# High School: Basic Geometry Detailed Curriculum Skills Map 4/07

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10 Οκτ 2013 (πριν από 4 χρόνια και 7 μήνες)

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2005

Math Curriculum

1

of
5

High School: Basic Geometry Detailed Curriculum Skills Map

4/07

Content Unit

Skills

Assessment

Standards

September

Chap 1, plus outside sources

Real Numbers and Number Sets

Numerical Sense and Operators

Order of Operations

Number Lines and Signed
Numbers

Classifying Angles

Tools for Geometric
Construction

Postulates of Equality

Geometry of Planes

Identify subsets of real number system

Estimate and compute w/rational numbers

Compare and order integers

Simplify numeric expressions “by hand” and w/c
alculators

Translate word problems into equations

Solve problems with one variable

Identify, define, and name points, lines, rays, and
segments

Classify and construct angles, bisectors, perpendiculars
using protractors, compasses, straightedges

Draw conclu
sions about geometric figures using postulates

Daily warm up set

Daily homework check

Questioning and investigation responses

Board work

Observation of peer teaching during cooperative
exercises

Vocabulary journal

Weekly quizzes

Chapter test

A.12.1

A.12
.2

A.12.3

A.12.4

A.12.5

A.12.6

B.12.2

B.12.3

C.12.1

October

Outside sources

Fractions, Decimals, And
Percents

Chap 7

Ratios and Proportions

Maps and Scales

Chap 2

Introduction to Proofs

Supplementary and
Complementary Angle
Theorems

Parallel Lines I

Conditional Statements

Conclusive Reasoning

Writing 2 Column Proofs

Compare, order and convert among fractions, decimals,
and percents

Find ratios of numbers(measures) in simplest form

Write proportional equations

Solve problems using proportions

Apply pro
portions using the concept of scale factors in
maps and scale drawings

Convert measures of currency, weights, distance, etc, to
equivalent units

Use theorems to construct two column proofs

Interpret and write a conditional statement and its converse

Develo
p argument using the contra positive in proof and
the logic of indirect proof

Identify, define, and use the properties of parallel lines and
their angles formed by transversals

Construct equal angles and parallel lines

Daily warm up set

Daily homework chec
k

Questioning and investigation responses

Board work

Observation of peer teaching during cooperative
exercises

Vocabulary journal

Weekly quizzes

Chapter test

Demonstration of construction of maps and scale
drawings in projects

Real world application projec
t (e.g. Pack Your Bags

international travel assignment)

A.12.1

A.12.2

A.12.3

A.12.4

A.12.5

A.12.6

B.12.2

B.12.3

B.12.4

C.12.2

C.12.3

D.12.3

November

Chap 3, 4

Triangle Angle Sum Theorem

Exterior Angle Corollary

Classifying Triangles

Congruent Triang
les

Postulates and Theorems of
Corresponding Parts of
Congruent Triangles

Congruent Triangle
Constructions

Altitudes and Medians of
Triangles

Inscribed and Circumscribed
Circles

Properties of Isosceles Triangles

Compute angle measures using Triangle Angle
Sum
Theorem and Exterior Angles Corollary

Classify triangles by sides and angles: isosceles,
equilateral/equiangular, acute, scalene, obtuse, right

Identify congruent triangles by corresponding parts

Apply triangle angle and side theorems to prove
congruen
cy of triangles: SAS, SSS, ASA, AAS, HL

Prove segments and angles of triangles are equal using
the concept of corresponding parts

Demonstrate logic that supports the construction of angle
bisectors, perpendiculars (altitude/median), and equal
angles

Constr
uct inscribed and circumscribed circles

Implement isosceles triangle theorems in proofs

Use Geosketchpad (or other appropriate software
technology) for constructions

Daily warm up set

Daily homework check

Questioning and investigation responses

Board work

Observation of peer teaching during cooperative
exercises

Vocabulary journal

Weekly quizzes

Chapter test

Summary pamphlet on methods of proving congruency
using the appropriate theorems and postulates

Quarterly notebook check

Reflect
ion for self
-
assessment

A.12.1

A.12.2

A.12.3

A.12.4

A.12.5

A.12.6

C.12.1

C.12.2

C.12.3

D.12.3

2005

Math Curriculum

2

of
5

Content Unit

Skills

Assessment

Standards

December

Chap 5

Polygons

Angle Sums of convex Polygons

Properties of Parallelograms

Midpoints Theorem

Classify polygons: convex, not convex,
regular

Apply the polygon angle sum formula, and the exterior
angle sum theorem

Use angle sum theorems in informal proofs

Classify quadrilaterals as parallelograms, rectangles,
squares, rhombuses, trapezoids

