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Revised 7/19/13
Geometry Curriculum Map
2013-14 School Year

The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics
increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary,
middle and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connect
the mathematical practices to mathematical content in mathematics instruction. http://www.corestandards.org/Math/Practice

Course Description and ELA Standards: http://www.cpalms.org/Courses/PublicPreviewCourse36.aspx?kw=geometry

During the 2013-2014 school year Florida will be transitioning to the Common Core State Standards for Mathematics. The content
standards for Geometry are based upon these new standards; however, during this transition year students will be assessed using the
Geometry EOC for Geometry aligned with the Next Generation Sunshine State Standards. For this reason, instruction should include a
blend of the CCSS and the NGSSS.

The timeframes listed on this calendar are estimates. You may need to adjust some of them from time to time based on data to meet the
needs of your students as some concepts may take less time and some may take more time. The state Geometry EOC Assessment will be
administered May 19-23, 2014. If possible, teachers may want to try to complete content instruction at a quicker pace than listed below
(FYI- it includes MA.912.T.2.1: Define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) in terms of
angles of right triangles.

Florida Continuous Improvement Model (FCIM) Mini Lessons are available on the Secondary Mathematics Moodle Site:
http://learn.pasco.k12.fl.us/course/view.php?id=163 The goal is to use the FCIM lesson as a review after the standard has already been
taught in the classroom. Each of the lessons follow the gradual release model (I Do, We Do, You Do) and have collaborative structures
embedded throughout.
Geometry EOC Assessment Practice Resources :
 Florida Virtual Algebra 1 EOC Materials www.flvs.net/eoc - click on Geometry
 Escambia County has developed some reviews for the Math EOC exams – http://ecsd-fl.schoolloop.com/EOCReviews
 Geometry FCIM Lessons (on Secondary Mathematics Moodle)
 Geometry EOC Practice Test (on Secondary Mathematics Moodle)
 FCAT Explorer (Geometry EOC) – see school technology www.focus.florida-achieves.com
 FCAT Explorer Florida Achieves Focus mini assessments – see school technology specialist www.focus.florida-achieves.com
Page 1 of 37
Revised 7/19/13
Common Core State Standards Math Resources:
www.cpalms.org or www.floridastandards.org (Florida standards, course descriptions and resource site)
www.corestandards.org (Common Core Standards Webpage)
www.ccsstoolbox.org (Resources for CCSS implementation)
www.parcconline.org (PARCC assessment information)
http://map.mathshell.org/materials/stds.php (Mathematics tasks and assessment resources)
www.Mathedleadership.org (Professional resources for math teachers)
www.Insidemathematics.org (Professional resources for math teachers)
http://illuminations.nctm.org/ (Professional resources for math teachers)
http://mathpractices.edc.org/ (8 Math practices - information and tasks)
www.teachingchannel.org/ (Common Core Videos)
http://katm.org/wp/wp-content/uploads/flipbooks/High-School-CCSS-Flip-Book-USD-259-2012.pdf (Provides information and instructional
strategies that further describe the standards).
Common Core State Standards under the 2013/14 Course Description not covered in the curriculum map
MACC.912.G-SRT.1.1
Verify experimentally the properties of dilations given by a center and a scale factor: A dilation takes a line not passing
through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
MACC.912.C-C.1.1
Prove that all circles are similar.
MACC.912.C-C.1.4
(+) Construct a tangent line from a point outside a given circle to the circle.
MACC.912.C-C.2.5
Define the radian measure of the angle as the constant of proportionality.
MACC.912.G-GPE.1.1
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the
center and radius of a circle given by an equation.
MACC.912G-SRT.3.7
Explain and use the relationship between the sine and cosine of complementary angles.
