• Course Description

    Students will use inductive and deductive reasoning to develop an axiomatic system which describes the properties of two and three
    dimensional objects.  A solid, working knowledge of Algebra I skills is necessary.

    Grade Level(s): 8th-12th, Duration 1 Year

    Related Priority Standards (State &/or National): K-12 Mathematics Missouri Learning Standards  

    Enduring Understanding/Big Ideas:

    • Students will determine expressions and values using mathematical operations, procedures and rules.
    • Students will translate mathematical information from a single representation or across multiple representations in order to develop processes to solve problems.
    • Students will recognize mathematical reasoning requires justification of both process and solution.
    • Students will use correct notation, language and mathematical conventions to classify concepts and communicate results or solutions.

    Course Level Scope & Sequence (Units &/or Skills):

    Intro Unit: Reasoning in Geometry

    • Creating Definitions
    • Inductive vs. Deductive Reasoning
    • Logical Statements
    • Visual Representations
    • Pythagorean Theorem

    Unit 1: Foundations of Geometry

    • Creating diagrams with tick marks
    • Segments, Rays and Midpoints
    •  Classifying Angles and Bisectors
    • Angle Pairs
    • Constructions
    • Slope, Midpoints & Distance

    Unit 2: Parallel and Perpendicular Lines

    • Constructions – Perpendicular Lines
    • Parallel Line Angle Pairs
    • Angle Pairs & Algebra
    • Properties of Proofs
    • Intro to proofs
    • Proofs

    Unit 3: Rigid Motions

    • Translations
    • Reflections
    • Rotations
    • Polygon Symmetry
    • Composition of Rigid Motions
    • Inverse Transformations

    Unit 4: Triangles

    • Polygon Constructions
    • Triangle Theorems
    • Corresponding Parts & Congruent Triangles
    • Congruent Triangle Proofs
    • CPCTC
    • CPCTC Extended
    • Polygon Angle Sum Theorems

    Unit 5: Quadrilaterals

    • Definitions of Quadrilaterals
    •   Properties of Parallelograms and Algebra
    • Properties of Other Quadrilaterals and Algebra
    • Classify Quadrilaterals with Slope
    • Classify Quadrilaterals with Slope & Distance

    Unit 6: Area and Perimeter

    • Introduction to Area
    • Perimeter and area of  Parallelograms & Triangles
    • Perimeter and area of Trapezoids
    • Area of a Circle and Circumference
    • Arc length and sector area
    • Maximizing Area

    Unit 7: Similarity

    • Ratios and proportions
    • Similar Polygons
    • Ratios of Perimeter and Area
    • Side Splitter Theorem
    •  AA Postulate
    • SAS and SSS Postulate
    • Dilations

    Unit 8: Trigonometry

    • Operations on Radicals
    • Special Right Triangles
    • Introduction to Trigonometry
    •  SOH-CAH-TOA Solve for Sides
    • SOH-CAH-TOA Solve for Angles
    • Trig Applications
    • Law of Sines 
    • Law of Cosines

    Unit 9: Circles

    • Circle Constructions
    • Arcs, Central Angles and Sectors
    • Inscribed Angles
    • Tangents
    • Perpendicular Chords
    • Other Angles
    • Chords, Secants, and Tangents
    • ​​Equation of a Circle

    Unit 10:  Volume and Surface Area

    • Rectangular and Square Prisms
    • Polygonal Prisms
    • Spheres
    • Pyramids
    • Cylinders
    • Cones
    • Ratios of Volume

    Course Resources & Materials: District and teacher-made materials

    Date Last Revised/Approved: 2002