 220; TE 11, 220; WB 4, 70; ACT 4, 65; CC 11, 17 SE 10-11, 219; TE 10-11, 219 7 2.0 Students interpret and evaluate expressions involving integer powers and simple roots: 7 2.1 Interpret positive whole-number powers as repeated multiplication and negative wholenumber powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that SE 320, 344 SE 320, 344; TE 320, 344 SE 320, 344 7

include exponents. 7 2.2 Multiply and divide monomials; extend the process of taking powers and extracting roots to monomials when the latter results in a monomial with an integer exponent. (California s Map, 7: AGS Life Skills Math, Cont.) ALGEBRA AND FUNCTIONS, Cont. 7 3.0 Students graph and interpret linear and some nonlinear functions: 7 3.1 Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. 7 3.2 Plot the values from the volumes of threedimensional shapes for various values of the edge lengths (e.g., cubes with varying edge lengths or a triangle prism with a fixed height and an equilateral triangle base of varying lengths). 8

7 3.3 Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio ( rise over run ) is called the slope of the graph. 7 3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities. (California s Map, 7: AGS Life Skills Math, Cont.) ALGEBRA AND FUNCTIONS 3.0, Cont. 7 4.0 Students solve simple linear equations and inequalities over the rational numbers: 7 4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results. 7 4.2 Solve multistep problems involving rate, SE 160, 176, 212, SE 161, 163, 165, SE 160, 162, 164, 9

average speed, distance, and time or a direct variation. 228; TE 160, 176 167, 169, 177-181, 183, 185, 186, 212, 229-230, 232, 233-235, 237-240, 261; TE 161, 163, 165, 167, 169, 177-181, 183, 185, 186, 212, 229-230, 232, 233-235, 237-240, 261; WB 48-57, 71-73, 78; ACT 43-52, 66-68 166, 168, 212, 229, 231, 232, 236, 260; TE 160, 229 (California s Map, 7: AGS Life Skills Math, Cont.) MEASUREMENT AND GEOMETRY 7 1.0 Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems: 7 1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters). SE 72-73, 274-275; TE 72-73, 274-275 SE 72-73, 274-275; TE 72-73, 274-275; WB 81; ACT 21, 77 SE 72-73, 274-275; TE 72-73, 274-275 10

7 1.2 Construct and read drawings and models made to scale. SE 276-277; TE 276-277 SE 276-277, 279, 281, 283-285, 286; TE 276-277, 279, 281, 283-285, 286; WB 82-86; ACT 78-82 SE 276, 278, 280, 282, 284; TE 276, 278, 280, 282, 284 7 1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer. SE 162, 164, 168, 212, 228; TE 162, 164, 168 SE 163, 165, 167, 169, 185, 186, 212, 229-230, 232, 233-235, 237-240, 261; TE 163, 165, 167, 169, 185, 186, 212, 229-230, 232, 233-235, 237-240, 261; WB 49-51, 57, 71-73, 78; ACT 44-47, 52, 66-68 SE 162, 164, 166, 168, 212, 229, 231, 232, 236, 260; TE 229 (California s Map, 7: AGS Life Skills Math, Cont.) MEASUREMENT AND GEOMETRY, Cont. 7 2.0 Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale. 7 2.1 Use formulas routinely for finding the SE 20, 105, 272, SE 20-28, 98, 109, SE 23, 25, 26, 11

perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders. 278; TE 20, 272, 278 272-273, 279, 281, 283-286; TE 20-28, 98, 109, 272-273, 279, 281, 283-286; WB 6-10, 80, 82-86; ACT 6-9, 76, 78-82 272, 278, 280, 282, 284; TE 23, 25, 26, 272, 278, 280, 282, 284 7 2.2 Estimate and compute the area of more complex or irregular two- and threedimensional figures by breaking the figures down into more basic geometric objects. SE 278; TE 278 SE 279, 281; TE 279, 281; WB 83-84; ACT 79-80 SE 278, 280; TE 278, 280 7 2.3 Compute the length of the perimeter, the surface area of the faces, and the volume of a three-dimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the scale factor and the volume is multiplied by the cube of the scale factor. SE 20, 105, 272, 278; TE 20, 272, 278 SE 20-28, 98, 109, 272-273, 279, 281, 283-286; TE 20-28, 98, 109, 272-273, 279, 281, 283-286; WB 6-10, 80, 82-86; ACT 6-9, 76, 78-82 SE 23, 25, 26, 272, 278, 280, 282, 284; TE 23, 25, 26, 272, 278, 280, 282, 284 (California s Map, 7: AGS Life Skills Math, Cont.) MEASUREMENT AND GEOMETRY 2.0, Cont. 7 2.4 Relate the changes in measurement with a SE 276-277; TE SE 276-277, 284; SE 276-277, 284; 12

change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1 square foot = 144 square inches of =[1 ft 2 ] = [144 in 2 ], 1 cubic inch is approximately 16.38 cubic centimeters or [1 in 3 ] = [16.38 cm 3 ]). 276-277 TE 276-277, 284 TE 276-277 7 3.0 Students know the Pythagorean theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures: 7 3.1 Identify and construct basic elements of geometric figures (e.g., altitudes, midpoints, diagonals, angle bisectors, and perpendicular bisectors; central angels, radii, diameters, and chords of circles) by using a compass and straightedge. 7 3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections. (California s Map, 7: AGS Life Skills Math, Cont.) MEASUREMENT AND GEOMETRY 3.0, Cont. 13

