CHAPTER 111. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS (TEKS) FOR MATHEMATICS 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; (B) convert between fractions, decimals, whole numbers, and percents mentally, on paper, or with a calculator; and Chapter 1: Lessons 1, 2; Chapter 3: Lessons 1-6; Chapter 4: Lessons 1-3 Examples: Chapter 3: Lessons 2-6, 12, 14; Chapter 4: Lessons 7, 9, 10; Chapter 6: Lessons 2, 3, 5, 9-14; Decimal, Percent, and Fraction Conversion Supp. Problems: Whole Numbers, Fractions, Decimals Examples: Chapter 3: Lessons 9, 11; Chapter 4: Lessons 3-5; Chapter 6: Lesson 6; Chapter 8: Lesson 2; Chapter 10: Lessons 3, 7 (C) represent squares and square roots using geometric models. Chapter 8: Lesson 5 Chapter 7: Lessons 9, 11, 12; Chapter 12: Lessons 2, 3 (7.2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve problems and justify solutions. The student is expected to: (A) represent multiplication and division situations involving fractions and decimals with concrete models, pictures, words, and numbers; Chapter 3: Lessons 7-10, ; Chapter 4: Lessons 6, 8, ; Chapter 6: Lessons 5-14, ; Chapter 12: Lessons 2-4; Supplementary Problems: Fractions Examples: Chapter 6: Lessons 4, 9; Chapter 7: Lesson 13; Chapter 10: Lesson 2; Chapter 12: Lesson 6; Supplementary Problems: Fractions; Decimals 1
(TEKS, Mathematics Grade 7, Cont.) CONT. (7.2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve problems and justify solutions. The student is expected to: (B) use addition, subtraction, multiplication, and division to solve problems involving fractions and decimals; (C) use models to add, subtract, multiply, and divide integers and connect the actions to algorithms; (D) use division to find unit rates and ratios in proportional relationships such as speed, density, price, recipes, and student-teacher ratio. (E) simplify numerical expressions involving order of operations and exponents; Chapter 3: Lessons 7-15, ; Chapter 4: Lessons 4-8, ; Chapter 6: Lessons 5-14, ; Chapter 12: Lessons 2-4; Supplementary Problems: Fractions Chapter 13: Lessons 2-7, Chapter 5: Lessons 1-4, ; Chapter 6: Lessons 7-13, Chapter 1: Lessons 8, 9; Chapter 4: Lesson 7; Chapter 13: Lesson 6; Supp. Problems: Whole Numbers Examples: Chapter 1: Lessons 11-13; Chapter 2: Lesson 9-12, ; Chapter 3: Lessons 2-4, 8-10; Chapter 4: Lessons 5, 6, 11, 13; Chapter 10: Lessons 1-3 Chapter 2: Lessons 11, 12; Chapter 5: Lessons 8, 9; Chapter 6: Lessons 2-5, 7, 9; Chapter 9: Lesson 3; Chapter 12: Lesson 7 Supp. Problems: Whole Numbers (F) select and use appropriate operations to solve problems and justify the selections; and (G) determine the reasonableness of a solution to a problem. See Exercises and Problem Solving sections throughout. See Exercises and Problem Solving sections throughout. (TEKS, Mathematics Grade 7, Cont.) 2
(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 (B) extimate and find solutions to application problems involving proportional relationships such as similarity, scaling, unit costs, and related measurement units. Chapter 6: Lessons 1-14, s; Supplementary Problems: Percents Chapter 4: ; Chapter 5: Lessons 1, 4, ; Chapter 6: Lessons 7-13, ; Chapter 12: Lessons 1-4, Throughout. Examples: Chapter 3: Lessons 2-4, 10; Chapter 4: Lessons 3, 10; Chapter 6: Lesson 6; Chapter 10: Lessons 1-3 Chapter 2: Lessons 11, 12; Chapter 6: Lessons 2-5, 7; Chapter 8: Lesson 2; Chapter 9: Lesson 3; Chapter 12: Lessons 6, 7 (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; (B) graph data to demonstrate relationships in familiar concepts such as conversions, perimeter, area, circumference, volume, and scaling; and (C) describe the relationship between the terms in a sequence and their positions in the sequence. Chapter 5: Lesson 4; Chapter 8: Lessons 4-8, 10, ; Chapter 9: Lessons 1, 2, 4, 6-11, ; Chapter 10: Lessons 2-4; Chapter 12: Lessons 1-4 Chapter 5: Lesson 4, s; Chapter 8: Lessons 7-9; Chapter 9: Lessons 1, 2, 4 Chapter 2: Lessons 2-5 Chapter 7: Lessons 3-7, 9-13; Chapter 8: Lessons 1, 2; Chapter 12: Lesson 6 Chapter 8: Lesson 2 3