Page 2 of 37
Revised 7/19/13
Geometry Pacing Guide
2013-14 School Year
Unit Name
Unit A: Tools of Geometry (19 days)
(Including beginning of year assessments)
Estimated Timeframe for Instruction and Assessment
Unit B: Reasoning and Proof (10 days)
September 16 – September 27
Unit C: Parallel and Perpendicular Lines (15 days)
September 30 – October 18
Note: 1st Quarter Ends October 18
Unit D: Congruent Triangles (14 days)
October 22 – November 8
Unit E: Relationships Within Triangles (14 days)
November 12 – December 4
Unit F: Polygons, Quadrilaterals and Exams (18 days)
December 5 –January 14
Note: 2nd Quarter Ends December 20
Unit G: Similarity (12 days)
January 15 – January 31
Unit H: Right Triangles and Trigonometry (10 days)
February 3 – February 14
Unit I: Area (18 days)
February 18 – March 13
Unit J: Surface Area and Volume (13 days)
March 24- April 9
Note: 3rd Quarter Ends March 13
Unit K: Circles (9 days)
April 10 to April 23
Unit L: Transformations (10 days)
April 24 – May 7
EOC and other Content Review and Assessment/Projects
EOC Exam Window is May 19 - 23
Note: 4th Quarter Ends June 3
Page 3 of 37
August 19 – September 13
Revised 7/19/13
Course Name:
Geometry, 2013-14
Unit Title:
(A) Tools of Geometry
Estimated Number of Days:
19
Know:
Understand:
Geometric solids have nets.
Geometry is a subject consisting of many symbols, Identify, draw and describe regular and
rules, formulas and properties.
non-regular polyhedra and their nets.
Points, lines, planes, segments, angles, and rays are
foundations of geometry.
Do:
Describe and compare points, lines, planes,
segments, angles, and rays.
Segments and angles can be measured and compared.
Draw, measure, and classify angles and segments.
There are relationships between angle pairs.
Identify angle pairs and determine their measures.
There are differences between sketches, drawings,
and constructions.
Distance and midpoint formulas apply to points and
line segments in the coordinate plane.
There are formulas for circumference and area of a
circle and for perimeter and area of a rectangle.
Page 4 of 37
Use constructions to copy and bisect angles and
segments.
Apply formulas to find the length and the
coordinates of the midpoint of a segment.
Find the area and circumference of circles, and the
area and perimeter rectangles and irregular shapes.
Revised 7/19/13
Course Name:
Unit Title:
Estimated Number of Days:
Key Learning:
Unit Essential Question:
Geometry, 2013-14
(A) Tools of Geometry
19
Geometry is a subject consisting of many building blocks including symbols, rules and properties.
What are the building blocks of geometry?
Concept:
Nets and Drawings for
Visualizing Geometry
Benchmark(s):
Lesson Essential Questions:
MA.912.G.7.1
1. How can I represent three-dimensional figures with two-dimensional
MACC.912.Gdrawings?
MG.1.1
Concept:
Benchmark(s):
Lesson Essential Questions:
Points, Lines, and Planes MA.912.G.8.
2. What are the relationships between points, lines, rays, segments and
MACC.912.G-CO.1.1 planes?
Concept:
Benchmark(s):
Lesson Essential Questions:
Measuring Segments and MA.912.G.1.1
3. How are segments and angles measured?
Angles
MA.912.G.1.3
MACC.912.G-CO.1.1
Concept:
Exploring Angle Pairs
Benchmark(s):
MA.912.G.4.2
Concept:
Basic Constructions
Benchmark(s):
MA.912.G.1.2
MA.912.G.4.1
MA.912.G.4.2
MA.912.G.8.6
MACC.912.G-CO.1.1
Page 5 of 37
Vocabulary:
net, isometric drawing, orthographic
drawing
Vocabulary:
point, space, line, collinear points,
plane, coplanar, ray, opposite ray,
postulate, axiom
Vocabulary:
coordinate, distance, congruent
segments, segment bisector,
midpoint, acute angle, right angle,
obtuse angle, straight angle,
congruent angles, angle (vertex,
sides)
Lesson Essential Questions:
Vocabulary:
4. What are the different ways to describe different kinds of angle pairs? vertical angles, adjacent angles,
complementary angles,
supplementary angles, linear pair,
angle bisector
Lesson Essential Questions:
Vocabulary:
5. How are angles and segments copied and bisected using construction construction, straightedge, compass,
techniques?
