A Correlation of Pearson Texas Geometry Digital, 2015


 Caitlin Cameron
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1 A Correlation of Pearson Texas Geometry Digital, 2015 To the Texas Essential Knowledge and Skills (TEKS) for Geometry, High School, and the Texas English Language Proficiency Standards (ELPS)
2 Correlations to the Texas Essential Knowledge and Skills (TEKS): Student Material Subject Subchapter Course Publisher Program Title Program ISBN Chapter 111. Mathematics Subchapter C. High School Geometry, Adopted 2012 (One Credit). Pearson Education, Inc., publishing as Prentice Hall Pearson Texas Geometry, Digital (a) General requirements. Students shall be awarded one credit for successful completion of this course. Prerequisite: Algebra I. (b) Introduction. (1) The desire to achieve educational excellence is the driving force behind the Texas essential knowledge and skills for mathematics, guided by the college and career readiness standards. By embedding statistics, probability, and finance, while focusing on fluency and solid understanding, Texas will lead the way in mathematics education and prepare all Texas students for the challenges they will face in the 21st century. (2) The process standards describe ways in which students are expected to engage in the content. The placement of the process standards at the beginning of the knowledge and skills listed for each grade and course is intentional. The process standards weave the other knowledge and skills together so that students may be successful problem solvers and use mathematics efficiently and effectively in daily life. The process standards are integrated at every grade level and course. When possible, students will apply mathematics to problems arising in everyday life, society, and the workplace. Students will use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution. Students will select appropriate tools such as real objects, manipulatives, paper and pencil, and technology and techniques such as mental math, estimation, and number sense to solve problems. Students will effectively communicate mathematical ideas, reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, and language. Students will use mathematical relationships to generate solutions and make connections and predictions. Students will analyze mathematical relationships to connect and communicate mathematical ideas. Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication. (3) In Geometry, students will build on the knowledge and skills for mathematics in KindergartenGrade 8 and Algebra I to strengthen their mathematical reasoning skills in geometric contexts. Within the course, students will begin to focus on more precise terminology, symbolic representations, and the development of proofs. Students will explore concepts covering coordinate and transformational geometry; logical argument and constructions; proof and congruence; similarity, proof, and trigonometry; two and threedimensional figures; circles; and probability. Students will connect previous knowledge from Algebra I to Geometry through the coordinate and transformational geometry strand. In the logical arguments and constructions strand, students are expected to create formal constructions using a straight edge and compass. Though this course is primarily Euclidean geometry, students should complete the course with an understanding that noneuclidean geometries exist. In proof and congruence, students will use deductive reasoning to justify, prove and apply theorems about geometric figures. Throughout the standards, the term "prove" means a formal proof to be shown in a paragraph, a flow chart, or twocolumn formats. Proportionality is the unifying component of the similarity, proof, and trigonometry strand. Students will use their proportional reasoning skills to prove and apply theorems and solve problems in this strand. The two and threedimensional figure strand focuses on the application of formulas in multistep situations since students have developed background knowledge in two and threedimensional figures. Using patterns to identify geometric properties, students will apply theorems about circles to determine relationships between special segments and angles in circles. Due to the emphasis of probability and statistics in the college and career readiness standards, standards dealing with probability have been added to the geometry curriculum to ensure students have proper exposure to these topics before pursuing their postsecondary education. (4) These standards are meant to provide clarity and specificity in regards to the content covered in the high school geometry course. These standards are not meant to limit the methodologies used to convey this knowledge to students. Though the standards are written in a particular order, they are not necessarily meant to be taught in the given order. In the standards, the phrase "to solve problems" includes both contextual and noncontextual problems unless specifically stated. (5) Statements that contain the word "including" reference content that must be mastered, while those containing the phrase "such as" are intended as possible illustrative examples. Page 1 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
3 (c) Knowledge and Skills. (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (A) apply mathematics to problems arising in everyday life, society, and the workplace (i) apply mathematics to problems arising in everyday life 236 Lesson58 Prob. 2 Assessment 208 Lesson 58 Prob. 2 Got It Assessment 212 Lesson 58 Ex Lesson 43 Prob. 2 Review 173 Lesson 45 Ex. 17 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (A) apply mathematics to problems arising in everyday life, society, and the workplace (ii) apply mathematics to problems arising in society 91 Lesson 31 Prob. 3 Review 92 Lesson 31 Ex. 14 Assessment 69 Lesson 31 Prob. 3 Got It Review 133 Lesson 38 Ex. 29 Review 444 Lesson 104 Ex. 21 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (A) apply mathematics to problems arising in everyday life, society, and the workplace (iii) apply mathematics to problems arising in the workplace 108 Lesson 34 Prob. 1 Review 150 Lesson 41 Ex Lesson 52 Prob. 4 Assessment 174 Lesson 52 Ex. 3 Review 434 Lesson 102 Ex. 19 Page 2 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
4 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (B) use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution (i) use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process Lesson 132 Prob. 5 Review 530 Lesson 132 Ex Lesson 154 Prob. 4 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (B) use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution (ii) use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the reasonableness of the solution Lesson 113 Prob. 4 Review 473 Lesson 113 Ex. 21 Assessment 483 Lesson 145 Ex. 6 Assessment 497 Lesson 146 Ex. 5 Assessment 515 Lesson 153 Ex. 6 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems (i) select tools, including real objects as appropriate, to solve problems 154 Lesson 42 Prob. 1 Review 156 Lesson 42 Ex. 2 Assessment 130 Lesson 42 Prob. 1 Got It Activity Lab 112 Act. Page 3 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
5 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems (ii) select tools, including manipulatives as appropriate, to solve problems 271 Lesson 64 Prob. 2 Review 274 Lesson 64 Ex. 24 Assessment 234 Lesson 64 Prob. 2 Got It (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems (iii) select tools, including paper and pencil as appropriate, to solve problems 339 Lesson 84 Prob. 1 Review 342 Lesson 84 Exs Lesson 36 Prob. 2 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems (iv) select tools, including technology as appropriate, to solve problems 250 Lesson 61 Prob. 1 Review 254 Lesson 61 Ex Lesson 95 Prob. 1 Page 4 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
6 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems (v) select techniques, including mental math as appropriate, to solve problems 523 Lesson 131 Prob. 4 Review 524 Lesson 131 Exs. 19, Lesson 101 Prob. 2 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems (vi) select techniques including estimation as appropriate, to solve problems 576 Lesson 143 Prob. 5 Review 578 Lesson 143 Ex. 16 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems (vii) select techniques, including number sense as appropriate, to solve problems 194 Lesson 51 Prob. 3 Review 197 Lesson 51 Ex. 33 Assessment 315 Lesson 88 Ex. 6 Page 5 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
7 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate (i) communicate mathematical ideas using multiple representations, including symbols as appropriate 321 Lesson 81 Prob. 4 Assessment 271 Lesson 81 Prob. 4 Got It Review 369 Lesson 88 Ex Lesson 92 Prob. 1 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate (ii) communicate mathematical ideas using multiple representations, including diagrams as appropriate 23 Lesson 14 Prob. 1 Review 59 Lesson 23 Ex Lesson 21 Prob. 2 Review 75 Lesson 26 Ex Lesson 39 Prob. 1 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate (iii) communicate mathematical ideas using multiple representations, including graphs as appropriate 124 Lesson 37 Prob. 1 Review 127 Lesson 37 Ex Lesson 85 Prob. 4 Review 361 Lesson 87 Exs. 7 9 Assessment 295 Lesson 85 Prob. 4 Got It Page 6 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
