GEOMETRY - Pasco School District...between postulates and theorems Use the distance theorem to solve...

1 Updated: Thursday, December 02, 2010

Mathematics Curricular Guide

GEOMETRY

2010-2011 SCHOOL YEAR

Pasco School District Geometry 2010 – 2011 School Year


MATHEMATICS SCOPE & SEQUENCE

Unit Title Dates Page 1. Building the Basics (Ch 1) ......................................................................................................................................................... 3

2. Conjectures, Inductive and Deductive, Oh My! (Ch 2) .............................................................................................................. 5

3. Perpendicular and Parallel Lines (Ch 3) .................................................................................................................................... 7

4. Chapter 12 ............................................................................................................................................................................... 9

5. Chapter 7 ............................................................................................................................................................................... 11

6. Congruent Triangles (Ch 4) ..................................................................................................................................................... 13

7. Cutting Up the Triangle (Ch 5) ................................................................................................................................................ 15

8. Exploring Quadrilaterals (Ch 6) .............................................................................................................................................. 18

9. Similarity (Ch 8) ...................................................................................................................................................................... 20

10. Right Triangles and Trigonometry (Ch 9) ................................................................................................................................ 22

11. Getting Around to Circles (Ch 10) .......................................................................................................................................... 24

12. Chapter 11 ............................................................................................................................................................................. 26



Unit Name: Building the Basics (Ch 1) [Starting Date] [Ending Date]

Standard Lesson & objective Days Formative Assessments/

Assignments Alignment Notes

G.1.A Distinguish between inductive and deductive reasoning. G.1.B Use inductive reasoning to make conjectures, to test the plausibility of a geometric statement, and to help find a counterexample.

1.1 Define and use inductive reasoning to make conjectures and find counterexamples.

1 day Additional Resources: Chapter Resource Books: Reteach With Practice 1.1

G.2.D Describe the intersections of lines in the plane and in space, of lines and planes, and of planes in space. G.1.F Distinguish between definitions and undefined geometric terms and explain the role of definitions, undefined terms, postulates (axioms), and theorems.

1.2 Understand and use the basic undefined terms and defined terms of geometry And sketch the intersections of lines and planes.

2 days Focus on vocabulary terms.

G.1.F Distinguish between definitions and undefined geometric terms and explain the role of definitions, undefined terms, postulates (axioms), and theorems. G.4.B Determine the coordinates of a point that is described geometrically.

1.3 Understand the difference between postulates and theorems Use the distance theorem to solve problems.

1 day

G.2.B Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal.

1.4 Use and Classify angles. 1 day Introduction to develop later angle theorems.

G.2.C Explain and perform basic compass and straightedge constructions related to parallel and perpendicular lines. G.4.B Determine the coordinates of a point that is described geometrically.

1.5 Use the midpoint formula to solve problems. Introduce basic constructions using the segment bisector/midpoint and angle bisector constructions.

2 days Geometer’s Sketchpad Introduction to construction to develop toward G.2.C


1.6 Identify vocabulary related to angles

1 day





G.4.C Verify and apply properties of triangles and quadrilaterals in the coordinate plane.

1.7 Find the perimeter and area of common plane figures

1 day


Activity 1.6 pg. 43, introduce Geometer’s Sketchpad. Construct intersecting lines and measure the angle formed by the lines.

2 days

G.6.D Predict and verify the effect that changing one, two, or three linear dimensions has on perimeter, area, volume, or surface area of two- and three dimensional figures

Lesson TBD Suggest use Geometer’s Sketchpad

1 day

TBD 3 days

Chapter Review and Assessment 2 days

Process Standards Addressed:

G.6.E Use different degrees of precision in measurement, explain the reason for using a certain degree of precision, and apply estimation strategies to

obtain reasonable measurements with appropriate precision for a given purpose.

Assessment: (type) Chapter Review and Assessment



Unit Name: Conjectures, Inductive and Deductive, Oh My! (Ch 2)

[Starting Date] [Ending Date]



G.1.D Write the converse, inverse, and contrapositive of a valid proposition and determine their validity.

