CHAPTER 111. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS (TEKS) FOR MATHEMATICS 111.22. Mathematics, Grade 6 (b) Knowledge and Skills (6.1) Number, operation, and quantitative reasoning. The student represents and uses rational numbers in a variety of equivalent forms. The student is expected to: (A) compare and order non-negative rational numbers; Pages 266, 294 (B) generate equivalent forms of rational numbers including whole numbers, fractions, and decimals; Examples on pages 12, 163, 187, 202, 260, 300, 301, 308-309 (C) use integers to represent real-life situations; Throughout. Examples on pages 8-11, 24-28, 45-48, 66, 82-85, 118-120, 146-149, 162-165, 170-174 (D) write prime factorizations using exponents; and Page 275 (E) identify factors and multiples including common factors and common multiples. Pages 288, 289, 291 (6.2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve problems and justify solutions. The student is expected to: (A) Model addition and subtraction situations involving fractions with objects, pictures, words, and numbers; Pages 12, 259, 260 1
(TEKS Grade 6 Math, Standard 6.2/Math for the World of Work, Cont.) (B) use addition and subtraction to solve problems involving fractions and decimals; Examples on pages 11, 12, 13, 15, 16, 19, 34-35, 198, 259, 260 (C) use multiplication and division of whole numbers to solve problems including situations involving equivalent ratios and rates; and Examples on pages 43-44, 91, 106-109, 118-120, 121-124, 125-128, 133-135, 184 (D) estimate and round to approximate reasonable results and to solve problems where exact answers are not required. Examples on pages 34, 40, 46, 58-59, 135, 148, 188-189, 196, 200, 230, 251, 265 (6.3) Patterns, relationships, and algebraic thinking. The student solves problems involving proportional relationships. The student is expected to: (A) use ratios to describe proportional situations; Pages 43-44 (B) represent ratios and percents with concrete models, fractions, and decimals; and Examples on pages 17, 24, 43-44, 87, 142, 206, 216 (C) use ratios to make predictions in proportional situations. Pages 43-44, 184 (6.4) Patterns, relationships, and algebraic thinking. The student uses letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes. The student is expected to: (A) use tables and symbols to represent and describe proportional and other relationships involving conversions, sequences, perimeter, area, etc.; and Pages 146-147, 184, 200 2
(TEKS Grade 6 Math, Standard 6.4/Math for the World of Work, Cont.) (B) generate formulas to represent relationships involving perimeter, area, volume of a rectangular prism, etc., from a table of date. Pages 67, 146-147, 182, 200, 202, 261 (6.5) Patterns, relationships, and algebraic thinking. The students uses letters to represent an unknown in an equation. The student is expected to formulate an equation from a problem situation. Letters are used for unknown quantities in formulas throughout. See pages 27, 40, 67, 118-124, 128, 131, 168, 170, 182, 200, 202, 261 (6.6) Geometry and spatial reasoning. The student uses coordinate geometry to identify location in two dimensions. The student is expected to: (A) use angle measurements to classify angles as acute, obtuse, or right; (B) identify relationships involving angles in triangles and quadrilaterals; and (C) describe the relationship between radius, diameter, and circumference of a circle. (6.7) Geometry and spatial reasoning. The students uses coordinate geometry to identify location in two dimensions. The student is expected to locate and name points on a coordinate plane using ordered pairs of non-negative rational numbers. Pages 159-161 3
(TEKS Grade 6 Math/Math for the World of Work, Cont.) (6.8) Measurement. The student solves application problems involving estimation and measurement of length, area, time, temperature, capacity, weight, and angles. The student is expected to: (A) estimate measurements and evaluate the reasonableness of results; Pages 200, 202, 260 (B) select and use appropriate units, tools, or formulas to measure and to solve problems involving length (including perimeter and circumference), area, time, temperature, capacity, and weight; Pages 200, 202, 260 (C) measure angles; and (D) convert measures within the same measurement system (customary and metric) based on relationships between units. Pages 200, 202, 260, 312-313 (6.9) Probability and statistics. The student uses experimental and theoretical probability to make predictions. The student is expected to: (A) construct sample spaces using lists, tree diagrams, and combinations; and (B) find the probabilities of la simple event and its complement and describe the relationship between the two. 4
