Course title

Pre-requisite

Course description

Geometry focuses on logical reasoning and spatial visualization skills. Students apply strategies of inductive and deductive reasoning to find the measures of angles and segments in polygons and circles. These strategies are extended to solid figures to find area and volume. Coordinate geometry and constructions are thematic throughout the course. Other topics covered are similar and congruent triangles; parallel lines and geometric probability. Students who earn below 70% will not be eligible to take the next level course. Core curriculum courses are designed for students to access the general curriculum with appropriate accommodations. This course is taught by a highly qualified special education teacher.
Standards Alignment:
• 1: Make sense of problems and persevere in solving them.
• 2: Reason abstractly and quantitatively.
• 3: Construct viable arguments and critique the reasoning of others.
• 4: Model with mathematics.
• 5: Use appropriate tools strategically.
• 6: Attend to precision.
• 7: Look for and make use of structure.
• 8: Look for and express regularity in repeated reasoning.
• HS: High School - Algebra
•HS: High School - Functions
•HS: High School - Geometry
oHS.G-C: Circles
•HS.G-C.A: Understand and apply theorems about circles
•HS.G-C.A.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.
•HS.G-C.A.3: Construct the inscribed and circumscribed circles of a triangle; and prove properties of angles for a quadrilateral inscribed in a circle.
•HS.G-C.B: Find arc lengths and areas of sectors of circles
•HS.G-C.B.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.
oHS.G-CO: Congruence
•HS.G-CO.A: Experiment with transformations in the plane
•HS.G-CO.A.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.
•HS.G-CO.A.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).
•HS.G-CO.A.3: Given a rectangle; parallelogram; trapezoid; or regular polygon; describe the rotations and reflections that carry it onto itself.
•HS.G-CO.A.4: Develop definitions of rotations; reflections; and translations in terms of angles; circles; perpendicular lines; parallel lines; and line segments.
•HS.G-CO.A.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.
•HS.G-CO.B: Understand congruence in terms of rigid motions
•HS.G-CO.B.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.
•HS.G-CO.B.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.
•HS.G-CO.B.8: Explain how the criteria for triangle congruence (ASA; SAS; and SSS) follow from the definition of congruence in terms of rigid motions.
•HS.G-CO.C: Prove geometric theorems
•HS.G-CO.C.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.
•HS.G-CO.C.10: Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; 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.
•HS.G-CO.C.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.
•HS.G-CO.D: Make geometric constructions
•HS.G-CO.D.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.
oHS.G-GMD: Geometric Measurement and Dimension
•HS.G-GMD.A: Explain volume formulas and use them to solve problems
•HS.G-GMD.A.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.
•HS.G-GMD.B: Visualize relationships between two-dimensional and three-dimensional objects
•HS.G-GMD.B.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.
oHS.G-GPE: Expressing Geometric Properties with Equations
•HS.G-GPE.A: Translate between the geometric description and the equation for a conic section
•HS.G-GPE.A.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.
•HS.G-GPE.B: Use coordinates to prove simple geometric theorems algebraically
•HS.G-GPE.B.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).
•HS.G-GPE.B.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).
•HS.G-GPE.B.6: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
•HS.G-GPE.B.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles; e.g.; using the distance formula.
oHS.G-MG: Modeling with Geometry
•HS.G-MG.A: Apply geometric concepts in modeling situations
•HS.G-MG.A.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).
•HS.G-MG.A.2: Apply concepts of density based on area and volume in modeling situations (e.g.; persons per square mile; BTUs per cubic foot).
•HS.G-MG.A.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).
oHS.G-SRT: Similarity; Right Triangles; and Trigonometry
•HS.G-SRT.A: Understand similarity in terms of similarity transformations
•HS.G-SRT.A.1: Verify experimentally the properties of dilations given by a center and a scale factor:
•HS.G-SRT.A.1.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.
•HS.G-SRT.A.1.b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
•HS.G-SRT.A.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.
•HS.G-SRTA.3: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
•HS.G-SRT.B: Prove theorems involving similarity
•HS.G-SRT.B.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.
•HS.G-SRT.B.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
•HS.G-SRT.C: Define trigonometric ratios and solve problems involving right triangles
Assessments:
Teacher observation
Aligned formative assessments
Quizzes
Weekly checks for understanding
Course assessment
Resources:
AchieveTheCore.org
Math: AchieveTheCore.org has free tasks and lesson plans for all standards K-12. This is a free sign up website
ADE Instructional Resources
PLANNING WEBSITE: Arizona Department of Education Teacher Toolbox with a variety of instructional materials for Algebra I; Geometry; and Algebra II.
ADE Math Standards
TEACHER RESOURCE: This is a link to the Arizona Department of Education website for teachers to access their grade level standards; along with examples and explanations provided by ADE.
AZCCRS Math Vocabulary & Formula Progression
PLANNING DOCUMENT: This document is a formula and vocabulary matriculation guide. It shows the progression of academic vocabulary and introduction/use of formulas from grade level to grade level as outlined in the AZCCRS.
BetterLesson.com
BetterLesson.com: lessons for many standards in Curriculum Frameworks-Free; but you need to sign up
Core Math Tools Help Guide
RESOURCE: Help Guide for use with Core Math Tools App
Formative Assessment Examples
PLANNING WEBSITE: This site contains links to a variety of engaging formative assessment strategies that can be used with students of all ages.
Progressions Documents for the Common Core Math Standards
PLANNING DOCUMENT: The Common Core State Standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels; informed both by research on children's cognitive development and by the logical structure of mathematics. These documents were spliced together and then sliced into grade level standards. They can explain why standards are sequenced the way they are; point out cognitive difficulties and pedagogical solutions; and give more detail on particularly knotty areas of the mathematics. Progressions documents also provide a transmission mechanism between mathematics education research and standards.
Planning from the Instructional Units
PLANNING DOCUMENT: This is a planning support document to help teachers lesson plan from the Instructional Unit level down to the day to day lesson level.
Math PLD Geometry
PLANNING DOCUMENT: Geometry AzMerit Performance Level Descriptors. This is a resource document which identifies what students should know and be able to do to achieve various levels towards proficiency according to the AzMerit Assessment.
High School Flip Book
PLANNING DOCUMENT: This document is intended to show the connections of the Standards for Mathematical Practices to the content standards in each conceptual category and provide information and instructional strategies that further describe the standards. The “Flip Book” is designed as a resource tool to assist teachers in deepening their understanding of what each standard means in terms of what students must know and be able to do. It outlines only a sample of instructional strategies and examples.
Geometry Textbook Alignment
At-a-Glance alignment of textbook to Instructional Units. Please use links in each IU under Resources for up-to-data and more specific information.
LearnZillion K-8 Math Curriculum Resource
LearnZillion is a cloud-based resource that includes a K-8 full math curriculum and math instructional videos for grades 2-12 searchable by grade; domain; or standard. Requires teachers to set up a free account.

School country

School state

School city

School / district Address

School zip code

Requested competency code

Date submitted

Approved

Approved competency code

• MTH2
• 4 years of Math

Approved date

Online / Virtual