8 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate (iv) communicate mathematical ideas using multiple representations, including language as appropriate 135 Lesson 39 Prob. 1 Review 137 Lesson 39 Exs. 2 4, 5 Assessment 118 Lesson 39 Prob. 1 Got It 304 Lesson 72 Prob. 3 Review 306 Lesson 72 Exs (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate (v) communicate mathematical reasoning using multiple representations, including symbols as appropriate 321 Lesson 81 Prob. 4 Assessment 271 Lesson 81 Prob. 4 Got It Review 369 Lesson 88 Ex Lesson 92 Prob. 1 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate (vi) communicate mathematical reasoning using multiple representations, including diagrams as appropriate 216 Lesson 54 Prob. 3 Review 218 Lesson 54 Ex. 10 Assessment 185 Lesson 54 Prob. 3 Got It 304 Lesson 72 Prob. 3 Review 306 Lesson 72 Exs Page 7 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
9 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate (vii) communicate mathematical reasoning using multiple representations, including graphs as appropriate 124 Lesson 37 Prob. 1 Review 127 Lesson 37 Ex Lesson 85 Prob. 4 Review 361 Lesson 87 Exs. 7 9 Assessment 295 Lesson 85 Prob. 4 Got It (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate (viii) communicate mathematical reasoning using multiple representations, including language as appropriate 73 Lesson 26 Prob. 1 Review 75 Lesson 26 Ex. 7 Assessment 62 Lesson 26 Prob. 1 Got It 135 Lesson 39 Prob. 1 Review 137 Lesson 39 Exs. 2 4, 5 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate (ix) communicate [mathematical ideas'] implications using multiple representations, including symbols as appropriate 321 Lesson 81 Prob. 4 Assessment 271 Lesson 81 Prob. 4 Got It Review 369 Lesson 88 Ex Lesson 92 Prob. 1 Page 8 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
10 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate (x) communicate [mathematical ideas'] implications using multiple representations, including diagrams as appropriate 469 Lesson 113 Prob. 3 Review 473 Lesson 113 Ex Lesson 133 Prob. 3 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate (xi) communicate [mathematical ideas'] implications using multiple representations, including graphs as appropriate 124 Lesson 37 Prob. 1 Review 127 Lesson 37 Ex Lesson 85 Prob. 4 Review 361 Lesson 87 Exs. 7 9 Assessment 295 Lesson 85 Prob. 4 Got It (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate (xii) communicate [mathematical ideas'] implications using multiple representations, including language as appropriate 73 Lesson 26 Prob. 1 Review 75 Lesson 26 Ex. 7 Assessment 62 Lesson 26 Prob. 1 Got It 135 Lesson 39 Prob. 1 Review 137 Lesson 39 Exs. 2 4, 5 Page 9 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
11 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate (xiii) communicate [mathematical reasoning's] implications using multiple representations, including symbols as appropriate 321 Lesson 81 Prob. 4 Assessment 271 Lesson 81 Prob. 4 Got It Review 369 Lesson 88 Ex Lesson 92 Prob. 1 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate (xiv) communicate [mathematical reasoning's] implications using multiple representations, including diagrams as appropriate 469 Lesson 113 Prob. 3 Review 473 Lesson 113 Ex Lesson 133 Prob. 3 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate (xv) communicate [mathematical reasoning's] implications using multiple representations, including graphs as appropriate 124 Lesson 37 Prob. 1 Review 127 Lesson 37 Ex Lesson 85 Prob. 4 Review 361 Lesson 87 Exs. 7 9 Assessment 295 Lesson 85 Prob. 4 Got It Page 10 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
12 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate (xvi) communicate [mathematical reasoning's] implications using multiple representations, including language as appropriate 73 Lesson 26 Prob. 1 Review 75 Lesson 26 Ex. 7 Assessment 62 Lesson 26 Prob. 1 Got It 135 Lesson 39 Prob. 1 Review 137 Lesson 39 Exs. 2 4, 5 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (E) create and use representations to organize, record, and communicate mathematical ideas (i) create representations to organize mathematical ideas 614 Lesson 151 Prob. 2 Review 640 Lesson 156 Exs Lesson 25 Prob. 3 Review 69 Lesson 25 Exs. 7 8 Assessment 57 Lesson 25 Prob. 3 Got It part a (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (E) create and use representations to organize, record, and communicate mathematical ideas (ii) create representations to record mathematical ideas 180 Lesson 47 Prob. 2 Review Lesson 47 Exs. 8 11, 13, 15, 16 Assessment 489 Lesson 146 Ex Lesson 151 Prob. 2 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (E) create and use representations to organize, record, and communicate mathematical ideas (iii) create representations to communicate mathematical ideas 231 Lesson 57 Prob. 4 Review 440 Lesson 103 Ex. 30a 561 Lesson 141 Prob. 4 Review 563 Lesson 141 Ex. 13 Page 11 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
