advanced geometry trig. pacing guide lynchburg city …€¦ · · 2014-01-14advanced geometry...

Advanced Geometry Trig. Pacing Guide

Lynchburg City Schools 2013-2014

Curriculum Framework Geometry VDOE: SOL Instructional Materials Curriculum Framework Trigonometry Teacher Direct

Grading Period: 1st Nine Weeks Total Days to Teach = 44 days

SOL & Enabling Objectives: Description

Text

Recommended Activities

Time Frame

Begin the school year with relationship building activities – continue integrating relationship building throughout the school year

Activity Ideas

PRE-TEST (for Teacher Evaluation & School Improvement: Interactive Achievement) will be released by the division to be administered at a time TBA

Begin teaching the 3rd day of school. DO NOT FEEL BOUND TO THE TEXT BOOK! PLEASE USE ONLINE RESOURCES, APPLETS, & HANDS-ON ACTIVITIES

Basics of Geometry

Prereq. Understand basic definitions, algebra review (p.24) G.4a Construct & justify the construction of:

1-2, 1-3, 1-4, p. 24

1-5

Video: Thinking About Geometry Part 1 Section A (2-53)

Video: Points, Lines, Planes, and Space (Part 1 Section B) (6-38)

Total for this unit = 8 days 4 days

2 days




-a line segment congruent to a given line segment -perpendicular bisector of a line segment -bisector of a given angle -angle congruent to a given angle G.3f Apply the distance formula to find the length of a line segment when given the coordinates of the endpoints. (Show using the Pythagorean Theorem) G.3a Find the coordinates of the midpoint of a segment, using the midpoint formula

1-6, 7-2

1-6

ESS G.4a Constructions

Constructions

ESS G.3af Distance & Midpoint Formulas

Distance Formula Applet

Video Disc Math: Pt 01 Ex 1: The Cart Coord. Sys (2-23)

Video Discovering Math: Pt. 1 Ex 3: Dist.

And Mid – DC (2-54)

1 day

1 day

Reasoning and Proofs

G.1a Identify the converse, inverse, & contrapositive of a condition statement. G.1g Interpret Venn diagrams.

2-1, 2-3, 5-4

2-1, 2-3

ESS G.1ab Inductive & Deductive Reasoning

Venn Diagram Worksheet

ESS G.1a-h Logic & Conditional

Total for this unit = 7 days

1 day




G.1c Determine the validity of a logical argument. G.1h Recognize & use the symbols of formal logic, which include G.1f Use Venn diagrams to represent relationships, such as intersection & union. G.1d Use valid forms of deductive reasoning, including the law of syllogism, the law of contrapositive, the law of detachment, & counterexamples. G.1e Select & use various types of reasoning & methods of proof as appropriate.

2-1, 2-2, Supp. 5-4

2-3, 2-2

2-4, 2-5

Statements

Logic and Truth Value

Intersection Union

Sets and the Venn Diagram

Reasoning

Video: Many-sided World, Prog 1: Postulates & Theorems (6-37)

Illuminations Lesson Pieces of Proof

Illuminations Lesson Venn Diagrams &

Logic

1 day

1 day

1 day

2 days

Angle Relationships

Prereq. Vertical, supplementary, complementary angles.

2-5

Introduction to Angles

Angle Classification

Complementary Angles Supplementary Angles

Total for this unit = 1 day 1 day




Vertical Angles Video: Many-Sided World of Geo: Prog

1: Pt 2 angles (5-20)

Parallel & Perpendicular Lines G.2abc Use algebraic & coordinate methods as well as deductive proofs to verify whether 2 lines are parallel. Solve problems by using the relationships between pairs of angles formed by the intersection of 2 parallel lines & a transversal including corresponding angles, alternate interior angles, alternate exterior angles, & same-side (consecutive) interior angles. Solve real-world problems involving intersecting & parallel lines in a plane. G.10a Solve real-world problems involving the measures of interior & exterior angles of polygons (specifically triangles).

3-1, 3-2

3-3

ESS G.2ab Lines & Angles

Interactive Lines and Angles

Parallel Lines

Angle Sum: Theorem

Exterior Angle Sum Theorem

Interior Angle sum Theorem

Interior angle Sum Proof

ESS G.10bcd Angles in Polygons

ESS G.3bc Slope


2 days

2 days




G.10a Solve real-world problems involving the measures of interior & exterior angles of polygons (all other polygons). G.10c Find the sum of the measures of the interior & exterior angles of a convex polygon. G.10d Find the measure of each interior & exterior angle of a regular polygon. G.10e Find the number of sides of a regular polygon given the measures of interior or exterior angles of the polygon. G.3b Use a formula to find the slope of a line. G.3c Compare the slopes to determine whether 2 lines are parallel, perpendicular, or neither.