perpendicular lines, perpendicular
bisector
Revised 7/19/13
Concept:
Benchmark(s):
Midpoint and Distance in MA.912.G.1.1
the Coordinate Plane
Lesson Essential Questions:
6. How do I use the distance and midpoint formulas?
Vocabulary:
Distance Formula, Midpoint Formula
Concept:
Benchmark(s):
Perimeter, Circumference MA.912.G.2.1
and Area
MA.912.G.2.5
MA.912.G.6.5
MACC.912.GGPE.2.7
Lesson Essential Questions:
7. How do I calculate the perimeter, circumference, and area of basic
shapes?
Vocabulary:
perimeter, circumference, area,
irregular shapes
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook. Textbook resources are 1-1 to 1-8.
*Early in this unit, you will be administering the Differentiated Accountability (CORE K12) assessment.
*Use flexibility with teaching algebraic concepts as needed. Resources are flexible.
Math Benchmark: MA.912.G.8.2
Page 6 of 37
Revised 7/19/13
Course Name:
Geometry, 2013-14
Unit Title:
(B) Reasoning and Proof
Estimated Number of Days:
10
Know:
Understand:
Do:
Logic and truth tables involve conditional statements, Mathematical reasoning concepts are used to make Find the converse, inverse, and contra-positive of a
converses, bi-conditionals, definitions, negations,
conclusions in algebra, geometry, and real world
conditional statement.
inverses and contra-positives.
situations.
Identify and use symbolic forms of logical
Logical statements have symbolic forms.
statements.
Truth tables are used to determine truth values of
propositional statements.
The properties of equality and congruence apply to
algebra and geometry.
Conclusions about angles can be made from the way
they are drawn.
Some angle pairs may be classified as complementary
or supplementary.
Complete truth tables.
Use truth tables to determine truth values of
propositional statements.
Justify simple proofs using algebraic and geometric
properties of equality and congruence.
Distinguish between types of angle pairs from given
diagrams.
Prove angles congruent using theorems.
Angles that are equal in measure are congruent.
Page 7 of 37
Revised 7/19/13
Course Name:
Unit Title:
Estimated Number of Days:
Key Learning:
Unit Essential Question:
Geometry, 2013-14
(B) Reasoning and Proof
10
Mathematical reasoning concepts are used to make conclusions in algebra, geometry, and real-world situations.
What are the key elements of reasoning?
Concept:
Patterns and Inductive
Reasoning
Concept:
Logic and Truth Tables
Benchmark(s):
MA.912.G.8.4
Lesson Essential Questions:
1. How is inductive reasoning used to find patterns?
Benchmark(s):
MA.912.D.6.2
MA.912.D.6.3
MA.912.D.6.4
MA.912.G.8.1
Lesson Essential Questions:
2. How is logical reasoning used in geometry?
Concept:
Reasoning in Algebra
Benchmark(s):
MA.912.D.6.4
MA.912.G.8.5
Lesson Essential Questions:
3. How is reasoning used to construct a formal algebraic proof?
Vocabulary:
reflexive property, symmetric property,
transitive property, proof, two-column proof
Concept:
Proving Angles
Congruent
Benchmark(s):
MA.912.D.6.4
MA.912.G.8.1
MA.912.G.8.5
MACC.912.GCO.3.9
Lesson Essential Questions:
4. How can angle relationships be identified, solved and proved?
Vocabulary:
theorem, paragraph proof
Vocabulary:
inductive reasoning, conjecture,
counterexample
Vocabulary:
conditional, hypothesis, conclusion, truth
value, converse, bi-conditional, negation,
inverse, contra-positive, equivalent
statements, indirect reasoning, indirect
proof, Law of Detachment, Law of
Syllogism, deductive reasoning
Additional Information:
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook. Textbook resources are 2-1 through 2-2 and 2-4 through 2-6.