(TEKS Grade 6 Math/Math for the World of Work, Cont.) (6.10) Probability and statistics. The student uses statistical representations to analyze data. The student is expected to: (A) draw and compare different graphical representations of the same data; Pages 70, 92, 94, 97, 159, 161, 162 (B) use median, mode, and range to describe data; Page 277 (C) sketch circle graphs to display data; and Page 70 (D) solve problems by collecting, organizing, displaying, and interpreting data. Pages 70, 92, 94, 97, 159, 161, 162. In addition, see tables throughout; examples on pages 62, 72, 90. (6.11) Underlying processes and mathematical tools. The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside school. The student is expected to: (A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics; AGS Math for the World of Work teaches students math skills needed in the workforce. Throughout the text students are engaged in problem solving and application activities that relate mathematical concepts directly to common workplace activities. See examples on pages 72, 73, 83, 93, 95,102, 169, 174, 175. (B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; Problem solving is modeled is modeled in Example boxes in each lesson. These follow the steps for problem solving by demonstrating understanding, planning, execution, and evaluation. See examples on pages 16, 20, 34, 42, 56, 78, 82,86, 105, 119. 5
(TEKS Grade 6 Math, Standard 6.11/Math for the World of Work, Cont.) (C) select or develop an appropriate problemsolving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and A variety of problem-solving methods is used in the Student Text. See examples on pages 119, 135, 136, 152, 158. In addition, the Teacher s Edition presents many other types of methods in Learning Styles boxes in the marginal notes. See examples on TE pages 43, 48, 56, 72, 81, 94, 104, 111. (D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve a problem. Paper/pencil and computers/calculators are the primary tools used in the Student Text. For computer/calculator exercises, see Technology Connection exercises on pages 23, 48, 69, 87, 108, 123, 147, 164, 181, 202, 219, 233, 262. The Teacher s Edition has additional technology exercises (Examples on TE pages 39, 48, 55, 61, 68, 84). Techniques such as mental math, estimation, and number sense are encouraged throughout the Student Text (Examples on pages 9, 20, 34, 135, 196, 251, 259) and the Teacher s Edition (Examples on TE pages 26, 35, 64, 88, 108, 128, 165). (6.12) Underlying processes and mathematical tools. The student communicates about Grade 6 mathematics through informal and mathematical language, representations, and models. The student is expected to: (A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models; and See Exercises and Problem Solving assignments throughout. (B) evaluate the effectiveness of different representations to communicate ideas. Different representations, including formulas, charts, graphs, and so forth, are used throughout. 6
(TEKS Grade 6 Math/Math for the World of Work, Cont.) (6.13) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to: (A) make conjectures from patterns or sets of examples and nonexamples; and (B) validate his/her conclusions using mathematical properties and relationships. 111.23. Mathematics, Grade 7 (b) Knowledge and Skills (7.1) Number, operation, and quantitative reasoning. The student represents and uses numbers in a variety of equivalent forms. The student is expected to: (A) compare and order integers and positive rational numbers; Pages 266, 278, 294 (B) convert between fractions, decimals, whole numbers, and percents mentally, on paper, or with a calculator; and Examples on pages 12, 17, 24, 87, 142, 163, 187, 202, 206, 216, 260, 300, 301, 308-309 (C) represent squares and square roots using geometric models. 7
(TEKS Grade 7 Math/Math for the World of Work, Cont.) (7.2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, or divides to solve problems and justify solutions. The student is expected to: (A) represent multiplication and division situations involving fractions and decimals with concrete models, pictures, words, and numbers; Examples on pages 58-61, 100, 118-120, 121-124, 133-136, 252-255 (B) use addition, subtraction, multiplication, and division to solve problems involving fractions and decimals; Examples on pages 27, 35-36, 61, 105, 112, 118-120, 121-124, 128, 135 (C) use models to add, subtract, multiply, and divide integers and connect the actions to algorithms; Examples on pages 8, 11, 12, 66, 188, 198, 204, 216, 224, 230, 259, 260 (D) use division to find unit rates and ratios in proportional relationships such as speed, density, price, recipes, and student-teacher ratio; Examples on pages 43-44, 54-57, 91-92, 118-120, 135, 243 (E) simplify numerical expressions involving order of operations and exponents; (F) select and use appropriate operations to solve problems and justify the selections; and See Exercises and Problem Solving assignments throughout. Examples on pages 47, 57, 59, 91, 93, 120, 123-124, 174 (G) determine the reasonableness of a solution to a problem. Students can determine reasonableness in many problems throughout by using estimation or by examining the answer in the context of the problem. 8
