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Middle School
Grade 8 Geometry
Curriculum Map
Second Semester, 2012/2013
-Chapter Overview:
In this Semester students will continue studying chapter 8 introducing ratio and proportions through
similarity.
In Chapter 9 Students will solve right triangles with trigonometry.
In Chapter 10 the students will identify segments and lines related to circles, using properties of arcs and
chords of circles, using inscribed angles and properties of inscribed polygons .Students find the lengths of
the segments of chords, tangents, and secants, they find the equation of a circle and use it to graph it to
graph and solve problems. The chapter ends by students drawing loci that satisfy given condition.
Chapter 11 explores many topics which relate to the area of polygons and circles. It begins by finding the
measures of the interior and exterior angles of polygons. Then students are introduced to the
circumference of a circle and the area of a sector of a circle. The chapter ends by introducing geometric
probability.
IN Chapter 12 students will investigate the surface area and volume of solids. First, they will learn to
distinguish polyhedral from other solids and to classify polyhedral. They will identify the Platonic solids
and use Euler’s Theorem, They will use different methods to explore and identify surface areas and
volumes.
From algebra 1 curriculum the students will move on to solving systems of linear inequalities with
quadratic equations and their graphs.
The unit then ends will factor polynomial expressions and use factoring to solve quadratic equations.
-Focus Standards:
Geometry
G.10
G.3.1
G.11
G.3.1
G.4
G.7
G.2.3
G.3.2
G8
G.3.2
G.12
G.3.1
G.14
G.3.1
G.13
G.3.1
Algebra:
A.12
AI.3.2
A.12
AI.2.2
Learning Objectives, students will be able to:
Geometry:
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Use similar polygons to solve real-life problems.
be able to draw dilations
A.11
AI.2.1
A.9
AI.2.1
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be able to solve problems involving similar right triangle
use Pythagorean Theorem
Be able to use trigonometric ratios.
Use arcs, angles and segments in circles to solve real-life problems.
Be able to use the graph of an equation of a circle to model real-life situations.
find angle measures and areas of polygons
compare perimeters and areas of similar figures
Find the circumference and area of a circle and find other measurements related to circles.
calculate the surface area and volume of various solids
use surface area and volume in real-life situations
Use surface area and volume in real-life situations.
Calculate the surface area and volume of various solids.
Algebra:
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use linear combinations and substitution to solve a system of linear equations
Solve a polynomial equation in factored form.
Be able to factor a quadratic expression
Use the distributive property to factor a polynomial.
-Terminology, literary terms/vocabulary list to be studied:
Geometry:
Similar polygons
Dilation
Enlargement
Pythagorean triples
Special right triangles
Trigonometric ratios
Angle of elevation
Angle of depression
Magnitude of a vector
Direction vector
Circle
Secant
Tangent
Point of tangency
Central angle
Arc
Measure of an arc
Inscribed angle
Intercepted arc
Inscribed polygon
Circumscribed circle
Standard equation of a circle
Locus
Apothem of a polygon
Central angle of a regular polygon
Circumference
Arc length
2
Sector of a circle
Probability
Geometric probability
Polyhedron
Platonic solids
Prism
Cylinder
Pyramid
Circular cone
Sphere
Algebra:
Factoring form
Zero-product property
Factor a quadratic expression
Factor completely
-Suggested works/ themes/selections/readers:
We will study the geometry text book together with algebra 1 sheets.
From the geometry textbook lessons:
8.4 Similar Triangles
8.5 Proving Triangles are Similar
8.6 Proportions and Similar Triangles
8.7 Dilations
9.1 Similar Right Triangles
9.2 The Pythagorean Theorem
9.3 The Converse of the Pythagorean Theorem
9.4 Special Right Triangles
9.5 Trigonometric Ratios
9.6 Solving Right Triangles
9.7 Vectors
10.1 Tangents to Circles
10.2 Arcs and Chords
10.3 Inscribed Angles
10.4 Other Angle Relationships in Circles
10.5 Segment Lengths in Circles
10.6 Equations of Circles
11.1 Angle Measures in Polygons
11.2 Areas of Regular Polygons
11.3 Perimeters and Areas of Similar Figures
11.4 Circumference and Arc Length
11.5 Areas of Circles and Sectors
11.6 Geometric Probability
12.1 Exploring Solids
12.2 Surface Area of Prisms and Cylinders
3
12.3 Surface Area of Pyramids and Cones
12.4 Volume of Prisms and Cylinders
12.5 Volume of Pyramids and Cones
12.6 Surface Area and Volume of Spheres
12.7 Similar Solids
From Algebra 1 textbook we will cover the following lessons
7.2 Solving Linear Systems by Substitution
7.3 Solving Linear Systems by Linear Combinations
7.6 Solving Systems of Linear Inequalities
9.4 Solving Quadratic Equations by Graphing
9.5 Solving Quadratic Equations by the Quadratic Formula
9.6 Applications of the Discriminant
10.3 Special Products of Polynomials
10.4 Solving Polynomial Equations in Factored Form
10.5 Factoring x2 + bx + c
10.6 Factoring ax2 + bx + c
10.7 Factoring Special Products
10.8 Factoring Using the Distributive Property
-Curriculum Activities:
Activity on dividing a segment into equal parts p. 500
Activity on index cards p.527
Focus on career (architect) design of a skyscraper p.537
Activity on Inscribed Angles p.612
Activity on segment Lengths p.628
Timekeeping research p.648
Activity on the sum of polygon angle measures p.661
Activity on Surface area p.727
Activity on Volumes p.751
Focus on career (construction) Concrete Weighs p.745
-Suggested Interdisciplinary unit:
Geometry on a Sphere Textbook page 714 - 718
-Assessment:
Homework Assignments
Class work
Quizzes
Project
Tests
Quarter Exam
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Uniform
Punctuality
Class preparation
Class contribution
Attendance
10%
10%
20%
10%
20%
25%
5%
4