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Pine Bluff School District (PBSD)

Geometry Curriculum Guide Module 2014-2015

Additional Online Resources:

www.engageny.org/resource/geometry-module1 http://map.mathshell.org/materials/index.php

northcarolinaunpackingthestandards http://illuminations.nctm.org/

https://docs.google.com/spreadsheet/pub?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE&output=html

Unit Name: Module 1 (Test: 9/19/2014)

Date: 8/18/2014 – 9/18/2014 (Teaching Days: 23 days Remediation Days: 2 days)

Common Core Standards CO - Congruence

Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

Using slope, prove lines are parallel or perpendicular

Find equations of lines based on certain slope criteria such as; finding the equation of a line parallel or perpendicular to a given line that passes through a given point.

Bellwork: TE Warm Up page 190 TE Motivate page 190 Textbook Pages: 190 - 197

Lessons: Section 4-7 EXT

Performance Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Given two points, find the point on the line segment between the two points that divides the segment into a given ratio.

Bellwork: TE Motivate page 515

Textbook Pages: 515 - 516

Lessons: Section 7-6 EXT Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

G.G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula..

Use coordinate geometry and the distance formula to find the perimeters of polygons and the areas of triangles and rectangles.

Bellwork: TE Warm Up page 704 TE Motivate page 704

Textbook Pages: 704 - 709

Lessons: Sections 10-4 & 10-5

Discovering the Distance Formula Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

Performance Tasks:

Geometry Project: Distance & Midpoint

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

Prove theorems pertaining to lines and angles.

Prove vertical angles are congruent.

Prove when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angels are congruent. Prove points on a perpendicular bisector

Bellwork: TE Warm Up page 146 TE Motivate page 146

Textbook Pages: 146 - 154, 155 - 161, 162 - 171, 172 - 179

Lessons: Sections 2-1 thru 2-17

Lesson 6: Solve for Unknown Angles-S

Lesson 6: Solve for Unknown Angles-T

Lesson 7: Solve for Unknown Angles-Transversal-S

Lesson 7: Solve for Unknown Angles- Transversal-T

Lesson 8: Solve for Unknown Angles-Angles in a Triangle-S

Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

Apply the definitions, properties and theorems about line segments, rays and angles to support geometric constructions. Apply properties and theorems about parallel and perpendicular lines to support constructions.

From Appendix A: Build on prior student experience with simple constructions. Emphasize the ability to formalize and explain how these constructions result in the desired objects. Some of these constructions are closely related to previous standards and can be introduced in conjunction with them.

Copy a segment

Copy an angle

Bisect a segment

Bisect an angle

Construct perpendicular lines, including the perpendicular bisector of a line segment

Construct a line parallel to a given line through a point not on the line

Construct a triangle given the lengths of two sides and the measure of the angle between the two sides

Construct the circumcenter of a given triangle

Bellwork: TE Guided Instruction Page 14

Textbook Pages: 14, 16, 22 - 23, 170 - 171, 172 - 179

Lessons: Sections 1-2, 1-3, Lab 3-3, & Lab 3-4

Lesson 3: Copy & Bisect an Angle- S

Lesson 3: Copy & Bisect an Angle Sorting Activity-T

Tasks:

Polly Gone

Circular Reasoning Performance Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

Understand and use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined term of a point, a line, the distance along a line, and the length of an arc.

Bellwork: TE See “Motivate”-page 6 TE Warm UP - Page 6

Textbook Pages: 6 - 8, 20 - 27, 146 - 151 Lessons: Sections 1-7 & Lab 1-7

Tasks:

Geometry Sketch Game

Geometry Sketch Game Material

Once Upon a Time Performance Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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Unit Name: Module 2 (Test: 10/24/2014) Date: 9/24/2014 – 10/23/2014 (Teaching Days: 21 days Remediation Days: 2 days)

Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

Use various technologies such as transparencies, geometry software, interactive whiteboards, and digital visual presenters to represent and compare rigid and size transformations of figures in a coordinate plane. Comparing transformations that preserve distance and angle to those that do not.

Describe and compare function transformations on a set of points as inputs to produce another set of points as outputs, to include translations and horizontal and vertical stretching.