*Use flexibility with teaching algebraic concepts as needed. Resources are flexible.
Also included are:
Math Benchmark: MA.912.G.8.2
Page 8 of 37
Revised 7/19/13
Course Name:
Geometry, 2013-14
Unit Title:
(C) Parallel and Perpendicular Lines
Estimated Number of Days:
15
Know:
Understand:
Do:
Angles are formed from intersecting lines.
Parallel and perpendicular line properties lead to
several angle relationships.
Classify angles formed from various types of
intersecting lines.
Angle relationships can be used to prove whether or
not lines are parallel.
Prove lines parallel given angle relationships.
Lines in the coordinate plane can be expressed
algebraically.
Analyze linear equations to determine whether their
graphs are parallel, perpendicular or neither.
The Triangle-Angle-Sum theorem is used to
determine missing angle measures in a triangle.
Apply the Triangle-Angle-Sum Theorem to find
missing angles of triangles.
Relationships exist between the slopes of parallel and
perpendicular lines.
Use slopes of lines to prove line relationships.
Knowledge of line properties can be used to construct
parallel and perpendicular lines.
Page 9 of 37
Construct parallel and perpendicular lines given
specific constraints.
Revised 7/19/13
Course Name:
Geometry, 2013-14
Unit Title:
Estimated Number of Days:
(C) Parallel and Perpendicular Lines
15
Key Learning:
Parallel and perpendicular line properties lead to several angle relationships.
Unit Essential Question:
How are parallel and perpendicular line properties used to define angle relationships?
Concept:
Lines and Angles
Benchmark(s):
Lesson Essential Questions:
Vocabulary:
MA.912.G.7.2
1. What relationships exist between lines, planes and angles in space? parallel lines, skew lines, parallel planes,
MACC.912.G-CO.1.1
transversal, alternate interior angles,
MACC.912.Gsame-side interior angles, corresponding
MG.1.1
angles, alternate exterior angles
MACC.912.GMG.1.3
Concept:
Properties of Parallel
Lines
Benchmark(s):
Lesson Essential Questions:
MA.912.G.1.3
2. What are the relationships between pairs of angles formed by
MA.912.G.8.5
parallel lines and transversals?
MACC.912.G-CO.3.9
Vocabulary:
Concept:
Benchmark(s):
Lesson Essential Questions:
Proving Lines are Parallel MA.912.G.1.3
3. What are the different ways to prove lines parallel or
and Perpendicular
MA.912.G.8.5
perpendicular?
MACC.912.G-CO.1.1
MACC.912.G-CO.3.9
MACC.912.GMG.1.3
Vocabulary:
flow proof
Concept:
Parallel Lines and
Triangles
Vocabulary:
auxiliary line, exterior angle of a
polygon, remote interior angle
Page 10 of 37
Benchmark(s):
Lesson Essential Questions:
MA.912.G.2.2
4. What is unique about the measures of angles in triangles?
MA.912.G.4.1
MA.912. G.8.5
MACC.912.G-CO.3.9
MACC.912.GCO.3.10
Revised 7/19/13
Concept:
Benchmark(s):
Constructing Parallel and MA.912.G.1.2
Perpendicular Lines
MA.912.G.4.1
MACC.912.GCO.4.12
Concept:
Benchmark(s):
Equations of Lines in the Pre-Req. for
Coordinate Plane
MA.912.G.3.3
Lesson Essential Questions:
5. How are parallel or perpendicular lines constructed using only a
compass and a straightedge?
Vocabulary:
Lesson Essential Questions:
6. How are lines on the coordinate plane expressed algebraically?
Vocabulary:
slope, slope-intercept form, point-slope
form
Concept:
Slopes of Parallel and
Perpendicular Lines
Lesson Essential Questions:
7. What are the relationships between slopes of parallel and
perpendicular lines?
Vocabulary:
Benchmark(s):
Pre-Req. for
MA. 912.G.3.3
Additional Information:
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook. Text resources are 3-1 through 3-8.
*Use flexibility with teaching algebraic concepts as needed. Resources are flexible.