Demonstrate the use of the properties of various

parallelograms/trapezoids in computation and proofs

Derive the midpoint theorem for trapezoids

Demonstrate the application of the midpoint theorem in
geometry

Daily warm up set

Daily homework check

Questioning and investigation responses

Board work

Observ
ation of peer teaching during cooperative
exercises

Vocabulary journal

Weekly quizzes

Chapter test

Real world application project (e.g. Golden Rectangles)

A.12.1

A.12.2

A.12.3

A.12.4

A.12.5

A.12.6

B.12.5

C.12.1

C.12.2

C.12.3

D.12.3

January

Skill build
ers Unit

Rationalization of Irrational
numbers

Factoring and Simplifying

Perfect Squares and Square
Roots

Distributive Property of
Multiplication

Semester Review

Recognize inverse relations of squares and square roots

Reduce ra
dical expressions to simplest terms by factoring

Rationalize fractions w/radicals in the denominator

Perform operation w/radical expressions

Solve for variables in equations with radical expressions

Distribute scalar and variable factors across parentheses

Combine like terms in polynomials to simplify expressions

Synthesize concepts from the semester to create a final
exam to be used as a study tool

Daily warm up set

Daily homework check

Questioning and investigation responses

Board work

Observation of peer

teaching during cooperative
exercises

Vocabulary journal

Weekly quizzes

Chapter test

KWL chart

Final exam project : student
-
created semester exam
w/solution key

Quarterly notebook check

Reflection for self
-
assessment

Semester final exam

A.12.1

A.12.2

A.12
.3

A.12.4

A.12.5

A.12.6

B.12.2

B.12.3

B.12.4

B.12.5

C.12.2

D.12.3

F.12.2

F.12.3

February

Chap 6,8

Area and perimeter

Area of parallelograms,
rectangles, and squares

Area of a triangle

Area of a trapezoid

Circumference and Area of
Circles

Right Triang
les

Pythagorean’s Theorem
/Converse

Similar Polygons

Triangle Proportionality
Theorem

Similarity: Perimeters and Areas

Compute the area and perimeter(circumference) of the
given shapes: parallelograms, rectangles, squares,
triangles, trapezoids, circles

De
rive the formula for the areas of parallelograms and
trapezoids

Approximate the measures of circles using the decimal
equivalent of
pi.

Apply Pythagorean’s Theorem and its converse in
computation and as a tool to classify triangles

Estimate the square root

of a number

Use the AA postulate of similar triangles in proofs and
computations

Recognize and identify similar polygons and apply their
properties

Relate parallel line postulates to similar triangles

Create proportions among similar triangles by applying

the
Triangle Proportionality Theorem

Incorporate scale factors and ratios to calculate perimeters
and areas of similar triangles

Compare congruent and similar triangle postulates

Daily warm up set

Daily homework check

Questioning and investigation respons
es

Board work

Observation of peer teaching during cooperative
exercises

Vocabulary journal

Weekly quizzes

Chapter test

A.12.1

A.12.2

A.12.3

A.12.4

A.12.5

A.12.6

B.12.2

C.12.1

C.12.2

C.12.3

D.12.3

F.12.4

2005

Math Curriculum

3

of
5

Content Unit

Skills

Assessment

Standards

March

Chap 9

Circles and Terminology

Tangents

Chords, Arcs and Equality
Theorems

Chords, Diameters, and
Perpendicularity

Inscribed/Circumscribed
Polygons and Circles

Define and use the terms related to circles

Construct tangents to a circle at a given point

Use Geosketchpad (or other appropriate softw
are
technology) for construction

Apply theorems relating tangents and radii

Classify arcs

Compute the measure of an arc or angle

Apply theorems relating chords and arcs

Calculate the measure of an inscribed angle

Use theorems of equality of arcs and cho
rds

Find the measure of angles formed by chords, tangents,
and secants

Demonstrate the properties of proportions with segments of
intersecting chords to determine measurements of
segments

Daily warm up set

Daily homework check

Questioning and investigation

responses

Board work

Observation of peer teaching during cooperative
exercises

Vocabulary journal

Weekly quizzes

Chapter test

Summary pamphlet including illustrations which provide
geometric and algebraic relationships of arcs, chor
ds,
segments, and angles

