This course is available in the Fall and Spring Semesters.
Description:
This is the second of two courses that comprise Geometry. Throughout
the course, the student will use virtual manipulatives and tools to
explore area, surface area, and volume, and study the concept of
similarity as it relates to various figures. The student will use
Trigonometry and right triangle concepts, such as 30-60-90, 45-45-90,
and the Pythagorean Theorem to solve problems. The student will also be
introduced to vectors and learn to solve problems involving magnitude
and direction. In addition, the student will study transformation
concepts, such as translations, reflections, rotations, and dilations as
well as concepts associated with symmetry. The student will learn to
use formulas to find the areas of a variety of two-dimensional shapes.
This course concludes with an exploration of concepts related to
circles, such as arcs, angles, and intersecting lines such as chords,
secants, and tangents.
Throughout the course, the student will learn concepts through a variety
of instructional strategies, solve real-world applications, and
complete an assortment of activities.
Units:
Similarity
In
this unit on similarity, you will learn to use ratios to compare
quantities, write proportions, and solve problems. You will also use
ratios and proportions to determine whether two polygons are similar, to
find unknown side lengths of similar figures, and to solve problems
relating to scale factor. You will explore similar triangles and related
postulates and theorems. You will also use similarity to find indirect
measurements in right triangles, as well as the relationship between
segments and between lengths. Finally, you will complete a portfolio
assessment involving scale drawing.
Right Triangles and Trigonometry
In
this unit, you will explore concepts related to right triangles. You
will use the Pythagorean Theorem and explore the concept of a
Pythagorean triple, as well as properties of special right triangles.
You will use trigonometric ratios to find side lengths and angle
measures of right triangles. To solve real-world scenarios, you will use
angles of elevation and depression. Lastly, you will learn about
vectors and use them to describe the magnitude and directions of
objects. Your activities include a class discussion involving ramp
building codes and a unit portfolio that explores the history and many
proofs of the Pythagorean Theorem.
Transformations
Concepts
related to transformations are explored in this unit. Students will
explore translations, reflections (including glide reflection and
compositions of reflections), rotations, and dilations. Students will
identify, find, and compose transformations both on and off the
coordinate plane. Students will identify isometries as well as the type
of symmetry in figures and three-dimensional objects. Students will also
use reflection to minimize distance, find angles of rotation, and scale
factor for dilation. A variety of activities are used in lessons
through out the unit to aid instruction. Activities involving the
textbook, Teachlet® tutorials, and movie clips provide
information on concepts and using concepts to solve problems. Real-world
examples are incorporated into each lesson. A variety of worksheets,
such as question worksheets based on examples in the textbook, puzzle
worksheets, and practice worksheets involving problem-solving are used
to practice concepts and review vocabulary. Math writing journal
activities as well as online interactive activities provide discovery
learning opportunities for students.
A variety of assessment
tools are incorporated into each lesson. Online practices, self-check
activities, and feedback are used through out. Assessments such as quick
checks, quizzes, and a unit test appear at the end of each lesson. A
portfolio involving frieze patterns is also used for assessment
purposes.
Area
In
this unit, you will explore and find the area of polygons and circles.
You will use formulas to find areas of regular polygons, parallelograms,
triangles, trapezoids, rhombuses, kites, and circles, including parts
of circles such as sectors and segments. You will use trigonometry to
find the areas of regular polygons and triangles, as well as the area
formula for a triangle given SAS. In addition, you will use 30°-60°-90°
and 45°-45°-90° special triangles to find area. You will also learn and
apply concepts related to regular polygons, including perimeter and area
ratios of similar figures, as well as circle concepts like naming arcs,
finding arc measure and length, and finding the circumference of a
circle. You will use these concepts to find the area of composite
figures and missing dimensions of figures, in addition to using them
to solve real-world applications. Finally, you will complete a portfolio
project involving circle graphs, and participate in a discussion about
Heron's Formula.
Surface Area and Volume
This
unit covers area and volume of three-dimensional solids. The unit
begins with defining the polyhedron space figure, the parts of a
polyhedron, and examining cross sections. Euler's Formula is introduced
and used to find the number of faces, vertices, or edges of a
polyhedron. Students will explore and use formulas to find lateral
areas, surface areas, and volume of three-dimensional solids, such as
prisms, cylinders, pyramids, cones, and composite figures. Sphere
terminology such as center, radius, diameter, great circle, hemispheres, and circumference
are explored and defined. Students will use formulas to find the area
and volume of spheres. The unit ends with exploring the areas and
volumes of similar solids, including identifying similar solids, finding
scale factor, and using area and volume ratios to solve problems.
Circles
This
unit explores concepts related to circles, such as central angles,
inscribed angles, and angles formed by intersecting lines–including
chords, tangents, and secants. Students will examine the relationships
between angles both inside and outside of a circle and the measure of
the intercepted arcs. These relationships, as well as properties of
tangents, will be used to solve problems involving angle measure, arc
measure, and segment lengths. Students will also explore circles in the
coordinate plane, including writing an equation of a circle in standard
form. Using radius, circle center, or a point on the circle, students
will graph circles in the coordinate plane and be able to identify
circle center and radius in an equation of a circle in standard form.A
variety of instructional strategies and activities are used to engage
students and enhance instruction. Such activities include online
Teachlet® tutorials, Gizmos, activities, math writing journal
activities, puzzles, and practice worksheets. Online practice,
self-assessment, and problem feedback are included throughout the unit.
Students will also complete a unit portfolio involving paper-folding
activities to explore properties of chords.
Gifted and Talented Math 8 B Semester Exam
This
unit reviews concepts from Semester B of the Gifted and Talented Math 8
course. The unit begins with a review assignment which intends to help
the student recall topics from Units 1 through 6. A vocabulary activity
explores special terms and properties from the course. Two Quarter Tests
are also given for students to practice the concepts from this semester
in a more formal format. The assessment is included at the conclusion
of the unit in the form of the Semester Exam.
Online Text/eBook