Geometry is typically the second math course taken by high school students. Major topics discussed include introductory logic; coordinate geometry; congruence, similarity and proof; right triangle trigonometry; transformations; locus; constructions; circles; and three-dimensional objects. Students will garner reasoning skills and learn how to form logical and coherent arguments. This course is aligned with the Common Core Learning Standards and integrates the eight Standards for Mathematical Practice throughout the curriculum. Common Core Learning Standards denoted by “★”indicate opportunities to emphasize the concepts of modeling with mathematics. In order to earn an Advanced Regents Diploma, students must pass the Integrated Algebra, Geometry, and Algebra 2/Trigonometry Regents Exams, among others, prior to graduation The Common Core Standards for Mathematical Practice are:

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.

UNIT 1 – LOGIC (3 days)

TOPICS:

Truth Values, Conjunction, Disjunction, Conditional, Biconditional); Inverse, Converse, Contrapositive; Logical Equivalence RESOURCES:

jmap.org; regentsprep.org;

Prentice Hall: NY Geometry Chapter 2

ESSENTIAL QUESTIONS

How do we make convincing arguments?

NEW YORK STATE STANDARDS

G.G.24Determine the negation of a statement and establish its truth value G.G.25 Know and apply the conditions under which a compound statement (conjunction, disjunction, conditional, biconditional) is true G.G.26 Identify and write the inverse, converse, and contrapositive of a given conditional statement and note the logical equivalences

COMMON CORE LEARNING STANDARDS

(None)

ASSESSMENTS

Unit Quiz

UNIT 2 – CONNECTING ALGEBRA AND GEOMETRY THROUGH COORDINATES (20 days) TOPICS:

Use coordinates to prove simple geometric theorems algebraically. Translate between the geometric description and the equation for a conic section. RESOURCES

jmap.org; regentsprep.org;

Prentice Hall: NY Geometry Chapter 3

ESSENTIAL QUESTIONS

How can we use coordinate geometry to represent real-life situations?

NEW YORK STATE STANDARDS

G.G.62 Find the slope of a perpendicular line, given the equation of a line G.G.63 Determine whether two lines are parallel, perpendicular, or neither, given their equations G.G.64 Find the equation of a line, given a point on the line and the equation of a line perpendicular to the given line G.G.65 Find the equation of a line, given a point on the line and the equation of a line parallel to the desired line G.G.66 Find the midpoint of a line segment, given its endpoints G.G.67 Find the length of a line segment, given its endpoints G.G.68 Find the equation of a line that is the perpendicular bisector of a line segment, given the endpoints of the line segment G.G.69 Investigate, justify, and apply the properties of triangles and quadrilaterals in the coordinate plane, using the distance, midpoint, and slope formulas G.G.70 Solve systems of equations involving one linear equation and one quadratic equation graphically

COMMON CORE LEARNING STANDARDS

(CORRESPONDS TO CCLS GEOMETRY UNIT 4)

G.GPE.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). G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and uses them to solve geometric problems (e.g., find the equation of a line...