Enroll in Geometry with Dolphin STEM Academy

Course Overview

Geometry is a branch of mathematics that uses logic and formal thinking to establish
mathematical relationships between points, lines, surfaces, and solids. In Geometry B,
you will review the volume formulas for some common solid figures as you extend your
knowledge of two-dimensional shapes to three-dimensional shapes. You will also
transition from primarily Euclidean geometry to analytical geometry—a segment of
geometry focused on numerical measurements and coordinate algebra. You will use
analytical geometry and observations to investigate the properties of circles and
constructions related to circles. Geometry B closes with a study of independent and
conditional probability and how you can use probability models to represent situations
arising in everyday life.

Course Goals

By the end of this course, you will be able to do the following:
Explain volume formulas and use them to solve problems.
Explain relationships between two-dimensional and three-dimensional objects.
Translate between the geometric description and the equation for a conic section.
Use coordinates to prove simple geometric theorems algebraically.
Apply theorems about circles.
Find arc lengths and areas of sectors of circles.
Apply geometric concepts in modeling situations.
Use independence and conditional probability to interpret data.
Use the rules of probability to compute probabilities of compound events in a uniform
probability model.
Use probability to evaluate outcomes of decisions.

Math Skills

Geometry A is a prerequisite for Geometry B. Before beginning this course, you should
be able to do the following:
Mathematically define rotations, reflections, translations, dilations, and slides.
Prove theorems about lines, angles, triangles, and parallelograms.
Create formal geometric constructions with a variety of tools and methods.
Understand the definitions of trigonometric ratios and use them to solve problems.
Solve quadratic equations by factoring or using the quadratic formula.
Understand that the probability of a chance event is a number between 0 and 1.

General Skills

To participate in this course, you should be able to do the following:
Complete basic operations with word processing software, such as Microsoft Word or Google Docs.
Understand the basics of spreadsheet software, such as Microsoft Excel or Google
Spreadsheets. More advanced skills, such as writing formulas, aren’t required.
Perform online research using various search engines and library databases.
Communicate through email and participate in discussion boards.

For a complete list of general skills that are required for participation in online courses,
refer to the Prerequisites section of the Plato Student Orientation document, found at
the beginning of this course.

Credit Value

Geometry B is a 0.5-credit course.

Course Materials

Notebook
Compass
Ruler or straight edge
Scientific calculator
Computer with Internet connection and speakers or headphones
Microsoft Word or equivalent
Microsoft Excel or equivalent

Course Pacing Guide

This course description and pacing guide is intended to help you keep on schedule with
your work. Note that your course instructor may modify the schedule to meet the
specific needs of your class.

Unit 1: Extending to Three Dimensions

Summary

In this unit, you will review the circumference and area of a circle and the volume of
some common solid figures: cylinders, pyramids, cones, and spheres. You will also
solve real-world problems that contain one or more of these shapes. Finally, you will
explore how two-dimensional and three-dimensional figures are related.

Syllabus for Geometry, Semester B, Unit 1

Unit 2: Connecting Algebra and Geometry through Coordinates

Summary

In this unit, you will examine the relationship between algebra and geometry. You will
use coordinates and algebra to prove simple geometric theorems and derive equations
that describe circles and parabolas. You will also use coordinates to partition a line
segment and to compute the perimeter and area of common plane figures.

Syllabus for Geometry, Semester B, Unit 2

Unit 3: Circles With and Without Coordinates

Summary

In this unit, you will investigate the properties of circles and constructions involving
circles. Sometimes you will work with coordinates, but you’ll also develop
relationships and formulas for circles empirically and use them to solve problems.

Syllabus for Geometry, Semester B, Unit 3

Unit 4: Independent and Conditional Probability

Summary

In this unit, you will apply the addition and multiplication rules of probability to
calculate probabilities using a uniform model. You will understand that an event is
a set of outcomes that can be related to other events or independent of them. You
will also use permutations and combinations to find the probabilities of compound
events.

Syllabus for Geometry, Semester B, Unit 4

Unit 5: Applying Probability

Summary

In this unit, you will use probability models to assess situations that arise in the
real world. You will apply counting rules to determine probabilities and use them to
make fair decisions and analyze strategies. Finally, you will find and interpret the
conditional probability of an event as it relates to other events.