Quarterly notebook check

Reflection for self
-
assessment

A.12.1

A.12.2

A.12.3

A.12.4

A.12.5

A.12.6

C.12.1

C.12.2

C.12.3

D.12.3

F.12.4

April

Chap 10

Lines and Planes in Space

Areas and Volumes of Solids

Similar solids

Cross sect
ions

Right Triangles/Special Right
Triangles

Diagonals in Rectangular Solids

Trigonometric Ratios

Angles of Elevation and
Depression

Draw and interpret 3
-
dimensional representations of solid
figures

Identify the positions of points, lines, and planes with
respect to each other

Use formula to calculate the lateral area, total area, and
volume of right prisms, right circular cylinders, regular
pyramids, and spheres

Define and appropriately apply terminology of solids(e.g.
height, slant height)

Apply proportio
ns to compute and compare the ratio of
area and volume of similar solids

Visualize and draw cross sections of a variety of solid
figures

Relate cross
-
sections and geometric models to word
problems to help interpret, analyze, and develop solutions
to real
world problems

Use Geosketchpad to construct models

Recognize and solve problems using common/special right
triangle relationships (45
-
45
-
90 and 30
-
60
-
90), including
those involving pyramids and cones

Derive the formula for length of the diagonal of rectan
gular
solids and demonstrate its use

Create ratios of sine, cosine, and tangent to compute angle
measures in a right triangle

Calculate angles of depression and angles of elevations
seen in real world application

Daily warm up set

Daily homework check

Ques
tioning and investigation responses

Board work

Observation of peer teaching during cooperative
exercises

Vocabulary journal

Weekly quizzes

Chapter test

Graphic organizer

Real world application project (e.g. Package This

NASA theme
projects)

A.12.1

A.12.2

A.12.3

A.12.4

A.12.5

A.12.6

B.12.2

B.12.3

B.12.5

B.12.6

C.12.1

C.12.2

C.12.3

C.12.5

D.12.3

F.12.3

F.12.4

2005

Math Curriculum

4

of
5

Content Unit

Skills

Assessment

Standards

May

Chap 12

Coordinate geometry

Points on the Cartesian
coordinate plane

Distance and Midpoint formula

Slope

Slope interc
ept form, point slope
method, rate of change

Parallel/Perpendicular Lines and
Slope

Graphing Linear Equations

Coordinate Geometry Proofs

Specify points by their coordinates in the Cartesian
coordinate plane

Graph and ma
nipulate figures in the coordinate plane

Calculate distance between two points using a variety of
methods

Apply the midpoint theorem

Compute slope using a pair of coordinates

Develop and employ the point
-
slope form and
slope/intercept form of linear equat
ions

Graph linear equations using tables, slope, points,
intercepts

Use slope to find the equations of parallel/perpendicular
lines

Draw figures in the coordinate plane by plotting points and
graphing equations

Create tables of values for linear equations
and graph “by
hand” and using calculator technology

Prove theorems using coordinate geometry

Apply slope as rate of change in real world situations

Use Geosketchpad to construct models

Solve one and two variable linear equations and systems
of equations us
ing algebraic and graphing methods

Daily warm up set

Daily homework check

Questioning and investigation responses

Board work

Observation of peer teaching during cooperative
exercises

Vocabulary journal

Weekly quizzes

Chapter test

KWL

chart

Real world application project

A.12.1

A.12.2

A.12.3

A.12.4

A.12.5

A.12.6

B.12.3

B.12.5

C.12.1

C.12.2

C.12.4

D.12.3

F.12.1

F.12.2

F.12.3

F.12.4

2005

Math Curriculum

5

of
5

Content Unit

Skills

Assessment

Standards

June

Chap 13

Transformations

Rotations, Reflections,
Translations

Enlargements,
Reductions

Tessella
tions

Review of Second
Semester

Closing

Identify figures that have been transformed through
rotation, reflections, translation or a combination of these

Draw figures transformed by rotation, reflection, translation,
enlargement, or reduct
ion

Determine a line of symmetry or reflection

Determine a point of rotation

Analyze the relationship of the points of a figure and those
of its transformation

Create a tessellation using transformations

Synthesize concepts from the semester to create a fi
nal
exam to be used as a study tool

Daily warm up set

Daily homework check

Questioning and investigation responses

Board work

Observation of peer teaching during cooperative
exercises

Vocabulary journal

Weekly quizzes

Chapter test

Te
ssellation project

Quarterly notebook check

Final exam project

Semester final exam

A.12.1

A.12.2

A.12.3

A.12.4

A.12.5

A.12.6

B.12.1

C.12.2

C.12.4