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Geometry Pre-AP – Clements HS – FBISD – 1st 9 weeks 2014 – 2015 (Subject to Change) Monday August 25 Review Tuesday 26 Inductive, Deductive, prerequisite skills from Algebra I. Establish classroom norms, hand out Syllabus Intuitive, & Counterexample HW: WS – Do You Remember? Obj: Compare and contrast inductive, deductive, and intuitive reasoning. Understand and construct counterexamples. In Class: G5 Questions HW: 1-1 Patterns and Inductive Reasoning: page 6 #1-12; 17-24; 31-39 WS – Kinds of Reasoning Wednesday 27 2-1Conditional Statements Obj: Identify the hypothesis and conclusion of a conditional statement. Construct the converse of a conditional statement. Add in the idea of a venn diagram. HW: Page 83 #2-58 even Page 84 #59-61 WS – Rewriting If Then Statements – For odds, write venn diagrams on the back Thursday 28 2-2 Biconditionals & Friday 29 5-4 Negate, Inverse, Definitions Contrapositive Obj: Compare and contrast biconditionals and definitions with airline round trips. HW: Page 90 # 1, 2, 6, 7-17 odd; 18-22 even; 32-38; 45; 47 Obj: Negate statements. Identify and construct the inverse and contrapositive of a conditional statement. Determine statements that are equivalent. WS - Big Sky Airlines . Quiz over Alg. Review page 6 and Kinds of Reasoning, Conditionals & Converse HW: WS Equivalent Statements Page 283 #1-9; 24-29; 34-36 Pg 85 # 53 September 1 2 2-3 Deductive Reasoning & 3 Chain Rule (Extension of 2-3) 41-3 Points, Lines, Planes Obj: Apply equivalent conditional statements, law of syllogism, and the chain rule to solve logic puzzles Obj: Develop an awareness of the structure of a mathematical system, connecting definitions and postulates. Symbolic Logic Proofs Labor Day No School Obj: Understand and apply deductive reasoning in writing symbolic logic proofs. Work Luann puzzle in class HW: Finish WS – Valid/Invalid Reasoning & Error Analysis WS – Symbolic Logic Proofs 8 Test Reasoning and Algebra Review Finish HW from Thursday Page 19 #2-24 even; 30-44 even; 46-49 all; 55-60 all; 6567 all 15 Pythagorean Theorem and ( Hand out Ad and conditional statement project, Due Friday) 9 1-4 Segments, Rays, Parallel Lines and Planes Obj: Compare and contrast segments, rays, and lines. Define relationships between lines and planes. HW: Page 25 # 4-10 all; 11-35 all; 39, 44, 45 Page 20 #50-54 16 1-8 The Coordinate Plane Simplifying Radicals Obj: Review Pythagorean Theorem and simplifying radicals. Work an example where the sides of the rectangle are algebraic expressions HW: WS – Simplifying Radical Expressions & Pythagorean Theorem WS – Distance & Segment Measure #15-20 (more practice over 1-5) Obj: Apply Pythagorean Theorem to find the distance between two points on the coordinate plane. Develop the midpoint formula. Emphasize that the midpoint is the “average” of the endpoints. HW: Page 56 #3-9 odd; 10-17 all; 19-31 odd; 41-43, 45, 48 (change directions so that answers are exact, not nearest tenth) Quiz over 1-5, Subsets of Lines Perfect Squares Quiz Part 1 HW: WS – Working Logic Puzzles I & II Work 3 more symbolic logic proofs 5 Review for Test Obj: Review Objectives for Reasoning Test HW: Study for Test HW: Page 19 #2-24 even; 3044 even; 46-49 all; 55-60 all; 65-67 all (due Tuesday) AD project Due 10 1-5 Measuring Segments and 11 1-5 continued Subsets of Lines Obj: Find length of a segment on a number line. Integrate the terms midpoint and bisect. Apply set theory to extend knowledge of segments, rays, and lines. HW: Page 33 #1-12 all; 29-33 all; 36, 37 WS – Subsets of Lines Obj: Connect algebraic descriptions to geometric sets of points and review factoring concepts HW: WS – Subsets of Lines, Algebraic Connections WS – Distance and Segment Measure #1-14 (work 11 & 13 as examples in class) 17 1-8 Continued – Distance 18 1-6 Angles and 1-7 Angle Formula & Pythagorean Theorem Obj: Apply Pythagorean Theorem to find the distance between two points on the coordinate plane. Develop the midpoint formula. Emphasize that the midpoint is the “average” of the endpoints. HW: WS – Distance Formula & Pythagorean Theorem (work problems 11 & 13 in class) Bisector (Example 4) Perfect Squares Quiz Part 2 Obj: Compare and contrast concepts for angles with concepts for segments. WS – Overlapping Segments & Angles (done in class) Sample clock problems Quiz on segment distance, Pythagorean Thm, & midpoint HW: Page 40 #13--40; 42-45; 47 Page 47 #9-12; 21; 25 Page 112 #12, 13; 30-32 (DUE TUESDAY) 12 Obj: Review multiplying binomials and factoring quadratics. Quiz, 1-3, and 1-4. HW: WS – Fun with Factoring Progress Report 19 Review Obj: Synthesize previous material taught for review. Review perimeter, circumference, and area. Give problems to kids as examples of the types of problems they will be responsible for in the next unit. 1-9 page 65 #6-11 all; 17-23 odd; 26, 27, 29, 31, 37, 38, 39, 4750, 52, 53, 58-63, 66-70 (DUE TUESDAY) HW: Study! 