(TEKS Grade 7 Math/Math for the World of Work, Cont.) (7.3) Patterns, relationships, and algebraic thinking. The student solves problems involving proportional relationships. The student is expected to: (A) estimate and find solutions to application problems involving percent; and Examples on pages 24-28, 34, 36, 37, 45, 60-61, 82-85, 118-120, 121-124, 125-128 (B) estimate and find solutions to application problems involving proportional relationships such as similarity, scaling, unit costs, and related measurement units. Examples on pages 8-11, 43-44, 158-161, 184, 200 (7.4) Patterns, relationships, and algebraic thinking. The student represents a relationship in numerical, geometric, verbal, and symbolic form. The student is expected to: (A) generate formulas involving conversions, perimeter, area, circumference, volume, and scaling; Pages 146-147, 200, 202, 260, 261, 310 (B) graph data to demonstrate relationships in familiar concepts such as conversions, perimeter, area, circumference, volume, and scaling; and Examples on pages 94, 146-147, 159, 161 (C) describe the relationship between the terms in a sequence and their positions in the sequence. 9
(TEKS Grade 7 Math/Math for the World of Work, Cont.) (7.5) Patterns, relationships, and algebraic thinking. The student uses equations to solve problems. The student is expected to: (A) use concrete models to solve equations and use symbols to record the actions; and See Exercises, Problem Solving, and Application assignments throughout. (B) formulate a possible problem situation when given a simple equation. (7.6) Geometry and spatial reasoning. The student compares and classifies shapes and solids using geometric vocabulary and properties. The student is expected to: (A) use angle measurements to classify pairs of angles as complementary or supplementary; (B) use properties to classify shapes including triangles, quadrilaterals, pentagons, and circles; (C) use properties to classify solids, including pyramids, cones, prisms, and cylinders; and (D) use critical attributes to define similarity. (7.7) Geometry and spatial reasoning. The student uses coordinate geometry to describe location on a plane. The student is expected to: (A) locate and name points on a coordinate plane using ordered pairs of integers; and (B) graph translations on a coordinate plane. Pages 159-161 10
(TEKS Grade 7 Math/Math for the World of Work, Cont.) (7.8) Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to: (A) sketch a solid when given the top, side, and front views; (B) make a net (two-dimensional models) of the surface area of a solid; and (C) use geometric concepts and properties to solve problems in fields such as art and architecture. (7.9) Measurement. The student solves application problems involving estimation and measurement. The student is expected to estimate measurements and solve application problems involving length (including perimeter and circumference), area, and volume. Pages 200, 202, 260, 310 (7.10) Probability and statistics. The student recognizes that a physical or mathematical model can be used to describe the probability of real-life events. The student is expected to: (A) construct sample space for compound events (dependent and independent); and (B) find the approximate probability of a compound event through experimentation. 11
(TEKS Grade 7 Math/Math for the World of Work, Cont.) (7.11) Probability and statistics. The student understands that the way a set of data is displayed influences its interpretation. The student is expected to: (A) select and use an appropriate representation for presenting collected data and justify the selection; and Pages 70, 92, 94, 97, 159, 161, 162 (B) make inferences and convincing arguments based on an analysis of given or collected data. Pages 70, 92, 94, 97, 159, 161, 162, 176 (7.12) Probability and statistics. The student uses measure of central tendency and range to describe a set of data. The student is expected to: (A) describe a set of data using mean, median, mode, and range; and (B) choose among mean, median, mode or range to describe a set of data and justify the choice for a particular situation. (7.13) Underlying processes and mathematical tools. The student applies Grade 7 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics; AGS Math for the World of Work teaches students math skills needed in the workforce. Throughout the text students are engaged in problem solving and application activities that relate mathematical concepts directly to common workplace activities. See examples on pages 72, 73, 83, 93, 95,102, 169, 174, 175. 12
