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NNPS Curriculum Pacing Guide –
NNPS Curriculum Pacing Guide
Course Name: Geometry
Grade: 6 - 12
Course Description
Geometry is designed for students who have successfully completed the standards for Algebra I. All students are expected to
achieve the Geometry standards. The course includes, but is not limited to, properties of geometric figures, trigonometric
relationships, and reasoning to justify conclusions. Methods of justification will include paragraph proofs, two-column proofs,
indirect proofs, coordinate proofs, algebraic methods, and verbal arguments. A gradual development of formal proof will be
encouraged. Inductive and intuitive approaches to proof as well as deductive axiomatic methods should be used.
The geometry standards include emphasis on two- and three-dimensional reasoning skills, coordinate and transformational
geometry, and the use of geometric models to solve problems. A variety of applications and some general problem-solving
techniques, including algebraic skills, should be used to implement these standards. Calculators, computers, graphing utilities
(graphing calculators or computer graphing simulators), dynamic geometry software, and other appropriate technology tools will
be used to assist in teaching and learning. Any technology that will enhance student learning should be used.
Revised on:
NNPS Curriculum Pacing Guide –
Revised on:
NNPS Curriculum Pacing Guide –
1st Marking Period (45 days)
Topics (Big Ideas)
Estimated
Time
Enduring Understandings
Essential
Questions
Standards
2001 2009
Unit 1
Chapter 1: Tools of Geometry
 Defined and Undefined Terms
 Measuring Segments and Angles
 Identifying and Using Angle Pairs
 Basic Constructions
 Distance and Midpoint
*Perimeter, Area, and Circumference moved
to Unit 10
Unit 2
Chapter 2: Reasoning and Proof
 Patterns and Inductive Reasoning
 Conditional and Biconditional Statements
 Converses, inverses, and contrapositives
 Deductive Reasoning in Algebra and
Geometry
 Proving Angles Congruent
Unit 3
Chapter 3: Parallel and Perpendicular Lines
 Relationships between Lines and Angles
 Properties, Constructions, and Proofs of
Parallel and Perpendicular Lines
 Triangle Angle Theorems
 Equations and slopes of Lines in the
Coordinate Plane
Block
6
Daily
12
Geometry is a mathematical system
built on basic terms, definitions,
postulates, theorems, and formulas.
How do we identify
various figures and
express the
relationships presented
in postulates?
G.1,
G.2a
G.3
G.4
G.10
G.11
G.3a
G.4a
G.4b
G.4e
G.4f
7
14
How is inductive
reasoning used to make
conjectures?
How is deductive
reasoning used to solve
problems and make
predictions?
G.1
G.3
G.10
G.1a
G.1b
G.1d
8
16
Inductive reasoning is used to make
conjectures that will promote an
intuitive understanding of geometric
principles, while deductive reasoning
is used to develop proofs as a tool for
building a system of geometry based
upon definitions, postulates, and
theorems.
Lines can be identified as parallel or
perpendicular using special angle
pairs, slopes, or the equations of the
lines.
How do we identify and
graph the equations of
lines?
How do we prove lines
to be parallel or
perpendicular?
G.1
G.2a
G.3
G.4
G.9
G.11
G.1d
G.2a
G.2b
G.2c
G.3a
G.3b
G.4c
G.4d
G.4g
Review/Quarterly Assessment
1.5
3
TOTAL
22.5
45
Revised on:
NNPS Curriculum Pacing Guide –
2nd Marking Period (45 days)
Estimated
Time
Topics (Big Ideas)
Enduring Understandings
Essential Questions
Standards
2001 2009
Unit 4
Chapter 4: Congruent Triangles
 Congruent figures
 Triangle congruence
 Using congruent triangles
 Isosceles and equilateral triangles
 Right triangle congruence
 Congruence in overlapping triangles
Block
5.5
Daily
11
Postulates and theorems are used
to promote an understanding of
ways to prove triangles congruent.
Congruent triangles can then be
used to draw conclusions about
triangles, discover properties of
isosceles triangles, and prove other
triangles congruent.
How do we identify congruent figures?
How do we prove figures to be congruent?
How can congruent triangles be used to
prove that parts of triangles are congruent?
How does congruence help in determining
the properties of isosceles triangles?
How can congruent triangles help in proving
two other triangles congruent?
G1
G5
G7
G.4a
G.6
Unit 5
Chapter 5: Relationships Within
Triangles
 Midsegments of triangles
 Indirect reasoning
 Inequalities in triangles
4.5
9
Logical reasoning can be used to
hypothesize about geometric
relationships within triangles, to
deduce information about
inequalities in triangles, and to
support indirect proof.
How can midsegments be used for indirect
measurements?
How can inequalities in triangles be used to
find possible side and angle measures of the
triangles?
