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

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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



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