Also included are:
Math Benchmark: MA.912.G.8.2
Page 11 of 37
Revised 7/19/13
Course Name:
Geometry, 2013-14
Unit Title:
(D) Congruent Triangles
Estimated Number of Days:
14
Know:
Understand:
Do:
Congruent figures have congruent corresponding parts.
Properties, postulates and theorems are
used to prove triangle congruence.
Determine if figures are congruent by analyzing their
corresponding parts.
Triangles can be classified by their sides or angles.
Classify triangles according to their sides or angles.
Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-SideAngle (ASA), Angle-Angle-Side (AAS), Hypotenuse-Leg
(HL), and Corresponding Parts of Congruent Triangles are
Congruent (CPCTC) are methods used to prove congruent
triangles or congruent parts of triangles.
Isosceles, equilateral and right triangles have specific
theorems to prove triangles congruent.
Page 12 of 37
Prove that triangles are congruent and use the
concept of Corresponding Parts of Congruent
Triangles are Congruent (CPCTC).
Apply isosceles, equilateral and right triangle
theorems to prove congruence.
Revised 7/19/13
Course Name:
Geometry, 2012-13
Unit Title:
Estimated Number of Days:
(D) Congruent Triangles - Chapter 4
14
Key Learning:
Properties, postulates and theorems are used to prove triangle congruence.
Unit Essential Question:
What are the important elements needed to prove that two triangles are congruent?
Concept:
Congruent Figures
Benchmark(s):
Lesson Essential Questions:
MA.912.G.2.4
1. What are the characteristics of congruent figures?
MA.912.G.4.6
MACC.912.G-CO.2.6
MACC.912.G-CO.2.7
MACC.912.G-CO.2.8
MACC.912.G-CO.3.9
MACC.912.GSRT.2.5
MACC.912.GMG.1.1
Vocabulary:
congruent polygons, corresponding parts
Concept:
Methods of Proving
Triangles Congruent
Benchmark(s):
Lesson Essential Questions:
MA.912.G.4.3
2. What are the methods used to prove triangles are congruent?
MA.912G.4.6
MACC.912.G-CO.2.6
MACC.912.G-CO.2.7
MACC.912.G-CO.2.8
MACC.912.GCO.3.10
MACC.912.GSRT.2.5
Vocabulary:
SSS (Side-Side-Side), SAS (Side-AngleSide), ASA (Angle-Side-Angle), AAS
(Angle-Angle-Side)
Concept:
Using Congruent
Triangles: CPCTC
Benchmark(s):
MA.912.G.2.3
MA.912.G.4.4
MA.912.G.4.6
MACC.912.GCO.3.10
MACC.912.GSRT.2.5
Vocabulary:
CPCTC (Corresponding Parts of Congruent
Triangles are Congruent)
Page 13 of 37
Lesson Essential Questions:
3. What conclusions can I draw about triangles based on
congruency statements?
Revised 7/19/13
Concept:
Benchmark(s):
Isosceles and Equilateral MA.912.G.4.1
Triangles
MACC.912.GSRT.2.5
Lesson Essential Questions:
4. How are the congruence properties used with isosceles and
equilateral triangles?
Vocabulary:
legs of an isosceles triangle, base of an
isosceles triangle, vertex angle of an
isosceles triangle, base angles of an
isosceles triangle, corollary
Concept:
Congruence in Right
Triangles
Benchmark(s):
Lesson Essential Questions:
MA.912.G.4.6
5. What relationships of right triangles help me prove triangles
MA.912.G.5.4
congruent?
MACC.912.G-CO.2.6
MACC.912.G-CO.2.7
MACC.912.GCO.3.10
MACC.912.GSRT.2.5
Vocabulary:
hypotenuse, legs of a right triangle, HL
(Hypotenuse-Leg) theorem
Concept:
Congruence in
Overlapping Triangles
Benchmark(s):
MA.912.G.4.6
MACC.912.GSRT.2.5
Vocabulary:
overlapping
Lesson Essential Questions:
6. How do you identify congruency in overlapping triangles?
Additional Information:
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook. Textbook resources are 4-1 through 4-7.
Students are expected to know their triangle classifications, if remediation is needed use PH- page 853, MA.912.G.4.1
Students will need to solve systems of equations for 4-6, review using PH- page 273
Also included are:
Math Benchmark: MA.912.G.8.2
Page 14 of 37
Revised 7/19/13
Course Name:
Geometry, 2013-14
Unit Title:
(E) Relationships Within Triangles
Estimated Number of Days:
14
Know:
Understand:
Do:
Mid-segments, angle bisectors, perpendicular
bisectors, altitudes, and medians exist in triangles.
Important segment and angle relationships exist
within triangles.
Identify various segments and their points of
concurrency within triangles.
Coordinate geometry can be used to prove various
geometric properties.
Prove the Triangle Mid-segment Theorem using
coordinate geometry.
The are four points of concurrency that are formed by
segments within triangles (circumcenter, incenter,
centroid, and orthocenter).
Find the center of a circle using coordinate
geometry.
Triangle inequalities involve angles and sides of
triangles.
Apply properties related to the segments within
triangles.
Use the triangle inequality theorems to compare
sides and angles related to triangles.
Construct tangents to circles.
Circumscribe and inscribe circles about and within
triangles and regular polygons.
Page 15 of 37
Revised 7/19/13
Course Name:
Geometry, 2013-14
Unit Title:
Estimated Number of Days:
(E) Relationships Within Triangles
14
Key Learning:
Important segment and angle relationships exist within triangles.
Unit Essential Question:
How are segments and angles formed within triangles related?
Concept:
Mid-segments of
Triangles
Benchmark(s):
Lesson Essential Questions:
MA.912.G.1.1
1. How do I locate a triangle's mid-segment?
MACC.912.GCO.3.10
MACC.912.GSRT.2.4
MACC.912.GGPE.2.5
MACC.912.G-MG.1.1
Vocabulary:
mid-segment, coordinate proof
Concept:
Benchmark(s):
Lesson Essential Questions:
Perpendicular and Angle MA. 912.G.4.2
2. What observations can be made about angle bisectors and
Bisectors
MACC.912.G-CO.3.9 perpendicular bisectors?
MACC.912.G-MG.1.3
Vocabulary:
Equidistant, distance from a point to a line
Concept:
Benchmark(s):
Lesson Essential Questions:
Points of Concurrency in MA.912.G.1.1
3. What are the properties of the four points of concurrency in a
Triangles
MA.912.G.4.2
triangle?
MA.912.G.4.5
MACC.912.GCO.3.10
MACC.912.C-C.1.3
MACC.912.G-MG.1.3
Concept:
Benchmark(s):
Lesson Essential Questions:
Indirect Proof
MA.912.G.8.5
4. How is indirect reasoning used in proofs?
Vocabulary:
concurrent, point of concurrency,
circumcenter of a triangle, circumscribed
about, incenter of a triangle, inscribed in,
median of a triangle, centroid, altitude,
orthocenter
Page 16 of 37
Vocabulary:
indirect reasoning, indirect proofs
Revised 7/19/13
Concept:
Benchmark(s):
Lesson Essential Questions:
Inequalities in Triangles MA.912.G.4.7
5. How are angles and sides of triangles related?
MACC.912.GCO.3.10
MACC.912.G-MG.1.1
MACC.912.G-MG.1.3
Additional Information:
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook. Textbook resources are 5-1 through 5-7.
*Use flexibility with teaching algebraic concepts as needed. Resources are flexible.
Also included are:
Math Benchmark: MA.912.G.8.2
Page 17 of 37
Vocabulary:
Revised 7/19/13
Course Name:
Geometry, 2013-14
Unit Title:
(F) Polygons and Quadrilaterals
Estimated Number of Days:
18
Know:
Understand:
Polygons have interior and exterior angle sums.
Classification techniques and proofs can be used to Identify and describe convex, concave, regular,
identify quadrilaterals.
equilateral and equiangular polygons.