Bellwork: TE Warm Up page 50 TE Motivate page 50 TE Motivate page 509

Textbook Pages: 50 - 55, 509 - 514, 611 - 617

Lessons: Sections Lab 1-7 & 7-6

Lesson 12: Transformations-The Next Level-S

Lesson 12: Transformations- The Next Level-T-Supplement

Lesson 12: Transformations-The Next Level-T

FAL: Transforming 2D Figures

Tasks: Between the Lines

Performance Tasks:

Circles in Triangles Performance Task

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

Describe the rotations and reflections of a rectangle, parallelogram, trapezoid, or regular polygon that maps each figure onto itself.

Bellwork: TE Motivate page 604

Textbook Pages: 604 - 610, 611 – 617, 619 - 625, 634 - 640

Lessons: Sections 9-1 & 9-5 Lesson 15: Rotations, Reflections,

& Symmetry-S Lesson 15: Rotations, Reflections,

& Symmetry-T Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

Performance Tasks:

Circles in Triangles Performance Task

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

Using previous comparisons and descriptions of transformations, develop and understand the meaning of rotations, reflections, and translations based on angles, circles, perpendicular lines, parallel lines, and line segments.

Bellwork: TE Warm Up page 611 TE Motivate page 611

Textbook Pages: 50 - 55, 604 - 610, 611 - 617, 619 - 625, 626 - 631

Lessons: Section 9-4

Lesson 18: Looking More Carefully at Parallel Lines-S

Lesson 18: Looking More Carefully at Parallel Lines-T

Lesson 16: Translations-S Lesson 16: Translations-T

Tasks: The Shape of Things Performance Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

Transform a geometric figure given a rotation, reflection, or translation using graph paper, tracing paper, or geometric software.

Create sequences of transformations that map a geometric figure on to itself and another geometric figure.

Bellwork: TE Motivate page 619

Textbook Pages: 50 - 55, 604 - 610, 611 - 617, 619 - 625

Lessons: Section 9-6

Lesson 13- Rotations-S

Lesson 13- Rotations-T

Lesson 14: Reflections-S

Lesson 14: Reflections-T

Lesson 19: Construct & Apply a Sequence of Rigid Motions-S

Lesson 19: Construct & Apply a Sequence of Rigid Motion-T

Performance Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor.

a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

a. Given a center and a scale factor, verify experimentally, that when dilating a figure in a coordinate plane, a segment of the pre-image that does not pass through the center of the dilation, is parallel to it’s image when the dilation is performed. However, a segment that passes through the center remains unchanged.

b Given a center and a scale factor, verify experimentally, that when performing dilations of a line segment, the pre-image, the segment which becomes the image is longer or shorter based on the ratio given by the scale factor.

Bellwork: TE Warm Up page 472 TE Motivate page 472

Textbook Pages: 472 - 479, 509 - 514, 650 - 657

Lessons: Section 9-7

Similarity, Congruence, & Proofs

Performance Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

Use descriptions of rigid motion and transformed geometric figures to predict the effects rigid motion has on figures in the coordinate plane.

Knowing that rigid transformations preserve size and shape or distance and angle, use this fact to connect the idea of congruency and develop the definition of congruent.

Bellwork: TE Warm Up page 216 TE Motivate page 216

Textbook Pages: 216 - 226

Lessons: Sections 4-1, 9-1 thru 9-4

Lesson 17: Characterize Points on a Perpendicular Bisector-S

Lesson 17: Characterize Points on a Perpendicular Bisector-T

Lesson 20: Applications of Congruence in Terms of Rigid Motion-S

Lesson 20: Applications of Congruence in Terms of Rigid Motion-T

Lesson 21: Correspondence and Transformations-S

Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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Unit Name: Module 3 (Test: 12/12/2014) Date: 10/29/2014 – 12/11/2014 (Teaching Days: 27 days Remediation Days: 2 days)

Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

Use the definition of congruence, based on rigid motion, to show two triangles are congruent if and only if their corresponding sides and corresponding angles are congruent

Bellwork: TE Warm Up page 239 TE Motivate page 239

Textbook Pages: 239 - 245

Performance Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

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G.G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Use the definition of congruence, based on rigid motion, to develop and explain the triangle congruence criteria; ASA, SSS, and SAS.

