Graduate Education Assistance

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide YEAR AT A GLANCE

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GEOMETRY 2020– 2021 Course Code: 120631001

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1ST Nine Weeks 2nd Nine Weeks 3rd Nine Weeks 4th Nine Weeks

~ Introduction to Online Learning

I. Transformations and Congruence

A. Tools of Geometry B. Transformations and Symmetry C. Congruent Figures

II. Lines, Angles, and Triangles – Part A

A. Lines and Angles B. Triangle Congruence Criteria

III. Lines, Angles, and Triangles – Part B A. Applications of Triangle

Congruence B. Properties of Triangles C. Special Segments in Triangles

IV. Quadrilaterals and Coordinate Proof A. Properties of Quadrilaterals B. Coordinate Proof Using Slope and

Distance

V. Similarity and Trigonometry – Part A A. Similarity and Transformations

VI. Similarity and Trigonometry – Part B A. Using Similar Triangles B. Trigonometry with right triangles

VII. Properties of Circles A. Angles and Segments in Circles B. Arc Length and Sector Area C. Equations of Circles

VIII. Measurement and Modeling in Two and Three Dimensions

A. Volume Formulas B. Visualizing Solids C. Modeling and Problem Solving

STEM Lessons – Model Eliciting Activities

• Yogurt Land Container

• Interchangeable Wristwatch Band

• NASA Space Shuttle Mission Patches

• Turning Tires Model Eliciting Activity

• It’s Not Waste—It’s Matter!

• Olympic Snowboard Design

IX. Geometry EOC Review

X. Getting Ready for Algebra II – Functions

A. Analyzing Functions B. Absolute Value Functions,

Equations, and Inequalities

Total Days Allotted for Instruction, Testing, and “Catch-Up” days:

T B Dates

Topic ~ 5 2 08/31-09/04

Topic I 22 11 09/08-10/08

Topic II 10 5 10/09-10/22

Total 37 18

Total Days Allotted for Instruction, Testing, and “Catch-Up” days:

T B Dates

Topic III 18 9 10/26-11/20

Topic IV 22 11 11/23-01/08

Topic V 9 4 01/11-01/22

Total 49 24

Total Days Allotted for Instruction, Testing, and “Catch-Up” days:

T B Dates

Topic VI 20 10 01/25-02/22

Topic VII 23 11 02/23-03/25

Total 43 21

Total Days Allotted for Instruction, Testing, and “Catch-Up” days:

T B Dates

Topic VIII 10 5 04/05-04/16

Topic IX 10 5 04/19-04/30

Topic X 27 13 05/03-06/09

Total 47 23

Social Emotional Learning Resources Are Available for All Topics

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide YEAR AT A GLANCE

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GEOMETRY 2020– 2021 Course Code: 120631001

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1ST Nine Weeks 2nd Nine Weeks 3rd Nine Weeks 4th Nine Weeks

I. Transformations and Congruence MAFS.912.G-CO.1.1 MAFS.912.G-CO.1.2 MAFS.912.G-CO.1.3 MAFS.912.G-CO.1.4 MAFS.912.G-CO.1.5 MAFS.912.G-CO.2.6 MAFS.912.G-CO.2.7

II. Lines, Angles, and Triangles – Part A MAFS.912.G-CO.2.7 MAFS.912.G-CO.2.8 MAFS.912.G-CO.3.9 MAFS.912.G-CO.3.10 MAFS. 912.G-CO.4.12 MAFS.912.G-CO.4.13 MAFS.912.G-GPE.2.5

III. Lines, Angles, and Triangles – Part B MAFS.912.G-C.1.3 MAFS.912.G-CO.3.10 MAFS.912.G-SRT.2.5

IV. Quadrilaterals and Coordinate Proof MAFS.912.G-CO.3.11 MAFS.912.G-GPE.2.4 MAFS.912.G-GPE.2.5 MAFS.912.G-GPE.2.7 MAFS.912.G-SRT.2.5