7 3.3 Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement. 7 3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the two figures. 7 3.5 Construct two-dimensional patterns for three dimensional models, such as cylinders, prisms, and cones. 7 3.6 Identify elements of three-dimensional geometric objects (e.g., diagonals of rectangular solids) and describe how two or more objects are related in space (e.g., skew lines, the possible ways three planes might intersect). (California s Map, 7: AGS Life Skills Math, Cont.) 14

STATISTICS, DATA ANALYSIS, AND PROBABILITY 7 1.0 Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program: 7 1.1 Know various forms of display for data sets, including a stem-and-leaf plot or boxand-whisker plot; use the forms to display a single set of data or to compare two sets of data. 7 1.2 Represent two numerical variables on a scatterplot and informally describe how the data points are distributed and any apparent relationship that exists between the two variables (e.g., between time spent on homework and grade level). 7 1.3 Understand the meaning of, and be able to compute, the minimum, the lower quartile, the median, the upper quartile, and the maximum of a data set. SE 52; TE 52 SE 52; TE 52 SE 52; TE 52 (California s Map, 7: AGS Life Skills Math, Cont.) 15

MATHEMATICAL REASONING 7 1.0 Students make decisions about how to approach problems. 7 1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. 7 1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed. See Exercise, Problem Solving, and Application problems throughout 7 1.3 Determine when and how to break a problem into simpler parts. 7 2.0 Students use strategies, skills, and concepts in finding solutions: 7 2.1 Use estimation to verify the reasonableness of calculated results. SE 44; TE 44 SE 44-45, 157; TE 44-45, 157 SE 156; TE 156 (California s Map, 7: AGS Life Skills Math, Cont.) 16

MATHEMATICAL REASONING 2.0, Cont. 7 2.2 Apply strategies and results from simpler problems to more complex problems. 7 2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques. In each lesson and chapter throughout, students begin with basic problems and then apply mathematical principles to increasingly complex problems. See, for example, Chapter 14: Working with Interest (SE/TE pages 226-243). Students begin by understanding simple interest (pages 228-230), move on to compound interest (pages 231-232), then apply concepts to issues of borrowing money and using credit (pages 233-238). Not applicable to this program. 7 2.4 Make and test conjectures by using both inductive and deductive reasoning. 7 2.5 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning. Throughout. See the following examples: Words: See definitions of key words and concepts in blue boxes at the beginning of each lesson. Numbers: SE/TE 104-105, 106-107, 108-110, 132-137 Symbols: SE 292-297, 303-305 Charts/Tables: SE 162, 182, 202, 209, 247, 248, 268, 269 Graphs: SE 10-11, 17, 219-221 Diagrams/Models: SE 272-273, 276-277, 280-281, 284, 301 17

(California s Map, 7: AGS Life Skills Math, Cont.) MATHEMATICAL REASONING 2.0, Cont. 7 2.6 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work. See Exercise, Problem Solving, and Application problems throughout 7 2.7 Indicate the relative advantages of exact and approximate solutions to problems and give answers to specified degree of accuracy. SE 26; TE 26 SE 26, 45, 137, 146, 158, 161, 200-204, 221, 239, 255, 272, 284-285; TE 26, 45, 137, 146, 158, 161, 200-204, 221, 239, 255, 272, 284-285; WB 43, 46, 48, 59, 62-64, 70, 84; ACT 9, 36, 38, 41, 54, 57-59, 65, 78 SE 135, 160, 193,199, 200, 231, 256, 280, 284; TE 135, 160 7 2.8 Make precise calculations and check the validity of the results from the context of the problem. See Exercise, Problem Solving, and Application problems throughout 18

(California s Map, 7: AGS Life Skills Math, Cont.) MATHEMATICAL REASONING 7 3.0 Students determine a solution is complete and move beyond a particular problem by generalizing to other situations: 7 3.1 Evaluate the reasonableness of the solution in the context of the original situation. See Exercise, Problem Solving, and Application problems throughout 7 3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems. 7 3.3 Develop generalizations of the results obtained and the strategies used and apply them to new problem situations. In each lesson throughout, problem solving is demonstrated in green Example sections. Students then solve similar problems in Exercise and Problem Solving sections. See, for example, SE pages 104, 106, 108-109, 144, 192-201, 233-237, 254, 256-257 In addition to the methods outlined in 3.2 above, students apply new problem-solving strategies in Application sections following each chapter. See pages 14, 28, 46, 66, 82, 98, 114, 126, 148, 170, 186, 206, 222, 240, 266, 286, 306 19