3-4

3-4

3-4

p. 151

3-6

Slope

Parallel & Perpendicular Line Applet

1 day

1 day

1 day

1 day

1 day

2 days

Constructions

G.4a Construct & justify the construction of: -perpendicular to a given line from a point not on

3-7

ESS G.4a Constructions





the line. -perpendicular to a given line at a point on the line. -line parallel to a given line thru a point not on the given line. G.4b Construct an equilateral triangle, a square, & a regular hexagon inscribed in a circle.

Supp.

Constructions

Constructions

1 day

Congruent Triangles

Prereq. Understand concepts of congruent figures. G.6a Use definitions, postulates, & theorems to prove triangles congruent. G.6c Use algebraic methods to prove 2 triangles are congruent.

4-1

4-2, 4-3, 4-5, 4-6

4-4

Video Many-sided world, Prog 2: triangles (pt 3, sec A (9-35)

ESS G.6a Congruent Triangles

SSS Congruence AAS Congruence

ASA Congruence SAS Congruence


1 day

3 days

1 day




G.6b Use coordinate methods, such as distance formula & the slope formula to prove 2 triangles are congruent.

4-5

Puzzle Proofs

CPCTC

Coordinate Proofs

1 day

Flex days/Remediation

7 days

Grading Period: 2nd Nine Weeks Total Days to Teach = 45 days

SOL & Enabling Objective: Description

Text


Time Frame

Triangle Inequalities

G.5abcde Order the sides of a triangle by their lengths when given the measures of the angles. Order the angles of a triangle by their measures when given the lengths of the sides.

5-5

ESS G.5abcd How many triangles

Triangle Inequalities

Inequalities in Triangles





Given the lengths of 3 segments, determine whether a triangle could be formed. Given the length of 2 sides of a triangle, determine the range in which the length of the 3rd side must lie. Solve the real-world problems given information about the lengths of sides &/or measures of angles in triangles.

Quadrilaterals

G.9a Solve problems, including real-world problems, using the properties specific to parallelograms, rectangles, rhombi, squares, isosceles trapezoids, & trapezoids. G.9b Prove that quadrilaterals have specific properties, using coordinate & algebraic methods, such as the distance formula, slope, & midpoint formula.

6-1, 6-2, 6-3, 6-4

6-5 6-6

Introduction to Quadrilaterals

Parallelogram Properties

Square Properties Rectangles Properties Rhombus Properties Trapezoid Properties


3 days




G.9c Prove the characteristics of quadrilaterals, using deductive reasoning algebraic, & coordinate methods.

6-7

Illuminations lesson Diagonals to Quadrilaterals

Square Properties Lesson Diagonals of Quadrilaterals

ESS G.9bc Properties of Quadrilaterals Coordinate Properties of Quadrilaterals Coordinate Properties of Quadrilaterals

3 days

Similarity Prereq. Solve for variables within proportions. G.7a Use definitions, postulates, & theorems to prove triangles similar. G.7b Use algebraic methods to prove that triangles are similar. G.7c Use coordinate methods, such as distance formula, to prove 2 triangles are similar.

8-1, 8-2

8-3, 8-4

8-3, 8-4

8-3, 8-4

Video Project Mathematics: Similarity: Similar Triangles (4.48)

ESS G.7abc Similar Triangles

Similar Triangle Proofs


2 days

2 days

2 days

EXAM WEEK Total for this unit




Exams Exam Review and Exams

Powerpoint: Jeopardy Geometry 1st

Semester Exam Review

= 9 days

Flex days/Remediation:

5 days

Grading Period: 3rd Nine Weeks Total Days to Teach = 48 days


Text


Time Frame

Pythagorean Theorem & Special Right Triangles

G.8e Solve real-world problems, using right triangle trig & properties of right triangles. G.8a Determine whether a triangle formed w/3 given lengths is a right triangle. G.8b Solve for missing lengths in geometric figures, using properties of 45-45-90 degree triangles. G.8c Solve for missing lengths in geometric figures using properties of 30-60-90 degree triangles.