Bellwork: TE Warm Up page 250 TE Motivate page 250 Textbook Pages: 250 – 257, 260 - 267 Lessons: Sections 4-5 & Lab 4-5

Lesson 22: Congruence Criteria for Triangles- SAS-S

Lesson 22: Congruence Criteria for Triangles-SAS-T

Lesson 23: Base Angles of Isosceles Triangles-S

Lesson 23: Base Angles of Isosceles Triangles-T

Lesson 24: Congruence Criteria for Triangles-ASA & SSS-S

Lesson 24: Congruence Criteria for Triangles-ASA & SSS-T

Lesson 25: Congruence Criteria for Triangles-SAA & HL-S

Lesson 25: Congruence Criteria for Triangles-SAA & HL-T

Lesson 26: Triangle Congruency Proofs Part 1-S

Lesson 26: Triangle Congruency Proofs Part 1-T

Lesson 27: Triangle Congruency Proofs Part 2-S

Lesson 27: Triangle Congruency Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

Use AA, SAS, SSS similarity theorems to prove triangles are similar.

Use triangle similarity to prove other theorems about triangles

Prove a line parallel to one side of a triangle divides the other two proportionally, and it’s converse

Prove the Pythagorean Theorem using triangle similarity.

Bellwork: TE Warm Up page 495 TE Motivate page 495

Textbook Pages: 495 - 501, 490 - 491, 360 - 367

Lessons: Sections Lab 5-6

Similarity, Right Triangle Trigonometry, and Proof

Similarity, Congruence, & Proofs

Performance Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

G.G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Using similarity theorems, prove that two triangles are congruent.

Prove geometric figures, other than triangles, are similar and/or congruent.

Bellwork: TE Warm Up page 250 TE Motivate page 250

Textbook Pages: 250 - 257, 260 - 267, 268 - 273

Lessons: Section 6-6

Similarity, Congruence, & Proofs FAL: Circles and Triangles

Tasks:

Triangle Congruence

Performance Tasks: Rhombus Performance Task

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180º; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

Prove theorems pertaining to triangles.

Prove the measures of interior angles of a triangle have a sum of 180º.

Prove base angles of isosceles triangles are congruent.

Prove the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length.

Prove the medians of a triangle meet at a point.

Bellwork: TE Motivate page 231 TE Warm Up page 239 TE Motivate page 239

Textbook Pages: 231 - 238, 239 - 245, 279 - 284, 285 - 291, 326 - 331

Lessons: Sections 5-3 thru 5-6

FAL: Possible Triangle Constructions

Lesson 29: Special Lines in Triangles-S

Lesson 29: Special Lines in Triangles-T

Lesson 30: Special Lines in Triangles-S

Lesson 30: Special Lines in Triangles-T

Tasks: Special Lines in Triangles

Triangle Inequality Theorem Activity

Performance Tasks:

Additional Resources:

Centers of Triangles Graphic Organizers

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Use the idea of dilation transformations to develop the definition of similarity.

Given two figures determine whether they are similar and explain their similarity based on the equality of corresponding angles and the proportionality of corresponding sides.

Bellwork: TE Warm Up page 466 TE Motivate page 466

Textbook Pages: 466 - 471, 472 - 479

Lessons: Section Lab 7-2

Similarity, Congruence, & Proofs Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

Performance Tasks:

Rhombus Performance Task

Hopewell Geometry Performance Task

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G.G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Use the properties of similarity transformations to develop the criteria for proving similar triangles; AA

Bellwork: TE Warm Up page 482 TE Motivate page 482

Textbook Pages: 482 - 489

Lessons: Section 7-3

Similarity, Congruence, & Proofs Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Using a corresponding angle of similar right triangles, show that the relationships of the side ratios are the same, which leads to the definition of trigonometric ratios for acute angles.

Students may use applets to explore the range of values of the trigonometric ratios as θ ranges from 0 to 90 degrees.

Bellwork: TE Warm Up page 541 TE Motivate page 541

Textbook Pages: 541 - 548

Lessons: Section 8-1

Trig Lessons

Performance Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.

Explore the sine of an acute angle and the cosine of its complement and determine their relationship.

Bellwork: TE Motivate page 549 Textbook Pages: 549 - 550

Lessons: Section 8-2 EXT Trig Lessons Performance Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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G.G,SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*

Apply both trigonometric ratios and Pythagorean Theorem to solve application problems involving right triangles.