(TEKS Grade 7 Math, Standard 7.13/Math for the World of Work, Cont.) (B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; Problem solving is modeled is modeled in Example boxes in each lesson. These follow the steps for problem solving by demonstrating understanding, planning, execution, and evaluation. See examples on pages 16, 20, 34, 42, 56, 78, 82,86, 105, 119. (C) select or develop an appropriate problemsolving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and A variety of problem-solving methods is used in the Student Text. See examples on pages 119, 135, 136, 152, 158. In addition, the Teacher s Edition presents many other types of methods in Learning Styles boxes in the marginal notes. See examples on TE pages 43, 48, 56, 72, 81, 94, 104, 111. (D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems. Paper/pencil and computers/calculators are the primary tools used in the Student Text. For computer/calculator exercises, see Technology Connection exercises on pages 23, 48, 69, 87, 108, 123, 147, 164, 181, 202, 219, 233, 262. The Teacher s Edition has additional technology exercises (Examples on TE pages 39, 48, 55, 61, 68, 84). Techniques such as mental math, estimation, and number sense are encouraged throughout the Student Text (Examples on pages 9, 20, 34, 135, 196, 251, 259) and the Teacher s Edition (Examples on TE pages 26, 35, 64, 88, 108, 128, 165). 13
(TEKS Grade 7 Math/Math for the World of Work, Cont.) (7.14) Underlying processes and mathematical tools. The student communicates about Grade 7 mathematics through informal and mathematical language, representations, and models. The student is expected to: (A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models; and See Exercises and Problem Solving assignments throughout. (B) evaluate the effectiveness of different representations to communicate ideas. Different representations, including formulas, charts, graphs, and so forth, are used throughout. (7.15) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to: (A) make conjectures from patterns or sets of examples and nonexamples; and (B) validate his/her conclusions using mathematical properties and relationships. 14
111.24. Mathematics, Grade 8 (b) Knowledge and Skills (8.1) Number, operation, and quantitative reasoning. The student understands that different forms of numbers are appropriate for different situations. The student is expected to: (A) compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals; Pages 266, 278, 294 (B) select and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships; Throughout. Examples on pages 60-61, 64-65, 118-120, 121-124, 180-183, 184-187, 188-190 (C) approximate (mentally and with calculators) the value of irrational numbers as they arise from problem situations (π, 2); and (D) express numbers in scientific notation, including negative exponents, in appropriate problem situations using a calculator. Page 299 (8.2) Number, operation, and quantitative reasoning. The student selects and uses appropriate operations to solve problems and justify solutions. The student is expected to: (A) select and use appropriate operations to solve problems and justify the selections; (B) add, subtract, multiply, and divide rational numbers in problem situations; See Exercises and Problem Solving assignments throughout. Examples on pages 47, 57, 59, 91, 93, 120, 123-124, 174 Examples on pages 27, 35-36, 61, 105, 112, 118-120, 121-124, 128, 135 15
(TEKS Grade 8 Math, Standard 8.2/Math for the World of Work, Cont.) (C) evaluate a solution for reasonableness; and Students can determine reasonableness in many problems throughout by using estimation or by examining the answer in the context of the problem. (D) use multiplication by a constant factor (unit rate) to represent proportional relationships; for example, the arm span of a gibbon is about 1.4 times its height, a = 1.4h. Examples on pages 8-10, 16-19, 20-23, 24-28, 56-57, 158-161 (8.3) Patterns, relationships, and algebraic thinking. The student identifies proportional relationships in problem situations and solves problems. The student is expected to: (A) compare and contrast proportional and non-proportional relationships; and Examples on pages 118-120, 121-124, 158-161 (B) estimate and find solutions to application problems involving percents and proportional relationships such as similarity and rates. Examples on pages 8-11, 24-28, 43-44, 58-61, 158-161, 184, 200 (8.4) Patterns, relationships, and algebraic thinking. The student makes connections among various representations of a numerical relationship. The student is expected to generate a different representation given one representation of data such as a table, graph, equation, or verbal description. Throughout the text, students are given equations that they use to fill in a graph or vice versa. See examples on pages 26, 28, 41, 46, 47, 59, 83. In addition, students use graphs to generate equations or descriptions. See examples on pages 70, 94, 159, 161, 176 16
(TEKS Grade 8 Math/Math for the World of Work, Cont.) (8.5) Patterns, relationships, and algebraic thinking. The student uses graphs, tables, and algebraic representations to make predictions and solve problems. The student is expected to: (A) estimate, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations; and See Exercises, Problem Solving, and Application assignments throughout. (B) use an algebraic expression to find any term in a sequence. (8.6) Geometry and spatial reasoning. The student uses transformational geometry to develop spatial sense. The student is expected to: (A) generate similar shapes using dilations including enlargements and reductions; and (B) graph dilations, reflections, and translations on a coordinate plane. (8.7) Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to: (A) draw solids from different perspectives; (B) use geometric concepts and properties to solve problems in fields such as art and architecture; (C) use pictures or models to demonstrate the Pythagorean Theorem; and (D) locate and name points on a coordinate plane using ordered pairs of rational numbers. 17