2.1 Recognize and analyze a conditional statement and write postulates using conditional statements.

2 days Supplemental Materials: Chapter Resource Books: Lesson 2.1 (A, B, C)

G.1.F Distinguish between definitions and undefined geometric terms and explain the role of definitions, undefined terms, postulates (axioms), and theorems. G.1.D Write the converse, inverse, and contrapositive of a valid proposition and determine their validity.

2.2 Recognize and use definitions.

1 day

G.1.A Distinguish between inductive and deductive reasoning.

Act 2.3 or a Sudoku lesson to use deductive reasoning

1 day

G.1.A Distinguish between inductive and deductive reasoning. G.1.D Write the converse, inverse, and contrapositive of a valid proposition and determine their validity.

2.3 Apply the laws of logic to inductive and deductive reasoning.


G.1.C Use deductive reasoning to prove that a valid geometric statement is true.

2.4 Use properties of algebra to justify segment and angle relationships.

1 day Standard is developed with more detail over throughout the text.

G.1.E Identify errors or gaps in a mathematical argument and develop counterexamples to refute invalid statements about geometric relationships.

2.5 Justify statements and write reasons for the steps in a proof.



2.6 Use angle congruence properties and prove properties of special pairs of angles.

2 days

Chapter Review and Assessment

2 days


G.7.A Analyze a problem situation and represent it mathematically.



G.7.B Select and apply strategies to solve problems.

G.7.E Read and interpret diagrams, graphs, and text containing the symbols, language, and conventions of mathematics.

G.7.F Summarize mathematical ideas with precision and efficiency for a given audience and purpose.

G.7.G Synthesize information to draw conclusions and evaluate the arguments and conclusions of others.

G.7.H Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures.




Unit Name: Perpendicular and Parallel Lines (Ch 3)




G.2.A Know, prove, and apply theorems about parallel and perpendicular lines. G.2.B Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal. G.2.C Explain and perform basic compass and straightedge constructions related to parallel and perpendicular lines.

3.1 Identify relationships between lines and angles formed by transversals.

1 day

G.2.A Know, prove, and apply theorems about parallel and perpendicular lines.

3.2 Prove results about perpendicular lines.

1 day

G.2.C Explain and perform basic compass and straightedge constructions related to parallel and perpendicular lines

Act 3.3 Parallel Lines and Angles using Geometer’s Sketchpad

1 day

G.2.A Know, prove, and apply theorems about parallel and perpendicular lines. G.2.B Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal.

3.3 Prove and use results about parallel lines and transversals

2 days

G.4.B Determine the equation of a line in the coordinate plane that is described geometrically, including a line through two points, a line through a given point parallel to a given line, and a line through a given point perpendicular to a given line.

Review writing linear equations 1 day Additional Support: Pg 124 (Chapter 2: Algebra Review) pg 793 (Skill Review Handbook) Chapter 5 in Algebra 1 textbook

G.2.A Know, prove, and apply theorems about parallel and perpendicular lines. G.2.B Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal.

3.4 Prove two lines are parallel and use properties of parallel lines to solve problems.

1 day





G.2.A Know, prove, and apply theorems about parallel and perpendicular lines. G.2.B Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal. G.2.C Explain and perform basic compass and straightedge constructions related to parallel and perpendicular lines

3.5 Use properties of parallel lines to construct parallel lines.

2 days





G.7.C Evaluate a solution for reasonableness, verify its accuracy, and interpret the solution in the context of the original problem.








Unit Name: Chapter 12 [Starting Date] [Ending Date]



11.2 Area of a Polygon 1 day Chose assignments with apothem and side given. Lessons for solving for side measurements with trig ratios are later.

Necessary review to developing understanding of formulas for surface area involving polygons

G.3.J Describe prisms, pyramids, parallelepipeds, tetrahedral, and regular polyhedral in terms of their faces, edges, vertices, and properties. G.3.K Analyze cross-sections of cubes, prisms, pyramids, and spheres and identify the resulting shapes.

12.1: Exploring Solids Use properties of polyhedron and Euler’s Theorem

2 days

G.6. C Apply formulas for surface area and volume of three-dimensional figures to solve problems.

12.2: Surface area of prisms & cylinders

3 days


12.3 Surface area of pyramids and cones

2 days


12.4 Volume of prisms and cylinders

2 days


12.5 Volume of pyramids and cones

2 days


12.6 Surface area and volume of spheres

2 days


Act 12.2






Act 12.5 Look for volume activity similar to textbook activity

G.6.D Predict and verify the effect that changing one, two, or three linear dimensions has on perimeter, area, volume, or surface area of two- and three dimensional figures.

12.7 Similar Solids Find and use the scale factor of similar solids

1 days

G.6.D Predict and verify the effect that changing one, two, or three linear dimensions has on perimeter, area, volume, or surface area of two- and three dimensional figures.

What’s In A Volume or Surface Area

3 day Supplemental activity What’s in a Volume or Surface Area

Review & Assessment 2 days









Assessment: (type)






G.5.A Sketch results of transformations and compositions of transformations for a given two dimensional figure on the coordinate plane, and describe the rule(s) for performing translations or for performing reflections about the coordinate axes or the line y = x. G.5.B Determine and apply properties of transformations.

7.1 Rigid Motion in a Plane 1 day


7.2 Reflections 1 day Additional practice for reflection across y =x can be found in Chapter resource book 7.2


7.3 Rotations 1 day


7.5 Glide Reflections and Compositions

1 day

Review 1 day

Assessment 1 day











Assessment: (type)



Unit Name: Congruent Triangles (Ch 4) [Starting Date] [Ending Date]



Les 4.1 – Classify triangles by their sides and angles

1.5 days Triangle Sorting Activity TBD Pre-assessment for background knowledge and prior vocabulary

Act 4.1 Investigating angles in triangles

.5 days

G.3.A Know, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle.

Les 4.1 Classify triangles by their sides and angles and find angle measures in triangles

1 day

G.3.A Know, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle. G.3.B Determine and prove triangle congruence, triangle similarity, and other properties of triangles.

4.2 Identify congruent figures and corresponding parts and prove two triangles are congruent.

2 days


4.3 Prove that triangles are congruent using the SSS and SAS Congruence Postulates.

2 days Possible extra credit Activity 4.3


4.4 Prove that triangles are congruent using the ASA congruence postulate and the AAS congruence theorem.

2 days

G.3.B Determine and prove triangle congruence, triangle similarity, and other properties of triangles.

4.5 Use congruent triangles to plan and write proofs and to prove constructions are valid.

1 day Section focuses on proofs





G.3.A Know, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle. G.3.B Determine and prove triangle congruence, triangle similarity, and other properties of triangles. G.3.C Use the properties of special right triangles (30°–60°–90° and 45°–45°–90°) to solve problems.

4.6 Use properties of isosceles, equilateral and right triangles.

2 days













Unit Name: Cutting Up the Triangle (Ch 5) [Starting Date] [Ending Date]



G.2.A Know, prove, and apply theorems about parallel and perpendicular lines. G.2.B Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal. G.2.C Explain and perform basic compass and straightedge constructions related to parallel and perpendicular lines. G.3.A Know, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle.

5.1 Use properties of perpendicular bisectors and angle bisectors to solve problems.

1 day


Act. 5.1 Explore the properties of a perpendicular bisector

1 day Find similar activity using Sketchpad

G.3.A Know, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle. G.2.B Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal.

5.2 Use properties of perpendicular bisectors and angle bisectors.

2 day


Act 5.3 Build vocabulary for and explore the properties of concurrent lines



5.3 Use properties of medians and altitudes of triangles

2 days

G.3.A Know, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle. G.4.B Determine the coordinates of a point that is described geometrically. G.4.C Verify and apply properties of triangles and quadrilaterals in the coordinate plane.

5.4 Identify and use properties of midsegments of a triangle

2 days






Review vocabulary and concepts by creating and presenting a poster in groups.

3 days

G.2.A Know, prove, and apply theorems about parallel and perpendicular lines. G.2.B Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal. G.2.C Explain and perform basic compass and straightedge constructions related to parallel and perpendicular lines. G.3.A Know, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle.

5.1 Use properties of perpendicular bisectors and angle bisectors to solve problems.

1 day


Act. 5.1 Explore the properties of a perpendicular bisector



5.2 Use properties of perpendicular bisectors and angle bisectors.

2 day


Act 5.3 Build vocabulary for and explore the properties of concurrent lines



5.3 Use properties of medians and altitudes of triangles

2 days

G.3.A Know, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle. G.4.B Determine the coordinates of a point that is

5.4 Identify and use properties of midsegments of a triangle

2 days



described geometrically. G.4.C Verify and apply properties of triangles and quadrilaterals in the coordinate plane.




Review vocabulary and concepts by creating and presenting a poster in groups.

3 days

Unit Assessments 1 day









Assessment: (type) Unit Assessments



Unit Name: Exploring Quadrilaterals (Ch 6) [Starting Date] [Ending Date]



G.4.A Determine the equation of a line in the coordinate plane that is described geometrically, including a line through two given points, a line through a given point parallel to a given line, and a line through a given point perpendicular to a given line.

Les 3.6 Write equations of parallel lines and use slope to identify parallel lines in a coordinate plane.

2 days Additional Support: Pg 124 (Chapter 2: Algebra Review) pg 793 (Skill Review Handbook) Chapter 5 in Algebra 1 textbook

G.4.A Determine the equation of a line in the coordinate plane that is described geometrically, including a line through two given points, a line through a given point parallel to a given line, and a line through a given point perpendicular to a given line.

Les 3.7 Write equations of perpendicular lines and use slope to identify perpendicular lines in the coordinate plane.

2 days Additional Support: Pg 124 (Chapter 2: Algebra Review) pg 793 (Skill Review Handbook) Chapter 5 in Algebra 1 textbook

G.4.B Verify and apply properties of triangles and quadrilaterals in the coordinate plane.

Les 4.7 Place geometric figures in a coordinate plane to write a proof.

1 day Need to focus on methods for determining coordinates of points described geometrically.

G.3.G Know, prove, and apply theorems about properties of quadrilaterals and other polygons.

Act 6.1 Identify, name, and describe polygons.

1.5 days

Sorting Activity as pre-assessment and to build vocabulary.


Les 6.1 Identify, name and describe polygons. Use the sum of the measure of interior angles of a quadrilateral.

1 day

G.3.F Know, prove, and apply basic theorems about parallelograms.

Les 6.2 Use properties of parallelograms to solve problems.

2 days


Les 6.3 Prove that a quadrilateral is a parallelogram

2 days Supplemental Materials: Chapter Resource Books: Reteach With Practice 6.3 Lesson 6.3 C


Les 6.4 Use properties of sides, angles and diagonals of rhombuses, rectangles and squares.

1 day Supplemental Materials: Chapter Resource Books: Lesson 6.4 (A, B)






Les 6.5 use properties of trapezoids and kites.

1 day Supplemental Materials: Chapter Resource Books: Lesson 6.5 (A, B)


Les 6.6 Identify and prove that a quadrilateral is a special type based on limited information.

2 days










Chapter Review and Assessment



Unit Name: Similarity (Ch 8) [Starting Date] [Ending Date]




Les 8.4 Identify similar triangles use them to solve problems.

2 days

G.6.F Solve problems involving measurement conversions within and between systems, including those involving derived units, and analyze solutions in terms of reasonableness of solutions and appropriate units.

Les 8.1 Find and simplify the ratio of two numbers. Use proportions to solve problems

1 day

Les 8.2 Problem solving using Proportions.

1 day Required to be successful later in determining similarity of polygons including triangles and quadrilaterals.