13 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (E) create and use representations to organize, record, and communicate mathematical ideas (iv) use representations to organize mathematical ideas 394 Lesson 93 Prob. 2B Review 583 Lesson 144 Ex Lesson 144 Prob. 2 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (E) create and use representations to organize, record, and communicate mathematical ideas (v) use representations to record mathematical ideas Lesson 25 Prob. 3 Review 212 Lesson 53 Ex Lesson 65 Prob. 2 Review 404 Lesson 94 Ex. 22 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (E) create and use representations to organize, record, and communicate mathematical ideas (vi) use representations to communicate mathematical ideas 561 Lesson 141 Prob. 4 Review 563 Lesson 141 Exs Assessment 456 Lesson 141 Prob. 4 Got It 567 Lesson 142 Prob. 1 Review 570 Lesson 142 Ex. 19 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (F) analyze mathematical relationships to connect and communicate mathematical ideas (i) analyze mathematical relationships to connect mathematical ideas 540 Lesson 134 Prob. 1 Review 543 Lesson 134 Exs Assessment 440 Lesson 134 Prob. 1 Got It 427 Lesson 101 Prob. 6 Review 428 Lesson 101 Ex. 14 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (F) analyze mathematical relationships to connect and communicate mathematical ideas (ii) analyze mathematical relationships to communicate mathematical ideas 381 Lesson 91 Prob. 2 Page 12 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
14 Review Lesson 91 Exs. 15, 21 Assessment 318 Lesson 91 Prob. 2 Got It 599 Lesson 147 Prob. 2 Review 601 Lesson 147 Exs. 1 3 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication (i) display mathematical ideas using precise mathematical language in written or oral communication 52 Lesson 22 Prob. 4 Review 54 Lesson 22 Exs Assessment 39 Lesson 22 Prob. 4 Got It 581 Lesson 144 Prob. 4 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication (ii) display mathematical arguments using precise mathematical language in written or oral communication 489 Lesson 121 Prob. 4 Review 564 Lesson 141 Ex. 22 Assessment 399 Lesson 121 Prob. 4 Got It 74 Lesson 26 Prob. 5 Review 331 Lesson 82 Ex. 17 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication (iii) explain mathematical ideas using precise mathematical language in written or oral communication 221 Lesson 55 Prob. 2 Review 222 Lesson 55 Ex. 6 Assessment 190 Lesson 56 Prob. 2 Got It 103 Lesson 33 Prob. 3 Review 105 Lesson 33 Ex. 20 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication (iv) explain mathematical arguments using precise mathematical language in written or oral communication 231 Lesson 57 Prob. 5 Review 233 Lesson 57 Ex. 9 Page 13 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
15 Assessment 203 Lesson 57 Prob. 5 Got It 489 Lesson 121 Prob. 4 Review 491 Lesson 121 Ex. 14 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication (v) justify mathematical ideas using precise mathematical language in written or oral communication 67 Lesson 25 Prob. 1 Review 151 Lesson 41 Exs Assessment 56 Lesson 25 Prob. 1 Got It 276 Lesson 65 Prob. 1 Assessment 240 Lesson 65 Prob. 1 Got It (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication (vi) justify mathematical arguments using precise mathematical language in written or oral communication 149 Lesson 41 Prob. 3 Review 172 Lesson 45 Ex. 5 Assessment 125 Lesson 65 Prob. 3 Got It 112 Lesson 35 Prob. 1 Review 114 Lesson 35 Ex. 1 (2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one and twodimensional coordinate systems to verify geometric conjectures. The student is expected to: (A) determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in one and twodimensional coordinate systems, including finding the midpoint (i) determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in onedimensional coordinate systems, including finding the midpoint Lesson 12 Prob. 4 Lesson 12 Prob. 6 Review Lesson 12 Exs. 6, 13 15, Assessment 9 Lesson 12 Prob. 4 Got It, Prob. 6 Got It Page 14 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
16 (2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one and twodimensional coordinate systems to verify geometric conjectures. The student is expected to: (A) determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in one and twodimensional coordinate systems, including finding the midpoint (ii) determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in twodimensional coordinate systems, including finding the midpoint Lesson 51 Prob. 2 Lesson 51 Prob. 3 Review Lesson 51 Exs. 1 6, 7, 33, 36, 37 Assessment 166 Lesson 51 Prob. 2 Got It, Prob. 3 Got It (2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one and twodimensional coordinate systems to verify geometric conjectures. The student is expected to: (B) derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines (i) derive the distance formula 194 Lesson 51 Prob. 4 Review 197 Lesson 51 Exs. 34, 35 (2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one and twodimensional coordinate systems to verify geometric conjectures. The student is expected to: (B) derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines (ii) use the distance formula to verify geometric relationships, including congruence of segments Lesson 71 Prob. 1 Lesson 73 Prob. 1 Review Lesson 71 Exs. 1 3, 7 10, 11 Lesson 73 Exs. 13, 15, 18, 20 Assessment 252 Lesson 71 Prob. 1 Got It Page 15 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
