Course/Grade Levels Units

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  • Course Code
    MA.MA065S/MA066S
    Content Area
    Math
    Description
    This course is a rigorous proof-based course designed to develop spatial concepts and insight into geometric relationships. A precise mathematical language is developed with an emphasis on reading and real-life problem solving.  Transformations on the coordinate plane provide opportunities for the formal study of congruence and similarity.  The study of similarity leads to right triangle trigonometry and connects to quadratics and circles through Pythagorean relationships.  The study of circles uses similarity and congruence to develop basic theorems related to circles and lines.  The link between probability and data is explored through conditional probability.  All units in this course will tie together geometric and previous advanced algebraic content knowledge such as systems of equations, factoring and solving quadratic equations.  Advanced proofs are integrated throughout the course and will allow students to experience Geometry as a useful and logical subject.

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Unit Description
Details
HGEOM01Foundations of Geometry
Students will understand the defined and undefined terms of Geometry, analyze and apply transformations to geometric figures and understand properties that are preserved by these transformations. They will construct geometric figures using a variety of tools and resources.

HGEOM02Introduction to Proofs
Students will be able to identify and prove angle relationships that occur with parallel lines that are cut by a transversal, intersecting lines and perpendicular lines.

HGEOM03Transformations
Students will be able to determine if two triangles are congruent and, if so, complete a proof showing that they are congruent.

HGEOM04Triangle Congruence
The student will define midsegment, median, centroid, perpendicular and angle bisectors, and altitude of triangles. They will apply and prove properties of these parts of triangles and use the coordinate plane to complete proofs.
HGEOM05Relationships in Triangles
Students will identify and apply similarity properties. They will prove polygons are similar/congruent, write similarity statements, identify scale factors and use properties of similar triangles to solve application and algebraic problems.
HGEOM06Similarity
Students will solve problems that involve finding the missing sides and angles of a triangle using trigonometry and finding the area of an oblique triangle.
HGEOM07Right Triangles and Trigonometry
The student will derive and use the properties of special quadrilaterals utilizing geometric and algebraic concepts on a coordinate plane. They will be able to calculate the area and perimeter of polygons in the coordinate plane.
HGEOM08Quadrilaterals and Other Polygons
Students will investigate and solve real-world problems involving area and volume.
HGEOM09Two- and Three-Dimensional Models
Students will discover that all circles are similar and the proportionality of the length of an arc intercepted by an angle to the radius. Students will learn the origin of radians and its role as the constant of proportionality and derive the formula for the area of a sector. In addition, students use their prior algebraic understanding of the quadratic equation and Pythagorean Theorem to find the equation of a circle. Students will understand how to utilize the coordinate plane to determine whether a given point is on a circle.
HGEOM10Circles
HGEOM10Circles and the Coordinate Plane
Students will discover the numerical relationship between arcs and angles of a circle and to provide ways of calculating segments related to circles.
HGEOM12Probability
Students will use conditional probability, represent sample space, use permutations and combinations, and find probabilities of compound events.