To Washington County Public School Geometry AT-A-GLANCE

A Correlation of envision A|G|A Geometry

A Correlation of

To the

Washington County Public School

Geometry At-A-Glance

Table of Contents

Module 1: Coordinate Geometry and Congruence

Module 2: Proving Geometric Theorems

Module 3: Similarity

Module 4: Trigonometry

Module 5: Constructions

Module 6: Circles

Module 7: Geometric Measurement, Dimension, & Modeling

A Correlation of envision A|G|A Geometry

To Washington County Public School Geometry AT-A-GLANCE

WCPS GeometryAT-A-GLANCE
Module, Focus,and Timing / Common Core State Standards / enVision A|G|A
Geometry Lessons

Module 1: Coordinate Geometry and

Congruence

Developing and understanding vocabulary, combined withusing definitions, is a critical to geometry and proofwriting; both will be used in the first module, anddeveloped throughout the remainder of the course. Coordinate geometry provides an algebraic way ofanalyzing geometric shapes and their properties. Thecoordinate system in geometry is used in therepresentation of transformations, yielding anunderstanding of rigid motion, which is the basis fordeveloping the concept of congruence. The concept ofcongruence is also applied to the properties of polygonsand development of the concept of congruent figures andtheir corresponding parts. Transformation and congruencehelp strengthen students’ understanding of proof, whichwill be the focus of the next module.
Marking Period 1
8-10 Weeks / G.GPE.B.4 / 9-1
G.GPE.B.5 / 2-4, Topic 2 MM3A, 5-3, 9-1, 9-2
G.GPE.B.6 / 1-3, 9-1, 9-2
G.GPE.B.7 / 1-3, 9-1
G.CO.A.1 / 1-1, 1-3
G.CO.A.2 / 3-1, 3-2, 3-3, 3-4, 4-1, 7-1, 7-2
G.CO.A.3 / 3-5, Topic 3 MM3A, 4-2
G.CO.A.4 / 3-1, 3-2, 3-3, 3-4
G.CO.A.5 / 3-1, 3-2, 3-3, 3-4, 4-1, 4-3
G.CO.B.6 / 3-1, 3-2, 3-4, 4-1, 4-5, 4-6
G.CO.B.7 / 4-1, 4-3, 4-4, 4-5
G.CO.B.8 / 4-1, Topic 4 MM3A, 4-3, 4-4, 4-5, 4-6

Module 2:ProvingGeometricTheorems

Proof is an essential part of geometry and developingunderstanding of geometric concepts. The first module oncongruence integrated algebraic proofs and developingcongruence criteria for triangles using rigidtransformations; in this module students further developtheir understanding of proofs by proving statements aboutlines, angles, triangles (with a focus on congruence) andparallelograms
Marking Period 2
5-6 Weeks / G.CO.C.9 / 1-7, 1-8, 2-1, 2-2, 4-5, 4-6, 5-1, 5-4, 6-4, 6-5, 6-6, 8-1, 10-5
G.CO.C.10 / 2-3, 4-2, 4-3, 4-4, 4-5, 5-3, 5-4, 6-6, 7-5, 9-2
G.CO.C.11 / 6-3, 6-4, 6-5, 6-6

Module 3: Similarity

In this module students revisit transformations,specifically dilations, to develop and solidify the concept ofsimilarity. Students utilize scale factor to determine theproperties of similar figures, and establish the criterion forsimilar triangles. The module includes proofs about similarfigures and their properties. The understanding thatcongruence is a special case of similarity is developed, inwhich the scale factor is 1:1, further connecting modules 2and 3.
Marking Periods 2
4-5 Weeks / G.SRT.A.1 / 7-1
G.SRT.A.1.A / 7-1
G.SRT.A.1.B / 4-1, 7-1, 7-3
G.SRT.A.2 / 7-1, 7-2, 7-3
G.SRT.A.3 / 7-3
G.SRT.B.4 / 7-5, 8-1
G.SRT.B.5 / 4-4, 4-6, 6-3, 7-3, 7-4, 7-5

Module 4: Trigonometry

Students will use their knowledge of right triangles todevelop an understanding of trigonometric ratios and theirrelationship to one another. This module relies on priormath courses with the use of the Pythagorean Theoremand simplifying radical expressions. Students will usetrigonometry to find missing angles and sides in righttriangles and develop an understanding of radian measurements. The plus standards require students to utilize the Law of Sines and Law of Cosines to determine unknown measurements in triangles.
Marking Period 3
4-5 Weeks / G. SRT.C.6 / 8-2, 8-5
G. SRT.C.7 / 8-2
G. SRT.C.8 / 6-5, 8-1, 8-2, 8-4, Topic 8 MM3A, 8-5, 9-1
G.SRT.D.9 (+) / 8-5
G.SRT.D.10 (+) / 8-3, 8-4
G.SRT.D.11 (+) / 8-3, 8-4

Module 5: Constructions

In this module students utilize tools to construct angles,segments, and polygons inscribed in a circle. Studentsshould practice precision and communication bydescribing the processes taken to produce specificconstructions. Constructions help students to solidify thetheorems and definitions of geometry, creating a deeperunderstanding of lines, angles, polygons, and theirproperties.
Marking Period 3
3-4 Weeks / G.CO.D.12 / 1-2, Topic 4 MM3A, 4-4, 5-1
G.CO.D.13 / Topic 10 MM3A, 10-3, 10-4

Module 6: Circles

Students utilize their definition and prior knowledge ofsimilarity to develop theorems about and definitions of theparts of a circle. Students will prove relationships betweenthe parts of a circle and derive formulas for circles. In thisunit, students will also construct inscribed andcircumscribed circles of a triangle, connecting to the priorunit and solidifying their understanding of the connectionsbetween properties of geometric figures. Honorsgeometry students will also construct tangent lines tocircles.
Marking Period 4
3-4 Weeks / G.C.A.1 / 7-2
G.C.A. 2 / 10-2, 10-3, 10-4
G.C.A.3 / 5-2
G.C.A. 4 (+) / 10-2
G.C.B.5 / 10-1
G.GPE.A.1 / 9-3

Module 7: Geometric Measurement, Dimension, & Modeling

In middle school students calculated volume, surface areaand area of two and three dimensional shapes. In this unitstudents will further their understanding by creatinginformal arguments for commonly used area,circumference and volume formulas (listed below), andutilizing them to calculate volume. Students solidify theirunderstanding of the relationship between two andthree-dimensional figures through the use ofcross-sections and identifying three dimensional objectscreated by the rotating two dimensional objects. This unitalso includes modeling, application and design standards;students should apply their knowledge of dimension andmeasurement to model authentic scenarios involvingvolume, density and properties of three-dimensionalfigures. Honors geometry students should also be able todevelop informal arguments using Cavalieri’s principle forvolume.
Marking Period 3
3-4 Weeks / G.MD.A.1 / 12-4
G.MD.A.3 / 12-4, 12-5
G.MD.A.2 (+) / 12-5
G.MD.B.4 / 12-4, 12-5
G.MG.A.1 / 6-1, Topic 6 MM3A, 6-2, 6-3, 6-4, 6-5, 6-6, 9-1
G.MG.A.2 / 11-2, 11-4
G.MG.A.3 / Topic 1 enVSP, Topic 2 enVSP, Topic 3 enVSP, Topic 4 enVSP, Topic 5 enVSP. Topic 6 enVSP, Topic 7 enVSP, Topic 8 enVSP, Topic 9 enVSP, Topic 10 enVSP, Topic 11 enVSP, Topic 12 enVSP

enVSP = enVision Stem Project

MM3A = Mathematical Modeling in 3 Acts