17 (2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one and twodimensional coordinate systems to verify geometric conjectures. The student is expected to: (B) derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines (iii) use the distance formula to verify geometric relationships, including parallelism or perpendicularity of pairs of lines Lesson 71 Prob. 3 Lesson 101 Prob. 6 Review Lesson 71 Ex. 4 Lesson 101 Ex. 14 Assessment Lesson 71 Prob. 3 Got It Lesson 101 Prob. 6 Got It (2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one and twodimensional coordinate systems to verify geometric conjectures. The student is expected to: (B) derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines (iv) derive the slope formula 124 Lesson 37 Prob. 1 Review 127 Lesson 37 Ex. 16 (2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one and twodimensional coordinate systems to verify geometric conjectures. The student is expected to: (B) derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines (v) use the slope formula to verify geometric relationships, including parallelism or perpendicularity of pairs of lines Lesson 71 Prob. 2 Lesson 71 Prob. 4 Lesson 73 Prob. 2 Review Lesson 71 Exs Lesson 72 Ex. 7 Lesson 73 Exs. 17, 21 Assessment Lesson 71 Prob. 2 Got It Lesson 73 Prob. 2 Got It Page 16 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
18 Lesson 38 Prob. 1 Lesson 38 Prob. 3 Review 132 Lesson 38 Exs. 1, 2, 7, 8 (2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one and twodimensional coordinate systems to verify geometric conjectures. The student is expected to: (B) derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines (vi) derive the midpoint formula 193 Lesson 51 Prob. 1 Review 197 Lesson 51 Ex. 32 (2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one and twodimensional coordinate systems to verify geometric conjectures. The student is expected to: (B) derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines (vii) use the midpoint formula to verify geometric relationships Lesson 71 Prob. 3 Lesson 71 Prob. 4 Lesson 73 Prob. 1 Lesson 73 Prob. 2 Review Lesson 71 Exs. 5, 27, 30 Lesson 73 Exs. 14, 16, 23 Assessment 266 Lesson 73 Ex. 3 (2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one and twodimensional coordinate systems to verify geometric conjectures. The student is expected to: (C) determine an equation of a line parallel or perpendicular to a given line that passes through a given point (i) determine an equation of a line parallel or perpendicular to a given line that passes through a given point Lesson 38 Prob. 2 Lesson 38 Prob. 4 Review Lesson 38 Exs. 3 6, 9 11, 12, Lesson 38 Prob. 2 Got It Assessment 113 Lesson 38 Prob. 4 Got It Page 17 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
19 (3) Coordinate and transformational geometry. The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and nonrigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity). (A) describe and perform transformations of figures in a plane using coordinate notation (i) describe transformations of figures in a plane using coordinate notation Lesson 81 Prob. 4 Lesson 82 Prob. 2 Lesson 83 Prob. 2 Lesson 87 Prob. 2 Lesson 87 Prob. 4A Review Lesson 81 Exs. 12, 17, 22, 23 Lesson 85 Exs. 1 6, Lesson 87 Exs. 7 9 Assessment Lesson 82 Exs. 3, Lesson 86 Prob. 3 Lesson 88 Prob. 2 Lesson 88 Prob. 5 Lesson 92 Prob. 2 Review Lesson 86 Exs. 1 3, 5 6 Lesson 88 4, 5, 11, 12, 14 Lesson 92 Exs. 4 6 (3) Coordinate and transformational geometry. The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and nonrigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity). (A) describe and perform transformations of figures in a plane using coordinate notation (ii) perform transformations of figures in a plane using coordinate notation Lesson 81 Prob. 3 Lesson 82 Prob. 2 Lesson 83 Prob. 2 Lesson 87 Prob. 2 Review Lesson 81 Exs. 15, 20, 21 Lesson 82 Exs. 1 6, Lesson 83 Exs. 1 3, 9, 17 Lesson 87 Exs. 7, 8, 13, 15, Lesson 87 Prob. 4B Lesson 88 Prob. 1 Lesson 88 Prob. 3 Lesson 92 Prob. 1 Review Lesson 88 Exs. 1 3, 6 7 Lesson 92 Exs. 1 3 Page 18 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
20 (3) Coordinate and transformational geometry. The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and nonrigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity). (B) determine the image or preimage of a given twodimensional figure under a composition of rigid transformations, a composition of nonrigid transformations, and a composition of both, including dilations where the center can be any point in the plane (i) determine the image or preimage of a given twodimensional figure under a composition of rigid transformations including dilations where the center can be any point in the plane Lesson 85 Prob. 3, Lesson 85 Prob. 4 Lesson 87 Prob. 3 Review Lesson 85 Exs. 8 17, 22, 23 Lesson 87 Exs. 18, 32 Assessment 295 Lesson 85 Prob. 3 Got It, Prob. 4 Got It 345 Lesson 85 Prob Lesson 85 Prob. 2 Review 348 Lesson 85 Exs (3) Coordinate and transformational geometry. The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and nonrigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity). (B) determine the image or preimage of a given twodimensional figure under a composition of rigid transformations, a composition of nonrigid transformations, and a composition of both, including dilations where the center can be any point in the plane (ii) determine the image or preimage of a given twodimensional figure under a composition of nonrigid transformations, including dilations where the center can be any point in the plane 366 Lesson 88 Prob. 3, Prob. 4 Review Lesson 88 Exs. 1 3, 6, 7, 8 10 Assessment 313 Lesson 88 Prob. 3 Got It Page 19 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
21 (3) Coordinate and transformational geometry. The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and nonrigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity). (B) determine the image or preimage of a given twodimensional figure under a composition of rigid transformations, a composition of nonrigid transformations, and a composition of both, including dilations where the center can be any point in the plane (iii) determine the image or preimage of a given twodimensional figure under a composition of both, including dilations where the center can be any point in the plane Lesson 87 Prob. 5 Lesson 92 Prob. 1 Review Lesson 87 Exs , 20 Lesson 92 Exs. 1 3 Assessment Lesson 87 Prob. 5 Got It Lesson 92 Prob. 1 Got It (3) Coordinate and transformational geometry. The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and nonrigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity). (C) identify the sequence of transformations that will carry a given preimage onto an image on and off the coordinate plane (i) identify the sequence of transformations that will carry a given preimage onto an image on the coordinate plane Lesson 86 Prob. 3 Review Lesson 86 Exs. 5, 6, 10 Assessment 301 Lesson 86 Prob. 3 Got It 387 Lesson 92 Prob. 2 Review 389 Lesson 92 Exs. 4 6 (3) Coordinate and transformational geometry. The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and nonrigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity). (C) identify the sequence of transformations that will carry a given preimage onto an image on and off the coordinate plane (ii) identify the sequence of transformations that will carry a given preimage onto an image off the coordinate plane Lesson 82 Prob. 3 Lesson 83 Prob. 4 Lesson 92 Prob. 4 Review Lesson 82 Ex. 7 Lesson 83 Exs. 15, 21, 22 Lesson 92 Exs. 7 9 Page 20 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
22 Assessment Lesson 82 Prob. 3 Got It Lesson 83 Prob. 4 Got It Lesson 92 Prob. 4 Got It (3) Coordinate and transformational geometry. The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and nonrigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity). (D) identify and distinguish between reflectional and rotational symmetry in a plane figure (i) identify reflectional symmetry in a plane figure 339 Lesson 84 Prob. 1 Assessment 288 Lesson 84 Prob. 1 Got It Review Lesson 84 Exs. 1, 14 18, 22 24, 36, Lesson 84 Prob. 3 (3) Coordinate and transformational geometry. The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and nonrigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity). (D) identify and distinguish between reflectional and rotational symmetry in a plane figure (ii) identify rotational symmetry in a plane figure 339 Lesson 84 Prob. 2 Review Lesson 84 Exs. 1, 19, Assessment 289 Lesson 84 Prob. 2 Got It 340 Lesson 84 Prob. 3 (3) Coordinate and transformational geometry. The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and nonrigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity). (D) identify and distinguish between reflectional and rotational symmetry in a plane figure (iii) distinguish between reflectional and rotational symmetry in a plane figure 340 Lesson 84 Prob. 3 Review Lesson 84 Exs. 2 13, 20, 21, 28 31, Assessment 289 Lesson 84 Prob. 3 Got It Page 21 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
23 (4) Logical argument and constructions. The student uses the process skills with deductive reasoning to understand geometric relationships. (A) distinguish between undefined terms, definitions, postulates, conjectures, and theorems (i) distinguish between undefined terms, definitions, postulates, conjectures, and theorems 74 Lesson 26 Prob. 4 Review 77 Lesson 26 Ex Assessment 63 Lesson 26 Prob. 4 Got It 6 Lesson 11 Prob. 3 Assessment 3 Lesson 11 Prob. 3 Got It (4) Logical argument and constructions. The student uses the process skills with deductive reasoning to understand geometric relationships. (B) identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse (i) identify the validity of the converse of a conditional statement 52 Lesson 22 Prob. 4 Review Lesson 22 Exs Assessment 39 Lesson 22 Prob. 4 Got It (4) Logical argument and constructions. The student uses the process skills with deductive reasoning to understand geometric relationships. (B) identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse (ii) identify the validity of the inverse of a conditional statement 52 Lesson 22 Prob. 4 Review 54 Lesson 22 Exs Assessment 39 Lesson 22 Prob. 4 Got It Page 22 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
24 (4) Logical argument and constructions. The student uses the process skills with deductive reasoning to understand geometric relationships. (B) identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse (iii) identify the validity of the contrapositive of a conditional statement 52 Lesson 22 Prob. 4 Review 54 Lesson 22 Exs Assessment 39 Lesson 22 Prob. 4 Got It (4) Logical argument and constructions. The student uses the process skills with deductive reasoning to understand geometric relationships. (B) identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse (iv) determine the validity of the converse of a conditional statement 52 Lesson 22 Prob. 4 Review Lesson 22 Exs Assessment 39 Lesson 22 Prob. 4 Got It (4) Logical argument and constructions. The student uses the process skills with deductive reasoning to understand geometric relationships. (B) identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse (v) determine the validity of the inverse of a conditional statement 52 Lesson 22 Prob. 4 Review 54 Lesson 22 Exs Assessment 39 Lesson 22 Prob. 4 Got It Page 23 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
25 (4) Logical argument and constructions. The student uses the process skills with deductive reasoning to understand geometric relationships. (B) identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse (vi) determine the validity of the contrapositive of a conditional statement 52 Lesson 22 Prob. 4 Review 54 Lesson 22 Exs Assessment 39 Lesson 22 Prob. 4 Got It (4) Logical argument and constructions. The student uses the process skills with deductive reasoning to understand geometric relationships. (B) identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse (vii) recognize the connection between a biconditional statement and a true conditional statement with a true converse 56 Lesson 23 Prob. 1, Prob. 2, Prob. 3 Review 45 Lesson 23 Exs. 1 4, 8 Assessment Lesson 23 Prob. 1 Got It, Prob. 2 Got It Lesson 23 Prob. 3 Got It (4) Logical argument and constructions. The student uses the process skills with deductive reasoning to understand geometric relationships. (C) verify that a conjecture is false using a counterexample (i) verify that a conjecture is false using a counterexample 46 Lesson 21 Prob. 5 Review 47 Lesson 21 Exs Assessment 33 Lesson 21 Prob. 5 Got It Page 24 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
26 (4) Logical argument and constructions. The student uses the process skills with deductive reasoning to understand geometric relationships. (D) compare geometric relationships between Euclidean and spherical geometries, including parallel lines and the sum of the angles in a triangle (i) compare geometric relationships between Euclidean and spherical geometries, including parallel lines 135 Lesson 39 Prob. 1 Review 138 Lesson 39 Exs. 6, 8, 10 Assessment 118 Lesson 39 Prob. 1 Got It 137 Lesson 39 Prob. 4 Review Lesson 39 Exs. 2, 9 (4) Logical argument and constructions. The student uses the process skills with deductive reasoning to understand geometric relationships. (D) compare geometric relationships between Euclidean and spherical geometries, including parallel lines and the sum of the angles in a triangle (ii) compare geometric relationships between Euclidean and spherical geometries, including the sum of the angles in a triangle 136 Lesson 39 Prob. 2, Prob. 3 Review Lesson 39 Exs. 1, 3, 4, 5, 15 Lesson 39 Prob. 2 Got It 118 Assessment Lesson 39 Prob. 3 Got it 119 (5) Logical argument and constructions. The student uses constructions to validate conjectures about geometric figures. (A) investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools (i) investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal 95 Lesson 32 Prob. 1 Review 100 Lesson 32 Ex. 20 Assessment 74 Lesson 32 Prob. 1 Got It Page 25 of 228 Pearson Education, Inc., publishing as Prentice Hall: Student Material
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