Do:
Polygons are classified by their sides.
Polygons may be convex or concave, equilateral,
equiangular and regular.
There are seven types of special quadrilaterals, each
with distinct properties.
The properties of special quadrilaterals can be proven
using coordinate geometry.
Page 18 of 37
Find the measures of interior and exterior angles of
polygons.
Distinguish between the different types of special
quadrilaterals.
Prove properties of special quadrilaterals using
coordinate geometry.
Revised 7/19/13
Course Name:
Geometry, 2013-14
Unit Title:
Estimated Number of Days:
(F) Polygons and quadrilaterals
18
Key Learning:
Classification techniques and proofs can be used to identify quadrilaterals.
Unit Essential Question:
What types of quadrilaterals exist and what properties are unique to them?
Concept:
Benchmark(s):
Polygon Angle-Sum MA.912.G.2.2
Theorem
Lesson Essential Questions:
1. How do you find the sum of the measures of the interior and
exterior angles of a polygon?
* see Additional Information
Vocabulary:
equilateral polygon, equiangular polygon,
regular polygon
Concept:
Properties of
Parallelogram
Lesson Essential Questions:
2. How are properties of parallelograms used in proofs?
Vocabulary:
parallelogram, opposite sides, opposite
angles, consecutive angles, diagonal
Lesson Essential Questions:
3. What are the similarities and differences between squares,
rectangles, and rhombuses?
Vocabulary:
rhombus, square, rectangles
Lesson Essential Questions:
4. What are the unique properties of trapezoids and kites?
Vocabulary:
trapezoid, base, leg, base angle, isosceles
trapezoid, mid-segment of a trapezoid, kite
Concept:
Properties of
Rhombuses,
Rectangles and
Squares
Benchmark(s):
MA.912.G.3.1
MA.912.G.3.4
MA.912.G.4.5
MA.912.G.8.5
MACC.912.GCO.3.11
MACC.912.GMG.1.1
Benchmark(s):
MA.912.G.3.1
MA.912.G.3.2
MA.912.G.3.4
MACC.912.GCO.3.11
Concept:
Benchmark(s):
Trapezoids and Kites MA.912.G.3.1
MA.912.G.3.2
MA.912.G.3.4
Page 19 of 37
Revised 7/19/13
Concept:
Benchmark(s):
Quadrilaterals in the MA.912.G.1.1
Coordinate Plane
MA.912.G.3.1
MA.912.G.3.3
MA.912.G.4.1
MA.912.G.8.5
MACC.912.GGPE.2.4
MACC.912.GGPE.2.5
Lesson Essential Questions:
5. How can you use coordinates to identify special figures? See
Additional Information
Vocabulary:
coordinate proof
Additional Information:
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook. Textbook resources are 6-1 through 6-9.
*Note* This unit will probably have to be split over quarter 2 & 3. Extra days have been added to this unit to include the days needed for Differentiated
Accountability Assessment (CORE K12) and semester testing.
Algebra review on simplifying radicals in on PH page 424. This needs to be reviewed before you cover the coordinate plane sections (6-7, 6-8, 6-9)
*Classifying polygons review is on PH page 65, 66, the book assumes that the students know these names and does not review them in chapter 6.
Also included are:
Math Benchmark: MA.912.G.8.2
Page 20 of 37
Revised 7/19/13
Course Name:
Geometry, 2013-14
Unit Title:
(G) Similarity
Estimated Number of Days:
12
Know:
Understand:
Do:
Proportions are formed by ratios and are used in unit The concepts of ratios, proportions and similarity
conversions.
are strongly interrelated and necessary for solving
problems with similar figures.
Similar triangles and other similar polygons have
congruent angles and proportional sides.
Set up ratios and proportions and solve using the
cross-product property.
There are specific theorems that describe the
proportions in triangle measurements.
Find missing sides and segments of triangles using
triangle proportion theorems.
Page 21 of 37
Use similarity properties to identify similar triangles
and other polygons.