Students may use graphing calculators or programs, tables, spreadsheets, or computer algebra systems to solve right triangle problems.

Example:

Find the height of a tree to the nearest tenth if the angle of elevation of the sun is 28° and the shadow of the tree is 50 ft.

Bellwork: TE Warm Up page 552 TE Motivate page 552

Textbook Pages: 552 - 558, 562 - 568

Lessons: Sections 8-3 & 8-4

Trig Lessons FAL: Calculating Volumes of

Compound Objects

Tasks:

Pythagorean Theorem Spiral Project

Pythagorean Theorem Project Fencing Yard

Real Life Trig

Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.SRT.9 (+) Derive the formula A=½ ab sin (C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

For a triangle that is not a right triangle, draw an auxiliary line from a vertex, perpendicular to the opposite side and derive the formula, A = ½ ab sin (C), for the area of a triangle, using the fact that the height of the triangle is, h = a sin(C).

Bellwork:

Textbook Pages: 701

Lessons: Section 8-5 Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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G.G.SRT.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems.

Using trigonometry and the relationship among sides and angles of any triangle, such as sin(C) = (h/a) , prove the Law of Sines.

Using trigonometry and the relationship among sides and angles of any triangle and the Pythagorean Theorem to prove the Law of Cosines.

Use the Laws of Sines to solve problems.

Use the Laws of Cosines to solve problems.

Bellwork: TE Warm Up page 569 TE Motivate page 569

Textbook Pages: 569—576

Lessons: Section 8-5

Proof of the Laws of Sines and Cosines

Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.SRT.11 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non- right triangles (e.g., surveying problems, resultant forces).

Understand and apply the Law of Sines and the Law of Cosines to find unknown measures in right triangles.

Understand and apply the Law of Sines and the Law of Cosines to find unknown measures in non-right triangles.

Example:

Tara wants to fix the location of a mountain by taking measurements from two positions 3 miles apart. From the first position, the angle

between the mountain and the second position is 78o. From the second

position, the angle between the mountain and the first position is 53o.

How can Tara determine the distance of the mountain from each position, and what is the distance from each position?

Bellwork: TE Warm Up page 569 TE Motivate page 569 Regents Bellringers

Textbook Pages: 569 - 576

Lessons: Section 8-5

Tasks: Trig Word Problems Performance Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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Unit Name: Module 4 (Test: 3/6/2015) Date: 1/5/2015 – 3/5/2015 (Teaching Days: 39 days Remediation Days: 4 days)

Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).

Use coordinate geometry to prove geometric theorems algebraically; such as prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).

Bellwork: TE Warm Up page 279 TE Motivate page 279

Textbook Pages: 279 - 284

Lessons: Section 4-8

Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net) Performance Tasks:

FAL: Finding Equations of Parallel

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G.G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Using similarity theorems, prove that two triangles are congruent.

Prove geometric figures, other than triangles, are similar and/or congruent.

Bellwork: TE Warm Up page 250 TE Motivate page 250

Textbook Pages: 250 - 257, 260 - 267, 268 - 273

Lessons: Sections 4-4, 4-7, 7-3, & 7-5

Similarity, Congruence, & Proofs FAL: Circles and Triangles

Performance Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.CO.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Prove theorems pertaining to parallelograms.

Prove opposite sides are congruent.

Prove opposite angles are congruent.

Prove the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Bellwork: TE Motivate page 403

Textbook Pages: 403 - 409, 410 - 417

Lessons: Sections 6-1 thru 6-5

FAL: Applying Angle Theorems

FAL: Describing Quadrilaterals Lesson 28: Properties of

Parallelograms-S

Lesson 28: Properties of Parallelograms-T

Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

Performance Tasks:

Quadrilateral Performance Task

Additional Resources:

Special Quadrilaterals Classroom Activity Interactive Bulletin Board

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Unit Name: Module 5 (Test: 5/1/2015) Date: 3/16/2015 – 4/30/2015 (Teaching Days: 28 days Remediation Days: 5 days)

Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).

Use coordinate geometry to prove geometric theorems algebraically; such as prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).