G.1
G2.a
G.3
G5
G6
G.1d
G.5a
G.5b
G.5c
G.5d
Unit 6
Chapter 6: Polygons and Quadrilaterals
 Polygon Angle Sum theorem
 Properties of parallelograms and
other quadrilaterals
 Proving that a quadrilateral is a
parallelogram
 Figures in the coordinate plane
Unit 7
Chapter 7: Similarity
 Ratios and proportions
 Similar polygons
 Proving triangles similar
 Similarity in right triangles
 Proportions in triangles
6.5
13
Basic properties of the sides, angles,
and diagonals of quadrilaterals
allow them to be classified as
special quadrilaterals such as
parallelograms, rhombuses,
rectangles, squares, trapezoids, and
kites.
How does angle measure of a polygon relate
to its number of sides?
How do the properties of quadrilaterals
relate to each other and allow us to classify
them?
How can we use these properties to place
figures in the coordinate plane?
G1
G2a
G8
G.2b
G.9
G.10
4.5
9
Proportions and algebraic ratios are
used to prove polygons similar, find
missing side lengths of similar
figures, and compare perimeter and
area of similar figures.
To what extent can two similar figures be
congruent?
How can we prove two triangles are similar
using a two column proof?
How do perimeter, area, and volume of
similar figures relate to one another?
G.2a
G.7
G.8c
G.7
G.14d
Review/Quarterly Assessment
2
4
TOTAL
23
46
Revised on:
NNPS Curriculum Pacing Guide –
3rd Marking Period (43 days)
Topics (Big Ideas)
Estimated
Time
Enduring Understandings
Essential Questions
Standards
2001 2009
Unit 8
Chapter 8: Right Triangles and
Trigonometry
 Pythagorean Theorem
 Special right triangles
 Trigonometry
 Angles of elevation and of
depression
Unit 12
Chapter 12: Circles
 Tangent lines
 Chords and arcs
 Inscribed angles
 Angle measures and segment
lengths
 Circles in the coordinate plane
Unit 9
Chapter 9: Transformations
 Translations, reflections,
rotations, and dilations
 Point and line symmetry
Block
6.5
Daily
13
The Pythagorean Theorem, ratios of
30-60-90 and 45-45-90 triangles,
trigonometric ratios are used to
solve problems involving right
triangles
How can the Pythagorean Theorem be
derived?
How can the ratios be used to solve for
unknown lengths of sides of triangles?
How can the ratios be used to solve for
unknown angles?
How do similar right triangles relate to
trigonometric ratios?
G.3
G.6
G.7
G.14b
G.8
7.5
15
Properties of lines, line segments,
and angles, relative to circles,
illustrate relationships to
intercepted arcs, intersecting
chords, tangents, and secants.
How can line segments form angles both
inside and outside of circles?
How can intercepted arcs be used to show
a relationship among angles, line
segments, and lines?
G.10
G.14b
G.11a
G.11b
G.12
Block
3.5
Daily
7
Isometric transformations describe a
change in the position of a figure
while the non-isometric
transformation, dilation, describes a
change in the size of a figure.
How is translation different from rotation?
How is a figure changed when two or more
transformations are applied?
How are isometric transformations
different from dilations?
G.2
G.3c
G.3d
G.10
Review/Quarterly Assessment
2.5
5
TOTAL
20
40
Revised on:
NNPS Curriculum Pacing Guide –
4th Marking Period (48 days)
Topics (Big Ideas)
Estimated
Time
Enduring Understandings
Unit 10
Chapter 10: Area
 Areas of triangles and
quadrilaterals
 Areas of regular polygons
 Perimeters and areas of
similar figures
 Circles and arcs
 Areas of circles and sectors
6.5
13
Formulas are used to find the area of
triangles, quadrilaterals, regular
polygons, circles, and sectors.
Formulas are also used to find the
circumference and arc length of
circles.
Unit 11
Chapter 11: Surface Area and
Volume
 Space figures and nets
 Surface areas of cylinders,
prisms, pyramids, cones, and
spheres
 Volumes of prisms, cylinders,
pyramids, cones, and
spheres
 Areas and volumes of similar
solids
TOTAL
6.5
13
Nets and space figures are used to
help in understanding three
dimensional figures and in finding
surface area and volume of these
solids.
13
26
Essential Questions
How can finding the area of a rectangle
help in finding the area of a parallelogram
or triangle?
How can the width and length as opposed
to the base and height affect the area of
some polygons?
How does the measure of an arc length
relate to the circumference of the circle?
How does the area of a shaded region
correspond to the area of a circle?
How can a two dimensional figure be
folded into a three dimensional solid?
To what extent does the area of a two
dimensional figure relate to the surface
area and volume of a three dimensional
figure?
How can ratios be applied to similar solids
to determine surface area and volume?
Standards
2001 2009
G.2a
G.7
G.8c
G.10
G.11b
G.11c
G.14a
G.14c
G.14d
G.12
G.13
G.14
G.13
G.14b
Remaining days to review for SOL
Revised on: