Mathematics Pacing Resource · PDF fileMathematics Pacing Resource Document ... (“ifandonlyif”}statements. Lesson Plans/Print Activities: ... ¾ Sec. 3.5 Proving Lines Parallel

Mathematics Pacing Resource Document

Indianapolis Public Schools Curriculum and Instruction

Geometry – Logic and Proofs Strand Standard: G.LP.1: Understand and describe the structure of and relationships within an axiomatic system (undefined terms, definitions, axioms and postulates, methods of reasoning, and theorems). Understand the differences among supporting evidence, counterexamples, and actual proofs. I can:

x Understand the differences among supporting evidence, counterexamples, and actual proofs. x Understand the structure of an axiomatic system.

Lesson Plans/Print Activities: Standard Geometry - McDougal Littell Textbook

¾ Sec. 1.1 Identify Points, Lines and Planes Challenge problem p. 8 #46

¾ Sec. 1.2 Segments and Congruence Challenge problem p. 14 #36

¾ Sec. 1.3 Use Midpoint and Distance Formulas Mixed Review p. 23 #1-8

¾ Sec. 2.1 Use Inductive Reasoning Problem Solving p. 77 #34, 35

¾ Sec. 2.2 Analyze Conditional Statements Problem Solving P. 84 #35

Web-based Practice:

http://www.math.uiuc.edu/~gfrancis/M302/handouts/postulates.pdf





Honors Geometry – Glencoe McGraw-Hill Textbook

¾ Sec. 1.1 Identify Points, Lines and Planes H.O.T. problems p. 11 #58, 59

¾ Sec. 1.2 Linear Measures H.O.T. problems p. 20 #38, 40

¾ Sec. 1.4 Angle Measure H.O.T. problems #52

¾ Sec. 2.1 Inductive Reasoning and Conjecture Real-World problems p. 95 # 47, 49

¾ Sec. 2.3 Conditional Statements Real-World problems p. 112 #59, 60, 61 H.O.T. problem p. 112 #63, 65



Geometry – Logic and Proofs Strand Standard: G.LP.2: Know precise definitions for angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, and plane. Use standard geometric notation. I can:

x Define angle, circle, perpendicular line, parallel line, and line segment in terms of point, line and plane. x Use proper geometric notation.


¾ Sec. 1.5 Describe Angle Pair Relationships Problem Solving p. 40 #53, 54

¾ Sec. 2.1 Use Inductive Reasoning

¾ Sec. 2.2 Analyze Conditional Statements

¾ Sec. 2.3 Deductive reasoning

¾ Sec. 2.4 Use Postulates and Diagrams Problem Solving problems p. 101 #34-39

¾ Sec. 2.5 Reason Using Properties of Algebra Problem Solving problem p. 110 #33

¾ Sec. 2.6 How Proofs are used in Mathematics: Angles and Segments Problem Solving problem p. 119 #29

Web-based Practice:

x http://www.insidemathematics.org/index.php/high-school-geometry

x New Jersey Center for Learning and Teaching: Geometry: Points, lines, angles, planes presentation and construction worksheet.

http://www.insidemathematics.org/index.php/high-school-geometry



¾ Sec. 2.7 Prove Angle Pair Relationship

Problem Solving p. 129 #36, 37 Honors Geometry – Glencoe McGraw-Hill Textbook

¾ Sec. 1.5 Angle Relationships H.O.T. problem p. 53 #51

¾ Sec. 2.1 Inductive Reasoning and Conjecture P. 95 #48

¾ Sec. 2.5 Postulates and Paragraph Proofs Real-World problem p. 130 #42

¾ Sec. 2.6 Algebraic Proofs Challenge problem p. 140 #37

¾ Sec. 2.7 Proving Segments Relationships H.O.T. problem p. 147 #17

¾ Sec. 2.8 Proving Angle Relationships H.O.T. problem p. 156 #32



Geometry – Logic and Proofs Strand Standard: G.LP.3: State, use, and examine the validity of the converse, inverse, and contrapositive of conditional (“if – then”) and bi-conditional (“if and only if”) statements. I can:

x Understand and use the converse, inverse, contrapositive of conditional (“if – then”} and bi-conditional (“if and only if”} statements. Lesson Plans/Print Activities: Standard Geometry - McDougal Littell Textbook

¾ Sec. 2.2 Analyze Conditional Statements Problem Solving problem p. 84 #35

¾ Sec. 2.3 Deductive Reasoning p. 92 #24

¾ Persuasive Letter Honors Geometry – Glencoe McGraw-Hill Textbook

¾ Sec. 2.3 Conditional Statements Problem Solving p. 112 #59-61, 63, 65

¾ Sec. 2.4 Deductive Reasoning H.O.T. problem p. 122 #45

Web-based Practice:

x www.virtualnerd.com/.../converse-inverse-contrapositive-truth-

example

http://www.virtualnerd.com/.../converse-inverse-contrapositive-truth-example

http://www.virtualnerd.com/.../converse-inverse-contrapositive-truth-example



Geometry – Logic and Proofs Strand Standard: G.LP.4: Develop geometric proofs, including direct proofs, indirect proofs, proofs by contradiction and proofs involving coordinate geometry, using two-column, paragraphs, and flow charts formats. I can:

x Develop geometric proofs using direct and indirect proofs. x Develop geometric proofs using contradiction and proofs involving coordinate geometry. x Develop geometric proofs using a two-column format, a paragraph format and a flow chart format.


¾ Sec. 2.4 Use Postulates and Diagrams p. 101 #34-39

¾ Sec. 2.5 Reason Using Properties of Algebra p. 110 #33

¾ Persuasive Letter

¾ Sec. 2.6 How Proofs are used in Mathematics: Angles and Segments p. 119 #29

¾ Sec. 2.7 Prove Angle Pair Relationships p. 129 #36, 37 Honors Geometry – Glencoe McGraw-Hill Textbook

¾ Sec. 2.5 Postulates and Paragraph Proofs p. 130

Web-based Practice: x feromax.com/cgi-bin/ProveIt.pl

x If need be goggle search geometric proofs and look for ProveIt! Two-Column Proofs Practice Tool



¾ Sec. 2.6 Algebraic Proofs

p. 140 #37

¾ Sec. 2.7 Proving Segments Relationship p. 147 #17

¾ Sec. 2.8 Proving Angle Relationship p. 156 #32

¾ Sec. 3.5 Proving Lines Parallel H.O.T. p. 211 #37



Geometry – Points, Lines, Angles, and Planes Strand Standard: G.PL.1: Identify, justify, and apply properties of planes. I can:

x Identify properties of planes. x Justify properties of planes. x Apply properties of planes.


¾ Not Covered in Quarter One


¾ Sec. 3.1 Parallel Lines and Transversals H.O.T. problem p. 175 #47

Web-based Practice:

x New Jersey Center for Teaching and Learning: Geometry - Points, lines, and Planes Presentation - Points, lines, and Planes Worksheet

x Khan Academy: Geometry

- Introduction to Euclidean Geometry: Specifying planes in three dimensions.

x Virtual Nerd: Geometry

-Fundamentals of Geometry: What is a plane





Geometry – Points, Lines, Angles, and Planes Standard: G.PL.3: Prove and apply theorems about lines and angles, including the following: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent, alternate exterior angles are congruent, and corresponding angles are congruent; when a transversal crosses parallel lines, same side interior angles are supplementary; and points on a perpendicular bisector of a line segment are exactly those equidistant from the endpoints of the segment. I can:

x Prove and apply the theorem about vertical angles are congruent. x Prove and apply the theorem about alternate interior angles are congruent when parallel lines are cut by a transversal. x Prove and apply the theorem about alternate exterior angles are congruent when parallel lines are cut by a transversal. x Prove and apply the theorem about corresponding angles are congruent when parallel lines are cut by a transversal. x Prove and apply the theorem about same side angles are supplementary when parallel lines are cut by a transversal. x Prove and apply the theorem about points on a perpendicular bisector of a line segment are exactly those equidistant from the endpoints of the

segment. Lesson Plans/Print Activities: Standard Geometry - McDougal Littell Textbook