V. Similarity and Trigonometry – Part A MAFS.912.G-SRT.1.1 MAFS.912.G-SRT.1.2 MAFS.912.G-SRT.1.3

VI. Similarity and Trigonometry – Part B MAFS.912.G-SRT.2.4 MAFS.912.G-SRT.2.5 MAFS.912.G-GPE.2.6 MAFS.912.G-SRT.3.6 MAFS.912.G-SRT.3.7 MAFS.912.G-SRT.3.8

VII. Properties of Circles MAFS.912.G-C.1.1 MAFS.912.G-C.1.2 MAFS.912.G-C.1.3 MAFS.912.G-C.2.5 MAFS.912.G-GPE.1.1 MAFS.912.G-GMD.1.1

VIII. Measurement and Modeling in Two and Three Dimensions MAFS.912.G-GMD.1.1 MAFS.912.G-GMD.1.3 MAFS.912.G-GMD.2.4 MAFS.912.G-MG.1.1 MAFS.912.G-MG.1.2 MAFS.912.G-MG.1.3

IX. Geometry EOC Review

X. Getting Ready for Algebra II – Probability MAFS.912.S-CP.1.1 MAFS.912.S-CP.1.2 MAFS.912.S-CP.1.4 MAFS.912.S-CP.2.8

Total Days Allotted for Instruction, Testing, and “Catch-Up” days:

T B Dates

Topic ~ 5 2 08/31-09/04

Topic I 22 11 09/08-10/08

Topic II 10 5 10/09-10/22

Total 37 18

Total Days Allotted for Instruction, Testing, and “Catch-Up” days:

T B Dates

Topic III 18 9 10/26-11/20

Topic IV 22 11 11/23-01/08

Topic V 9 4 01/11-01/22

Total 49 24

Total Days Allotted for Instruction, Testing, and “Catch-Up” days:

T B Dates

Topic VI 20 10 01/25-02/22

Topic VII 23 11 02/23-03/25

Total 43 21

Total Days Allotted for Instruction, Testing, and “Catch-Up” days:

T B Dates

Topic VIII 10 5 04/05-04/16

Topic IX 10 5 04/19-04/30

Topic X 27 13 05/03-06/09

Total 47 23

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide YEAR AT A GLANCE

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GEOMETRY 2020– 2021 Course Code: 120631001

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Geometry Core – H.M.H. Resources Geometry Intensive Math – H.M.H. Resources

Unit Resources Unit Resources

Unit Tests – A, B, and C Math in Careers Video

Performance Assessment Assessment Readiness (Mixed Review)

Module Resources

Module Test B

Common Core Assessment Readiness

Advanced Learners – Challenge Worksheets

Lesson Resources

Lessons – Work text/Interactive Student Edition

Practice and Problem Solving: A/B

Advanced Learners – Practice and Problem Solving: C

PMT Preferences Auto-assign for intervention and enrichment: NO

PMT Preferences Auto-assign for intervention and enrichment: YES

Test and Quizzes Daily Intervention

Homework Standard-Based Intervention

Course Intervention

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GEOMETRY 2020– 2021 Course Code: 120631001

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Technology Integration: The SAMR Model

Video Link: Introduction to the SAMR Model

Link: Other Examples of Transformed Lessons/Tasks

Stages of the SAMR Model:

Examples of Tasks at each Stage:

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide YEAR AT A GLANCE

Division of Academics – Department of Mathematics Page 7 of 17 Year-at-a-Glance

GEOMETRY 2020– 2021 Course Code: 120631001

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YEAR AT A GLANCE ACADEMIC SUPPORT

REPORTING CATEGORY: Congruency, Similarity, Right Triangles, and Trigonometry % of Test: 46% 2019 Average % Correct: 44%

Standards Previous Grade

Standards Geometry Topic(s)

MAFS.912.G-CO.1.1 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.