Bellwork: TE Warm Up page 279 TE Motivate page 279

Textbook Pages: 279 - 284

Lessons: Section 4-8

T a sks : Created TLI Performance Tasks and Quiz Builders (www.tli.net) Performance Tasks:

FAL: Finding Equations of Parallel

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G.G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

Understand and use definitions of angles, circles, perpendicular lines, parallel lines, and line segments based on the undefined term of a point, a line, the distance along a line, and the length of an arc.

Bellwork: TE See “Motivate”-page 6 TE Warm UP - Page 6

Textbook Pages: 6 - 8, 20 - 27, 146 - 151

Lessons: Section 3-1

Tasks:

Geometry Sketch Game

Geometry Sketch Game Material

Once Upon a Time

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Construct an equilateral triangle so that each vertex of the equilateral triangle is on the circle.

Construct a square so that each vertex of the square is on the circle.

Construct a regular hexagon so that each vertex of the regular hexagon is on the circle

Bellwork: TE Discuss page 392

Textbook Pages: 392 - 393

Lessons: Section Lab 6-1

Construct Isosceles & Equilateral Triangle

Lesson 33: Review of the Assumptions-S

Lesson 33: Review of the Assumptions-T

G.G.C.1 Prove that all circles are similar.

Using the fact that the ratio of diameter to circumference is the same for circles, prove that all circles are similar.

Bellwork:

Textbook Pages: 474, 793

Lessons: Section 7-2

Circle Lessons

Performance Tasks: Created TLI

Performance Tasks and Quiz Builders

(www.tli.net)

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.C.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Using definitions, properties, and theorems, identify and describe relationships among inscribed angles, radii, and chords. Include central, inscribed, and circumscribed angles.

Understand that inscribed angles on a diameter are right angles.

Understand that the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Bellwork: TE Warm Up page 820 TE Motivate page 820

Textbook Pages: 820 - 827 Lessons: Sections 12-1, 12-2, 12-4 thru 12-6, Lab 12-4, & Lab 12-5

Tasks:

Angle Relationship in Circles

Circles in Triangles

Performance Tasks: Circles and Squares Performance

Tasks

Additional Resources:

G.G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

Construct inscribed circles of a triangle.

Construct circumscribed circles of a triangle.

Using definitions, properties, and theorems, prove properties of angles for a quadrilateral inscribed in a circle.

Bellwork:

Textbook Pages: 320 – 321 Lessons: Section 5-2

Performance Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.C.4 (+) Construct a tangent line from a point outside a given circle to the circle.

Construct a tangent line from a point outside a given circle to the circle. Bellwork:

Textbook Pages: 827

Performance Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

G.G.C.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

Use similarity to derive the fact that the length of the arc intercepted by an angle is proportional to the radius, identifying the constant of proportionality as the radian measure of the angle.

Find the arc length of a circle.

Using similarity, derive the formula for the area of a sector.

Find the area of a sector in a circle.

Bellwork: TE Warm Up page 810 TE Motivate page 810

Textbook Pages: 810 - 817

Lessons: Section 12-3 & Lab 12-3

FAL: Sectors of Circles

Performance Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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G.G.GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Use the Pythagorean Theorem to derive the equation of a circle, given the center and the radius.

Given an equation of a circle, complete the square to find the center and radius of a circle.

Bellwork: TE Warm Up page 847 TE Motivate page 847

Textbook Pages: 847 - 853 Lessons: Section 12-7

FAL: Equations of Circles 1

FAL: Equations of Circles 2

Modeling Geometry Performance Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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Unit Name: Module 6 (Test: No TLI Test) Date: 5/11/2015 – 6/1/2015 (Teaching Days: 20 days)

Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula..

Use coordinate geometry and the distance formula to find the perimeters of polygons and the areas of triangles and rectangles.

Bellwork: TE Warm Up page 704 TE Motivate page 704

Textbook Pages: 704 - 709

Lessons: Section 10-4 & 10-5

Discovering the Distance Formula

Performance Tasks:

Geometry Project: Distance & Midpoint

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.

Explain the formulas for the circumference of a circle and the area of a circle by determining the meaning of each term or factor.

Explain the formulas for the volume of a cylinder, pyramid and cone by determining the meaning of each term or factor.