(TEKS Grade 8 Math/Math for the World of Work, Cont.) (8.8) Measurement. The student uses procedures to determine measures of solids. The student is expected to: (A) find surface area of prisms and cylinders using concrete models and nets (twodimensional models); (B) connect models to formulas for volume of prisms, cylinders, pyramids, and cones; and (C) estimate answers and use formulas to solve application problems involving surface area and volume. (8.9) Measurement. The student uses indirect measurement to solve problems. The student is expected to: (A) use the Pythagorean Theorem to solve reallife problems; and (B) use proportional relationships in similar shapes to find missing measurements. (8.10) Measurement. The student describes how changes in dimensions affect linear, area, and volume measures. The student is expected to: (A) describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally; and (B) describe the resulting effect on volume when dimensions of a solid are changed proportionally. 18
(TEKS Grade 8 Math/Math for the World of Work, Cont.) (8.11) Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions. The student is expected to: (A) find the probabilities of compound events (dependent and independent); (B) use theoretical probabilities and experimental results to make predictions and decisions; and (C) select and use different models to simulate an event. (8.12) Probability and statistics. The student uses statistical procedures to describe data. The student is expected to: (A) select the appropriate measure of central tendency to describe a set of data for a particular purpose; (B) draw conclusions and make predictions by analyzing trends in scatterplots; and (C) construct circle graphs, bar graphs, and histograms, with and without technology. Pages 70, 93-94, 158-159, 160-161 (8.13) Probability and statistics. The student evaluates predictions and conclusions based on statistical data. The student is expected to: (A) evaluate methods of sampling to determine validity of an inference made from a set of data; and (B) recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis. 19
(TEKS Grade 8 Math/Math for the World of Work, Cont.) (8.14) Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics; AGS Math for the World of Work teaches students math skills needed in the workforce. Throughout the text students are engaged in problem solving and application activities that relate mathematical concepts directly to common workplace activities. See examples on pages 72, 73, 83, 93, 95,102, 169, 174, 175. (B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; Problem solving is modeled is modeled in Example boxes in each lesson. These follow the steps for problem solving by demonstrating understanding, planning, execution, and evaluation. See examples on pages 16, 20, 34, 42, 56, 78, 82,86, 105, 119. (C) select or develop an appropriate problemsolving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and A variety of problem-solving methods is used in the Student Text. See examples on pages 119, 135, 136, 152, 158. In addition, the Teacher s Edition presents many other types of methods in Learning Styles boxes in the marginal notes. See examples on TE pages 43, 48, 56, 72, 81, 94, 104, 111. (D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems. Paper/pencil and computers/calculators are the primary tools used in the Student Text. For computer/calculator exercises, see Technology Connection exercises on pages 23, 48, 69, 87, 108, 123, 147, 164, 181, 202, 219, 233, 262. The Teacher s Edition has additional technology exercises (Examples on TE pages 39, 48, 55, 61, 68, 84). Techniques such as mental math, estimation, and number sense are encouraged throughout the Student Text (Examples on pages 9, 20, 34, 135, 196, 251, 259) and the Teacher s Edition (Examples on TE pages 26, 35, 64, 88, 108, 128, 165). 20
(TEKS Grade 8 Math/Math for the World of Work, Cont.) (8.14) Underlying processes and mathematical tools. The student communicates about Grade 7 mathematics through informal and mathematical language, representations, and models. The student is expected to: (A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models; and See Exercises and Problem Solving assignments throughout. (B) evaluate the effectiveness of different representations to communicate ideas. Different representations, including formulas, charts, graphs, and so forth, are used throughout. (7.15) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to: (A) make conjectures from patterns or sets of examples and nonexamples; and (B) validate his/her conclusions using mathematical properties and relationships. 21