(TEKS, Mathematics Grade 7, 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 Throughout. Examples: Chapter 3: ; Chapter 4: ; Chapter 5: Lesson 4; Chapter 6: Lessons 5-14 Throughout. Examples: Chapter 4: Lesson 6; Chapter 7: Lessons 7-9, 11-13; Chapter 8: Lesson 2 (B) formulate a possible problem situation when given a simple equation. See "Problem Solving" exercises throughout. (7.6) Geometry and spatial reasoning. The student compares and classifies shapes and solids using geometry vocabulary and properties. The student is expected to: (A) use angle measurements to classify pairs of angles as complementary of supplementary; (B) use properties to classify shapes including triangles, quadriilaterals, pentagons, and circles; (C) use properties to classify solids, including pyramids, cones, prisms, and cylinders; and (D) use critical attributes to define similarity. Chapter 7: Lessons 2, 3 Chapter 7: Lesson 4; Supplementary Problems: Geometry Chapter 7: Lesson 5 Chapter 12: Lessons 1-4 (TEKS, Mathematics Grade 7, Cont.) 4
(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. Chapter 13: Lesson 9 (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 model) of the surface area of a solid; and (C) use geometric concepts and properties to solve problems and fields such as art and architecture. Chapter 7: Lesson 5 Chapter 7: Lesson 5 Chapter 8: Lessons 5, 6, ; Chapter 9: Lesson 7, ; Chapter 10: Lesson 3; Chapter 12: Lessons 1, 3, Chapter 7: Lessons 3-13 (7.9) Measurement. The student solves application problems involving estimation and measurement. The student is expected to: The student is expected to estimate measurements and solve application problems involving length (including perimeter and circumference), area and volume. (TEKS, Mathematics Grade 7, Cont.) Chapter 8: Lessons 2, 4-8, ; Chapter 9: Lessons 3-11, ; Chapter 10: Lessons 1-3 Chapter 7: Lessons 3-7, 9-13; Chapter 12: Lesson 6 5
(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 spaces for compound events (dependent and independent) and (B) find the approximate probability of a compound event through experimentation. (7.11) Probability and statistics. The student understands that they 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 (B) make inferences and convincing arguments based on an analysis of given or collected data. Chapter 11: Lessons 1-7, Chapter 11: Lessons 1-7, (7.12) Probability and statistics. The student uses measures 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. Chapter 1: Lesson 7; Chapter 11: Lesson 2 Chapter 4: Lesson 7; Chapter 5: Lesson 6; Chapter 9: Lesson 1 6
(TEKS, Mathematics Grade 7, Cont.) (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; See "Problem Solving" and exercises throughout. Examples: pp. 54, 71, 109, 118, 129, 133, 145, 164, 200, 208 See "Problem Solving" and exercises throughout. Examples: pp. 26, 70-71, 121, 134, 146, 181, 185, 202, 295 (B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; (C) select or develop an appropriate problem-solving 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 (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. See Problem Solving and exercises throughout. See Problem Solving and exercises throughout. Multiple means of problem solving are encouraged throughout. Specifically, "Calculator Practice" problems are included in each Chapter. See pages 29, 39, 65, 113, 127, 147, 183, 204, 233, 248, 268, 293, 333 in Basic Math and pages 23, 47, 61, 92, 119, 151, 182, 215, 256, 274, 318, 339 in Consumer Mathematics. Estimation and mental math can be used throughout. 7
(TEKS, Mathematics Grade 7, 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 Throughout. (B) evaluate the effectiveness of different representations to communicate ideas. While no formal evaluation other than regular testing is required, students communicate answers in practice problems, reinforcement problems, word problems, review problems, application problems, and supplementary problems, as well as in supplementary worktexts. This teaching/reteaching/reinforcement style allows for ample evaluation opportunities. (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. Examples used to teach concepts in each Lesson provide students with patterns and sets of examples from which to draw conjectures. They then apply and validate these conjectures in Exercises and Problem Solving sections. 8