Bellwork: TE Warm Up page 688 TE Motivate page 688 TE Warm Up page 749 TE Motivate page 749 TE Warm Up page 757 TE Motivate page 757

Textbook Pages: 688 - 693, 749 - 756, 757 - 764 Lessons: Sections Lab 10-1 & 10-2

Circle Lessons

Modeling Geometry Lessons Performance Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*

Solve problems using volume formulas for cylinders, pyramids, cones, and spheres.

Bellwork: TE Warm Up page 749 TE Motivate page 749 TE Warm Up page 757 TE Motivate page 757

Textbook Pages: 749 - 756, 757 - 764

Lessons: Sections 11-2 thru 11-4

Performance Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.GMD.4 Identify the shapes of two- dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

Given a three- dimensional object, identify the shape made when the object is cut into cross-sections.

When rotating a two- dimensional figure, such as a square, know the three-dimensional figure that is generated, such as a cylinder. Understand that a cross section of a solid is an intersection of a plane (two- dimensional) and a solid (three-dimensional).

Bellwork: TE Warm Up page 742 TE Motivate page 742

Textbook Pages: 742 - 748

Lessons: Section 11-1

FAL: 2D Representations of 3D Objects

FAL: Evaluating Statements About Enlargements

FAL: Calculating Volumes of Compound Objects

Performance Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

G.G.MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*

Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*

Bellwork: TE Warm Up page 224 TE Motivate page 224

Textbook Pages: 224 - 229

Lessons: Sections Lab 10-1 & 10-2 Performance Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

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Common Core Standards Background Knowledge/Examples Resources/Sample Lessons/Assessments Essential Vocabulary

G.G.MG.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).*

Use the concept of density when referring to situations involving area and volume models, such as persons per square mile.

Bellwork: TE Warm Up page 749 TE Motivate page 749

Textbook Pages: 749 - 756 Performance Tasks: Created TLI Performance Tasks and Quiz Builders (www.tli.net)

G.G.MG.3 Apply geometric methods to solve design problems (e.g. designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).*

Solve design problems by designing an object or structure that satisfies certain constraints, such as minimizing cost or working with a grid system based on ratios (i.e., The enlargement of a picture using a grid and ratios and proportions)

Bellwork: TE Warm Up page 509 TE Motivate page 509

Textbook Pages: 509 – 514

Lessons: Section 10-3

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Congruence

Common Core Cluster CO. 1 – CO.5

Experiment with transformations in the plane.

Instructional Expectations – Congruence The expectation for both pathways, in Geometry and CCSS Mathematics I, is to build on student experience with rigid motions from earlier grades. Point out the basis of rigid motions in geometric concepts, e.g., translations move points a specified distance along a line parallel to a specified line; rotations move objects along a circular arc with a specified center through a specified angle.

Common Core Cluster CO.6 – CO.8 Understand congruence in terms of rigid motions

Instructional Expectations The expectation for both pathways, in Geometry and CCSS Mathematics I, is to understand that rigid motions are at the foundation of the definition of congruence. Students reason from the basic properties of rigid motions (that they preserve distance and angle), which are assumed without proof. Rigid motions and their assumed properties can be used to establish the usual triangle congruence criteria, which can then be used to prove other theorems.

Common Core Cluster CO.9 – CO.11

Prove geometric theorems. Using logic and deductive reasoning, algebraic and geometric properties, definitions, and proven theorems to draw conclusions. (Encourage multiple ways of writing proofs, to include paragraph, flow charts, and two-column format)

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Instructional Expectations In the traditional pathway, the expectation in Geometry is to encourage multiple ways of writing proofs, such as in narrative paragraphs, using flow diagrams, in two-column format, and using diagrams without words. Students should be encouraged to focus on the validity of the underlying reasoning while exploring a variety of formats for expressing that reasoning. Implementation of G.CO.10 may be extended to include concurrence of perpendicular bisectors and angle bisectors as preparation for G.C.3 in Unit 5. In the international pathway, the expectation in CCSS Mathematics II is to encourage multiple ways of writing proofs, such as in narrative paragraphs, using flow diagrams, in two-column format, and using diagrams without words. Students should be encouraged to focus on the validity of the underlying reasoning while exploring a variety of formats for expressing that reasoning. Implementation of G.CO.10 may be extended to include concurrence of perpendicular bisectors and angle bisectors as preparation for G.C.3 in Unit 6.