22 Test Unit 1: 1-3, 4, 5, 8 and Pythagorean Theorem HW: Finish textbook homework from Thursday September 18th 23 Complementary & 24 Angles (continued) Supplementary Angles Obj: Integrate algebra with measures of angle pairs. Understand and apply overlapping segment and overlapping angle theorems. Identify previous definitions, postulates, and theorems in drawing conclusions. Obj: Integrate solving systems of equations with solving for measures of angles. Identify previous definitions, postulates, and theorems in drawing conclusions. HW: WS – Angle Pairs WS – Drawing Conclusions 2 HW: WS –Comp & Supp. Angles WS – Drawing Conclusions 1 30 October 1 Segment and Angle Proofs 3-1 Properties of Parallel Lines (angles created by transversals) Review for Test Work 2 more sample proofs. HW: WS - Proofs #1, 7, 8 WS – Drawing Conclusions 4 Obj: Define and identify pairs of angles created by a transversal and two parallel lines. Draw conclusions given parallel lines. HW: Page 131 #1-8; 11-18; 23-25; 30-36 WS – Finding Angle Measures 1 (HW due Friday) Proofs Obj: Write flow proofs including segment and angle concepts. Introduce proofs using substitution and transitive properties. (work 2 of the 4 samples Quiz (over assignments from section 1-6, 1-7, and 19) 26 Holiday – Fort Bend County Fair Day HW: WS – Drawing Conclusions 3 WS – Flow-proofs (substitution & transitive) WS – Supplements and Complements 29 Obj: Write flow proofs including segment and angle concepts. 25 Segment and Angle Go over Quiz & previous HW 2 3 3-2 Proving Lines Parallel || Test 1-9 and Angles Line proofs Obj: Determine the conditions to prove two lines are parallel. Write parallel line proofs. 2 sample proofs in class – 4 proofs for homework HW: Page 137 #1-8; 10-21 (identify transversal line); 2426; 41, 43 Drawing Conclusions // lines and proofs Obj: Identify previous definitions, postulates, and theorems in drawing conclusions. HW: WS – Proofs 2-5 HW: Drawing Conclusions 5 Finish flow proofs 8 Review then quiz 9 3-4 Parallel Lines & 10 3-5 The Polygon Angle- Triangle Angle-Sum Theorem Sum Theorems Obj: Prove the sum of the angles of a triangle is 180 and then extend that concept to the exterior angle of a triangle. Obj: Use inductive reasoning to understand the theorems about the sum of the interior and the sum of the exterior angles of convex polygons. Page 150 #1-6; 10-20; 23-28; 30-32; 38 WS – Test Review Page 161 #8-27;32-36; 3844; 47-53 Progress Report 6 3-1 & 3-2 Continued 7 3-3 Parallel and Perpendicular Remember that sum of angles of a triangle is 180° Lines Obj: Apply parallel line concepts in solving algebraic problems and in writing proofs. HW: WS – Crook Problems WS – Finding Angle Measures 2 Parallel Line Proofs 1-4 Obj: Understand and apply relationships between lines in a plane and in space. Quiz over || lines & angle pairs and a proof Page 143 #4-10; 14-21 WS – Parallel Lines & Angles Proofs 5-8 Proofs 9-12 WS – 4-2 Practice & Enrichment 13 Review Obj: Synthesize previous material to create a review for the test over chapter 3. 14 Obj: Compare and contrast four views of a function – graph, table, description, and equation. Hand out Equations of Lines Review Sheet HW: Finish test review 15 PSAT Testing Test over Chapter 3 Hw: Graphing Equations of Lines WS and pg. 177 (1-11 odd, 16, 18, 25-28, 40-43) – Due Thursday Take home equations of lines matching activity, due Thursday for daily grade Work on equation of lines matching activity, due tomorrow for daily grade. 16 3-6 Lines in the 17 3-7 More Equations of Coordinate Plane Lines Obj: Graph lines using intercepts, a point and a slope, or the slope and y-intercept. Obj: Write equations of lines that are parallel or perpendicular to a given line, including bisectors of segments. HW: Page 178 #12-15; 2023; 39, 45, 46, 48, 49, 50 WS More Writing Equations HW: Writing Equations WS and Page 169 (15 – 32, 38, 54) Equations of Lines Matching Activity Due End of 1st Nine Weeks