G.6.E Use different degrees of precision in measurement, explain the reason for using a certain degree of precision, and apply estimation strategies to obtain reasonable measurements with appropriate precision for a given purpose.

Act 8.3 Make conjectures about similarity.

1 day


Les 8.3 Identify similar polygons and use them to solve problems.

2 days


Les 8.5 Use similarity theorems to prove two triangles are similar and use them to solve problems.

2 days


Les 8.6 Proportions and Similar Triangles Use proportionality theorems to calculate segment lengths

1 day

G.5.B Determine and apply properties of transformations

Les 8.7 Dilations Identify dilations and use to construct real life perspective drawings

1 day












Assessment: (type) Chapter Assessment



Unit Name: Right Triangles and Trigonometry (Ch 9)





Les 9.1 Solve problems involving similar right triangles formed by the altitude drawn to the hypotenuse.

2 days

G.3.D Know, prove, and apply the Pythagorean Theorem and its converse.

Les 9.2 Use and prove the Pythagorean Theorem

2 days


Les 9.3 Use the converse of the Pythagorean Theorem. (Not goal 2)

1 day


Act 9.3 How do the angle measures and side lengths relate in triangles.

1 day

G.3.C Use the properties of special right triangles (30°–60°–90° and 45°–45°–90°) to solve problems.

Act 9.4 Discover the properties of right triangles

2 days

G.3.C Use the properties of special right triangles (30°–60°–90° and 45°–45°–90°) to solve problems.

Les 9.4 Find the side lengths of special right triangles and solve problems.

2 days

G.3.E Solve problems involving the basic

trigonometric ratios of sine, cosine, and tangent.

Les 9.5 Find the sine, the cosine and the tangent of an acute angle and use to solve problems.

3 days

G.3.E Solve problems involving the basic trigonometric ratios of sine, cosine, and tangent

Les 9.6 Solve right triangles and use to solve problems.

2 days

Chapter Review & Assessment

2 days








Unit Name: Getting Around to Circles (Ch 10) [Starting Date] [Ending Date]



G.3.H Know, prove, and apply basic theorems relating circles to tangents, chords, radii, secants, and inscribed angles.

Les 10.1 Identify parts of a circle and use properties of tangents.

1 day

G.3.H Know, prove, and apply basic theorems relating circles to tangents, chords, radii, secants, and inscribed angles. G.6.A Derive and apply formulas for arc length and area of a sector of a circle.

Les 10.2 Use properties of arcs and chords to solve problems

2 days

G.3.H Know, prove, and apply basic theorems relating circles to tangents, chords, radii, secants, and inscribed angles. G.3.I Explain and perform constructions related to the circle.

Act 10.3 Identify and explore the properties of inscribed angles.

1 day


Les 10.3 Use inscribed angels to solve problems

2 days


Les 10.4 Use special lines and segments of a circle to solve problems.

2 days

G.3.H Know, prove, and apply basic theorems relating circles to tangents, chords, radii, secants, and inscribed angles. G.3.I Explain and perform constructions related to the circle.

Act. 10.5 Exploring the lengths of segments in a circle.

1 day


Les 10.5 Find the lengths of special lines and segments of a circle.

2 days

G.4.D Determine the equation of a circle that is described geometrically in the coordinate plane and, given equations for a circle and a line, determine the coordinates of their intersection(s).

Les 10.6 Write the equation of a circle and graph it to solve problems.

3 days







11.1

11.3 G.6.A Derive and apply formulas for arc length and area of a sector of a circle.

11.4

G.6.A Derive and apply formulas for arc length and area of a sector of a circle.

11.5

Act 11.3

Act 11.4 G.6.B Analyze distance and angle measures on a sphere and apply these measurements to the geometry of the earth.

Project Geometry on a Sphere Pg 714-715

2 days Pg 714-715 investigation questions

Review & Assessment 2 day

Process Standards Addressed: Unit theme: What happens as polygons add more sides?








Assessment: (type)

GEOMETRY - Pasco School District...between postulates and theorems Use the distance theorem to solve...

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