Common Core Cluster CO.12 - CO.13 Make geometric constructions. Create formal geometric constructions using a compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software.

.

Instructional Expectations In both pathways, for Geometry and CCSS Mathematics I, the expectation is to build on prior student experience with simple constructions. Emphasize the ability to formalize and explain how these constructions result in the desired objects. Some of these constructions are closely related to previous standards and can be introduced in conjunction with them.

Similarity, Right Triangles, and Trigonometry G.SRT Common Core Cluster Understand similarity in terms of similarity transformations. SRT.1 - SRT.3

Common Core Cluster Prove theorems involving Similarity. SRT.4 – SRT.5

Common Core Cluster Define trigonometric ratios and solve problems involving right triangles. SRT.6 – SRT.8

Common Core Cluster Apply trigonometry to general Triangles. SRT.9 – SRT.11

Instructional Expectations In both pathways, Geometry and CCSS Mathematics III, the expectation is with respect to the general case of the Laws of Sines and Cosines, the definitions of sine and cosine must be extended to obtuse angles.

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Circles Common Core Cluster Understand and apply theorems about circles. C.1 – C.4

Common Core Cluster Find arc lengths and areas of sectors of circles. C.5

Instructional Expectations In both pathways, Geometry and CCSS Mathematics II, the expectation is to emphasize the similarity of all circles. Note that by similarity of sectors with the same central angle, arc lengths are proportional to the radius. Use this as a basis for introducing radian as a unit of measure. It is not intended that it be applied to the development of circular trigonometry in this course.

Expressing Geometric Properties with Equations G.GPE Common Core Cluster Translate between the geometric description and the equation for a conic section. GPE. 1 – GPE.3

Common Core Cluster Use coordinates to prove simple geometric theorems algebraically. GPE.4 – GPE.7

Instructional Expectations In both pathways, in Geometry and CCSS Mathematics II, connect G.GPE.1 to G.GPE.4 and reasoning with triangles is limited to right triangles; e.g., derive the equation for a line through two points using similar right triangles. Relate work on parallel lines in G.GPE.5 to work on A.REI.5 in High School Algebra I involving systems of equations having no solution or infinitely many solutions. G.GPE.7 provides practice with the distance formula and its connection with the Pythagorean theorem. In both pathways, G.GPE.4 in Geometry and CCSS Mathematics III, indicates including proofs involving circles.

Geometric Measurement and Dimension G.GMD Common Core Cluster Explain volume formulas and use them to solve problems. GMD.1 – GMD.3

Instructional Expectations In both pathways, the expectation for Geometry and CCSS Mathematics II is the understanding that informal arguments for area and volume formulas can make use of the way in which area and volume scale under similarity transformations: when one figure in the plane results from another by applying a similarity transformation with scale factor k, its area is k2 times the area of the first. Similarly, volumes of solid figures scale by k3 under a similarity transformation with scale factor k.

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Domains Congruence Similarity, Right Triangles, and Trigonometry

Circles Expressing Geometric Properties with Equations

Geometric Measurement and Dimension

Modeling with Geometry

Clusters

Experiment with transformations in the plane Understand congruence in terms of rigid motions

Prove geometric theorems

Make geometric constructions

Understand similarity in terms of similarity transformations

Prove theorems involving similarity

Define trigonometric ratios and solve problems involving right triangles

Apply trigonometry to general triangles

Understand and apply theorems about circles

Find arc lengths and areas of sectors of circles

Translate between the geometric description and the equation for a conic section

Use coordinates to prove simple geometric theorems algebraically

Explain volume formulas and use them to solve problems

Visualize relationships between two dimensional and three-dimensional objects

Apply geometric concepts in modeling situations

Mathematical Practices

1. Make sense of problems and 3. Construct viable arguments and 5. Use appropriate tools strategically. 7. Look for and make use of structure. persevere in solving them. critique the reasoning of others. 6. Attend to precision. 8. Look for and express regularity in

2. Reason abstractly and 4. Model with mathematics. repeated reasoning. quantitatively.

Common Core Cluster Visualize relationships between two-dimensional and three-dimensional objects. GMD.4

Modeling with Geometry G.MG Common Core Cluster Apply geometric concepts in modeling situations. MG.1 – MG.3