Download Geometry Course Expectations

Mr. Kleinhenz’s
Geometry course expectations
E-mail: [email protected]
I expect students to come to class prepared. Complete all homework. Be present every day in
class (no daydreaming), speak up and listen. Respect all. Do your best. Participate in class and in
your teams. Stay organized. Ask for help and be positive.
Study team expectations: Discuss questions with your team before calling the teacher over. Don’t
talk to other teams. Within your team, keep your conversation on mathematics. You must try to
help anyone in your study team who asks. Helping your teammate does not mean giving
answers. Help by giving hints and asking good questions. Explain and justify your ideas; give
statements and reasons. Do not leave anyone behind or let anyone work ahead. Your team is not
done until everyone is done.
This course is designed for students to make sense of problems and persevere in solving them.
The course will offer students opportunities to construct viable arguments and critique reasons of
other. Students will make and test conjectures and be able to compare the effectiveness of two
plausible arguments. Students will look for and make use of structure to connect new material.
Students will attend to precision in use of clear definitions, symbols and units when
communicated to others.
Chapter 1 Shapes and Transformations: Investigations will introduce you to some basic
building-blocks of geometry: shapes, motions, measurements, patterns, reasoning and symmetry. You
will learn about transformations as you study how to flip, turn, and slide shapes. Then you will learn how
to use these motions to build new shapes and to describe symmetry. A “shape bucket” will introduce you
to a variety of basic shapes that you will describe, classify and name according to their attributes.
Chapter 2 Angles and Measurement: You will broaden your understanding of angle to include
relationships between angles, such as those formed by intersecting lines or those inside a triangle. You
will develop methods to find the areas of triangles, parallelograms, and trapezoids as well as more
complicated shapes. You will review the relationship among the sides of a right triangle called the
Pythagorean Theorem. This will allow you to find the perimeter of triangles, parallelograms, and
trapezoids, and to find the distance between two points on a graph.
Chapter 3 Justification and Similarity: As students discover the conditions that cause triangles
to be similar or congruent, they will learn about using a flowchart to organize facts and support their
conclusions.
Chapter 4 Trigonometry and Probability: Students will investigate the relationship between the
slope of a line and the slope angle. The slope ratio will be used to find missing measurements of a right
triangle and to solve real world problems. Students will continue their study of probability by using tree
diagrams and area models to calculate probabilities of events that are not equally likely. Students will
calculate expected values and probabilities of unions, intersections, and complements of events.
Chapter 5 Completing the Triangle Toolkit: Students will extend their understanding of
trigonometric ratios. Students will find missing side lengths and angle measures in non-right triangles.
Chapter 6 Congruent Triangles: You will develop strategies to directly conclude that two
triangles are congruent without first concluding that they are similar.
Chapter 7 Proof and Quadrilaterals: While investigating what congruent triangles can inform
you about the sides, angles, and diagonals of a quadrilateral, you will develop an understanding of proof.
This section begins a focus on coordinate geometry, the study of geometry on coordinate axes. During
this section, you will use familiar algebraic tools (such as slope) to make and justify conclusions about
shapes.
Chapter 8 Polygons and Circles: This section begins with an investigation of the interior and
exterior angles of a polygon and ends with a focus on the areas and perimeters of regular polygons. In this
section, similar figures are revisited in order to investigate the ratio of the areas of similar figures.
Chapter 9 Solids and Constructions: This section is devoted to the study of three-dimensional
solids and their measurement. This section will introduce you to the study of constructing geometric
shapes and relationships. For example, you will learn how to construct a perpendicular bisector using
only a compass and a straightedge.
Chapter 10 Circles and Conditional Probability: The relationships between angles, arcs,
and line segments in a circle will be investigated to develop “circle tools” that can help solve
problems involving circles. Area models and two-way tables provide the basis for calculating
conditional probabilities and determining whether events are independent. Some sample spaces
are so large that models cannot easily represent them. Based on the Fundamental Principal of
Counting, other formulas for permutations and combinations are developed that can be used to
solve more complex problems.
Chapter 11 Solids and Circles: In this section, you will learn how regular polygons can be used to
form three-dimensional solids called “polyhedra.” You will extend your knowledge of finding volume
and surface area to include other solids, such as pyramids, cones, and spheres. You will also investigate
the geometric relationships created when tangents and secants intersect a circle.
Chapter 12 Conics and Closure: You will start with what you know geometrically about a circle,
and extend it to write an algebraic equation for a circle. By studying the different cross-sections of a cone
(the conic sections), and a parabola in particular, you will further discover how geometry and algebra can
each define a shape.