MAFS.4.MD.3.5 MAFS.4.G.1.1 MAFS.4.G.1.2

Topic I

MAFS.912.G-CO.1.2 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).

MAFS.8.G.1.1 MAFS.8.G.1.2 MAFS.8.G.1.3 MAFS.8.G.1.4 MAFS.912.F-BF.2.3 Topic I

MAFS.912.G-CO.1.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

MAFS.8.G.1.1 MAFS.8.G.1.3

MAFS.912.G-CO.1.5 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.

MAFS.8.G.1.2 MAFS.8.G.1.3 Topic I

MAFS.912.G-CO.1.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

MAFS.912.G-CO.2.6 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

MAFS.8.G.1.2

Topic I

MAFS.912.G-CO.2.7 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.

Topic I Topic II

MAFS.912.G-CO.2.8 Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse-Leg) follow from the definition of congruence in terms of rigid motions.

Topic II

MAFS.912.G-CO.3.9 Prove theorems about lines and angles; use theorems about lines and angles to solve problems. 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.

MAFS.4.MD.3.7 MAFS.7.G.2.5 MAFS.8.G.1.5

Topic II

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide YEAR AT A GLANCE

Division of Academics – Department of Mathematics Page 8 of 17 Year-at-a-Glance

GEOMETRY 2020– 2021 Course Code: 120631001

THIS DOCUMENT IS SUBJECT TO CHANGE

YEAR AT A GLANCE ACADEMIC SUPPORT

REPORTING CATEGORY: Congruency, Similarity, Right Triangles, and Trigonometry % of Test: 46% 2019 Average % Correct: 44%

Standards Previous Grade

Standards Geometry Topic(s)

MAFS.912.G-CO.3.10 Prove theorems about triangles; use theorems about triangles to solve problems. Theorems include: measures of interior angles of a triangle sum to 180°; triangle inequality theorem; 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.

MAFS.7.G.1.2 MAFS.8.G.1.5

Topic II Topic III

MAFS.912.G-CO.3.11 Prove theorems about parallelograms; use theorems about parallelograms to solve problems. 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

MAFS.5.G.2.3 Topic IV

MAFS.912.G-CO.4.12 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.

MAFS.7.G.1.2

Topic II

MAFS.912.G-CO.4.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle

MAFS.4.MD.3.6 MAFS.7.G.1.2

Topic II

MAFS.912.G-SRT.1.1 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.

MAFS.8.G.1.4 Topic V

MAFS.912.G-SRT.1.2 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.

MAFS.8.G.1.4 Topic V

MAFS.912.G-SRT.1.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. MAFS.8.G.1.4 Topic V

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide YEAR AT A GLANCE

Division of Academics – Department of Mathematics Page 9 of 17 Year-at-a-Glance

GEOMETRY 2020– 2021 Course Code: 120631001

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YEAR AT A GLANCE ACADEMIC SUPPORT

REPORTING CATEGORY: Congruency, Similarity, Right Triangles, and Trigonometry % of Test: 46% 2019 Average % Correct: 44%

Standards Previous Grade

Standards Geometry Topic(s)

MAFS.912.G-SRT.2.4 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.

MAFS.8.G.2.6

MAFS.912.G-SRT.2.5 Use congruence and similarity criteria for triangles to solve problems & to prove relationships in geometric figures

Topic II Topic V

MAFS.912.G-SRT.3.8

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. ★ MAFS.8.G.2.6 MAFS.912.N-RN.2.3

Topic VI MAFS.912.G-SRT.3.6 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.

MAFS.912.G-SRT.3.7 Explain and use the relationship between the sine and cosine of complementary angles. MAFS.7.G.2.5 Topic V

YEAR AT A GLANCE ACADEMIC SUPPORT

REPORTING CATEGORY: Circles, Geometric Measurement, and Geometric Properties with Equations % of Test: 38% 2019 Average % Correct: 38%

Standards Previous Grade

Standards Geometry Topic(s)