¾ Not Covered in Quarter One Honors Geometry – Glencoe McGraw-Hill Textbook

¾ Sec. 3.2 Angles and Parallel Lines H.O.T. problem p. 183 #42

Web-based Practice:

x New Jersey Center for Teaching and Learning: Geometry - Parallel and Perpendicular Lines Presentation

x Khan Academy: Geometry - Angles and Intersecting Lines: Angles between Intersecting and

Parallel Lines

x Virtual Nerd: Geometry -Fundamentals of Geometry: Angle Pair Relationships



Geometry – Points, Lines, Angles, and Planes Strand Standard: G.PL.4: Know that parallel lines have the same slope and perpendicular lines have opposite reciprocal slopes. Determine if a pair of lines are parallel, perpendicular, or neither by comparing the slopes in coordinate graphs and in equations. Find the equation of a line, passing through a given point that is parallel or perpendicular to a given line.

I can: x Know that parallel lines have the same slope.

x Know that perpendicular lines have opposite reciprocal slopes.

x Determine whether a pair of lines are parallel, perpendicular or neither.

x Write the equation of the line passing through a given point that is parallel or perpendicular to a given line.


¾ Sec. 3.1 Identify Pairs of Lines and Angles ¾ Sec. 3.2 Use Parallel Lines and Transversals ¾ Sec. 3.3 Prove Lines are Parallel ¾ Sec. 3.4 Find and Use Slope of Lines ¾ Sec. 3.5 Write and Graph Equations of Lines ¾ Sec. 2.6 Prove Theorems about Perpendicular Lines


¾ Sec. 3.1 Parallel Lines and Transversals ¾ Sec. 3.2 Angles and Parallel Lines ¾ Sec. 3.3 Slopes of Lines ¾ Sec. 3.4 Equations of Lines ¾ Sec. 3.5 Proving Lines Parallel ¾ Sec. 3.6 Perpendiculars and Distance

Web-based Practice: x New Jersey Center for Teaching and Learning: Geometry

- Parallel and Perpendicular Lines Presentation

x Khan Academy: Geometry - Angles and Intersecting Lines: Angles between Intersecting and

Parallel Lines

x Virtual Nerd: Geometry - Parallel and Perpendicular Lines: Parallel Lines and Transversals



Geometry – Points, Lines, Angles, and Planes Standard: G.PL.5: Explain and justify the process used to construct, with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.), congruent segments and angles, angle bisectors, perpendicular bisectors, altitudes, medians, and parallel and perpendicular lines.

I can: x Explain and justify the process used to construct congruent segments and angles.

x Explain and justify the process used to construct angle bisectors and perpendicular bisectors.

x Explain and justify the process used to construct altitudes and medians.

x Explain and justify the process used to construct parallel and perpendicular lines.


¾ Sec. 1.4 Measure and Classify Angles Honors Geometry – Glencoe McGraw-Hill Textbook

¾ Sec. 1.3 Distance and Midpoint ¾ Sec. 1.4 Angle Measure ¾ Sec. 1.5 Angle Relationships ¾ Sec. 3.5 Proving Lines Parallel

Web-based Practice:

x New Jersey Center for Teaching and Learning: Geometry

- Parallel and Perpendicular Lines Presentation

Documents

Mathematics Pacing Resource · PDF fileMathematics Pacing Resource Document ... (“ifandonlyif”}statements. Lesson Plans/Print Activities: ... ¾ Sec. 3.5 Proving Lines Parallel