7-2, 7-3

7-3

Pythagorean Theorem

Pythagorean Theorem Lesson Plans

ESS G.8a Pythagorean Relationship

Video Project: Mathematics: Pythagorean Theorem (2-35)

Pythagorean Theorem Proof

ESS G.8bcd Special Rt Triangles & right


2 days

2 days




Triangle Trig

45-45-90 30-60-90

Video Many Sided World of Geometry

Program 5: The Pythagorean Thm. (pt 2 sec C)

Circles

Prereq. Determine area and circumference of a circle. G.11a Find the lengths, angle measures, & arc measures associated with: central angles G.11b Calculate the area of a sector & length of an arc of a circle, using proportions. G.11c Solve real-world problems associated with circles, using properties of angles, lines, & arcs. G.11acd Find the lengths, angle measures, & arc

1-7

7-6, 7-7

11-2, 11-2,

Video Project Mathematics: Pi Through the ages (4-14)

ESS G.11a Angles, Arcs & Segments in Circles

Illuminations Lesson Pi Line

Illuminations 3 Circles Lesson

Central vs Inscribed Angles

Inscribed Angles Applet


1 day

3 days

3 days




measures associated with: -2 intersecting chords -2 intersecting secants -intersecting secant & tangent -2 intersecting tangents -inscribed angles -Solve real-world problems associated with circles, using properties of angles, lines, & arcs. -Verify properties of circles, using deductive reasoning algebraic, & coordinate methods. G.9d Prove properties of angles for a quadrilateral inscribed in a circle. G.12abcdef Identify the center, radius, & diameter of a circle from a given standard equation. Use the distance formula to find the radius of a circle. Given the coordinates of the center & radius of the circle, identify a point on the circle. Given the equation of a circle in standard form, identify the coordinates of the center & find the radius

11-3, 11-4

11-3

11-5, (7-2)

Pi, Circumference, & Diameter

Chord Perpendicular to Diameter

Intersecting Chords

Intersecting Secants

Intersecting Tangents

Intersecting Tangent & secant

Intersecting secants

Intersecting Tangents

Intersecting Tangent & Secant

Quadrilateral Proof

Quadrilateral Inscribed Applet

Circle Equation: Tutorial

2 days

4 days




of the circle. Given the coordinates of the endpoints of a diameter, find the equation of the circle. Given the coordinates of the center & a point on the circle, find the equation of the circle. Recognize that the equation of a circle of given center & radius is derived using the Pythagorean Theorem.

Circle Equation Applet

Circle equation Applet 2

Constructions

G.4c Construct the inscribed & circumscribed circles of a triangle. G.4d Construct a tangent line from a point outside of a given circle to the circle.

Supp.

Constructions

Total for this unit = 1 day 1 day

Surface Area, Lateral Area, Volume

Prereq Find the area of triangles and parallelograms G.13a Find the total surface area of cylinders,

7-1

10-3, 10-4

Triangle Area

Parallelogram Area

Total for this unit =10 days

1 day




prisms, pyramids, cones, & spheres, using the appropriate formulas. G.13b Calculate the volume of cylinders, prisms, pyramids, cones, & sphere using the appropriate formulas. G.13c Solve problems including real-world problems involving total surface area & volume of cylinders, prisms, pyramids, cones & spheres as well as combinations of 3D figures.

10-7

10-5, 10-6,

10-7

10-3, 10-4, 10-5, 10-6,

10-7

ESS G.13abc Surface Area & Volume

Surface Area and volume Introduction

Surface Area & Volume

Surface Area of Prisms

Project Interactive SA Rectangular Prism

Lesson

Surface Area of Rectangular Prisms

Investigating Volume

Surface Area & Volume

Project Interactive Activity Surface Area & Volume

Volume of Rectangular Prisms

Surface Area & Volume of Combined

solids

3 days

3 days

3 days




Proportional Reasoning

G.14abcd Compare the ratios between side lengths, perimeters, areas, & volumes, given 2 similar figures. Describe how changes in 1 or more dimensions affect other derived measures (perimeter, area, total surface area, & volume) of an object. Describe how changes in 1 or more measures (perimeter, area, total surface area, & volume) affect other measures of an object. Solve real-world problems involving measured attributes of similar objects.

10-8, 8-6

ESS G.14ad Similar Solids & Proportional Reasoning

Proportions of Area & Volume Applet

Video Project Mathematics Similarity Perimeter, Areas, Volumes, & Recap

(4:00)


Symmetry & Transformations

G.3d Determine whether a figure has point symmetry, line symmetry, both, or neither.

12-5

ESS G.3d Symmetry

Symmetry Activities





G.3e Given an image & preimage, identify the transformation that has taken place as a reflection, rotation, dilation, or translation.

12-1, 12-3, 12-7, 12-2

ESS G.3e Transformations

Transformation Applet

Translations, Reflections, Rotations

Rotations

Reflections

Translations

Composition of Transformations

4 days

Tessellations

G.10b Identify tessellations in art, construction, & nature.

