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
Geosketchpad exercises
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
Quadrilaterals
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
Radicals
Rationalization of Irrational
numbers
Factoring and Simplifying
Radical Expressions
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
Geosketchpad exercises
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
Geosketchpad exercises
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
Geosketchpad exercises
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
Geosketchpad exercises
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
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