12-6

Geometry in Tessellations

ESS G.10cd Angles in Polygons

Tessellations Applet

Tessellations.org

Visual Patterns in Tessellations


Right Triangle Trigonometry





G.8d Solve problems involving right triangles, using sine, cosine, and tangent ratios. G.8f Explain & use the relationship between the sine & cosine of complementary angles. G.8e Solve real-world problems, using right triangle trig & properties of right triangles.

9-1, 9-2, 9-3

Supp.

9-1, 9-2, 9-3

ESS G.8bcd Special Rt. Triangles & right Triangle Trig.

Trig. Ratio Applet.

Right Triangle Solver

Video: Discovering Math: Part 2, Right

Triangle Trigonometry (10-07)

Trig Real World Problems

Trig Project Idea

Video: Discovering Math: Part 2: Using Trig Ratio apps. (9-17)

Trigonometry Lesson

2 days

2 days

Flex days/Remediation

7 days

Grading Period: 4th Nine Weeks Total Days to Teach = 43 days





Text


Time Frame

POST-TEST (for Teacher Evaluation & School Improvement – use same test as PRE-TEST)

1 day

SOL Review (before ANY SOL testing begins):

34 days

Expedited Retakes – Exam Review – Trig. Exam

8 days

Recommended Websites for additional lesson plans, activities, virtual manipulatives, and applets:

Illuminations NCTM Suffolk Geometry Resources Jefferson Lab SOL Review

Project Interactive Henrico Math resources




National Library of Virtual Manipulatives NLVM Texas Instrument Activities

Geometry: Math Crosswalk 2001 and 2009 SOLs

The length of the test has increased from 45 items to 50 items.

Changed to the reporting categories for the Geometry SOL test: Now there are 3 reporting categories instead of 5.

Lines & angles, Logic, and Coordinate Relations & Transformations have been combined into one reporting category

called: Reasoning, Lines & Transformations.

Triangles & Logic has become Triangles. The 2001 Triangles & Logic reporting category as been split with the Logic

content moving to the new Reasoning, Lines, & Transformations reporting category. As a result, the percentages shown

in the table mask the fact that the Triangles standards are now more heavily-weighted, while the Reasoning,

Lines, & Transformations standards are less heavily-weighted

o For example, suppose that of the 12 questions in the 2001 Triangles & Logic category, 3 of them typically

addressed Logic standards and 9 of them addressed Triangles standards; that would mean that the Triangles

standards comprised 9/45 = 20% on the 2001 SOL test, compared with 14/50 = 28% of the new 2009 SOL test




Similarly, the relative weight of each standard in the new Reasoning, Lines, & Transformations reporting category

has been diluted by the inclusion of the Logic standards in this category.

Polygons & Circles and Three-Dimensional Figures have been combined into one reporting category/strand.

The Geometry formula sheet has been revised.

2001 2009

Reporting Category

2009 SOL # items % of test # items % of test

Reasoning, Lines, & Transformations

G.1a-d, G.2 a-c, G.3a-d, G.4a-g

17 37.8% 18 36%

Triangles G.5a-d, G.6, G.7, G.8

12 26.7% 14 28%

Polygons, Circles, & Three-Dimensional Figures

G.9, G.10, G.11a-c, G.12, G.13, G.14a-d

16 35.6% 18 36%




Geometry: SOL Math course content overview

1st 9 Weeks 44 days

BASIC GEOMETRY 8 days

REASONING AND PROOFS 7 days

ANGLE RELATIONSHIPS 1 day

PAALLEL & PERPENDICULAR LINES 11 days

CONSTRUCTIONS 3 days

CONGRUENT TRIANGLES 6 days

2nd 9 Weeks 45 days




TRIANGLE INEQUALITIES 6 days

QUADRILATERALS 16 days

SIMILARITY 9 days

3rd 9 Weeks 48 days

PYTHAGOREAN THEREOM & SPECIAL RIGHT TRIANGLES 4 days

CIRCLES 13 days

CONSTRUCTIONS 1 day

SURFACE AREA, LATERAL AREA, VOLUME 10 days

PROPORTIONAL REASONING 2 days

SYMMETRY & TRANSFORMATIONS 5 days

TESSELLATIONS 2 days

RIGHT TRIANGLE TRIGONOMETRY 4 days

4th 9 Weeks 43 days

SOL REVIEW & TESTING 43 days

advanced geometry trig. pacing guide lynchburg city …€¦ · · 2014-01-14advanced geometry...

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