Revised 7/19/13
Course Name:
Unit Title:
Estimated Number of Days:
Key Learning:
Unit Essential Question:
Geometry, 2013-14
(G) Similarity
12
The concepts of ratios, proportions and similarity are strongly interrelated and necessary for solving problems
with similar figures.
How do ratios and proportions enable the solving of problems involving similar polygons?
Concept:
Ratios and
Proportions
Benchmark(s):
Pre-Req. for
MA.912.G.2.3
Concept:
Similar Polygons
Benchmark(s):
Lesson Essential Questions:
MA.912.G.2.3
2. What are similar polygons?
MACC.912.G-SRT.1.2
Vocabulary:
similar figures, similar polygons, extended
proportion, similarity ratio, scale factor,
golden rectangle, golden ratio
Concept:
Proving Triangles
Similar
Benchmark(s):
Lesson Essential Questions:
MA.912.G.4.4
3. How can I prove triangles similar?
MA.912.G.4.6
MACC.912.G-CO.3.10
MACC.912.G-SRT.1.2
MACC.912.G-SRT.1.3
MACC.912.G-SRT.2.4
MACC.912.G-SRT.2.5
Vocabulary:
indirect measurement
Concept:
Similarity in Right
Triangles
Benchmark(s):
Lesson Essential Questions:
Vocabulary:
MA.912.G.8.3
4. How does the altitude drawn to the hypotenuse of a right triangle geometric means
MA.912.G.5.2
demonstrate the use of a geometric mean?
MACC.912.G-CO.3.10
MACC.912.G-SRT.1.2
MACC.912.G-SRT.1.3
MACC.912.G-SRT.2.4
MACC.912.G-SRT.2.5
Page 22 of 37
Lesson Essential Questions:
1. How do I write and evaluate proportions using ratios?
Vocabulary:
proportion, ratio, means, extremes,
extended ratio, cross products property
Revised 7/19/13
Concept:
Proportions in
Triangles
Benchmark(s):
Lesson Essential Questions:
MA.912.G.4.5
5. How do I apply the side-splitter theorem and the triangle-angle
MACC.912.G-CO.3.10 bisector theorem in order to find missing sides of a triangle?
MACC.912.G-SRT.1.2
MACC.912.G-SRT.1.3
MACC.912.G-SRT.2.4
MACC.912.G-SRT.2.5
MACC.912.G-MG.1.1
Additional Information:
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook. Textbook resources are 7-1 through 7-5.
*Use flexibility with teaching algebraic concepts as needed. Resources are flexible.
Also included are:
Math Benchmark: MA.912.G.8.2
Page 23 of 37
Vocabulary:
Side-splitter Theorem, Triangle-angle
Bisector Theorem
Revised 7/19/13
Course Name:
Geometry, 2013-14
Unit Title:
(H) Right Triangles and Trigonometry
Estimated Number of Days:
10
Know:
Understand:
Do:
Special right triangles are defined as 30-60-90 degree Trigonometric ratios are developed as applications Prove and apply the Pythagorean Theorem and its
or 45-45-90 degree triangles.
of right triangle geometry.
converse.
In a right triangle, the sum of the squares of the
lengths of the legs is equal to the square of the length
of the hypotenuse (Pythagorean Theorem).
The converse of the Pythagorean Theorem uses
angles to classify triangles.
The trigonometric ratios of tangent, sine, cosine,
cotangent, secant, and cosecant are used to find
missing angles and sides in right triangles.
Angles of elevation and depression have many realworld applications.
Page 24 of 37
Use special right triangles to solve problems.
Set up and solve equations using tangent, sine,
cosine, cotangent, secant, and cosecant functions to
find missing angles and sides in right triangles.
Solve real world problems involving trigonometric
functions and angles of elevation and depression.
Revised 7/19/13
Course Name:
Unit Title:
Estimated Number of Days:
Key Learning:
Unit Essential Question:
Concept:
The Pythagorean
Theorem and its
Converse
Benchmark(s):
MA.912.G.5.1
MA.912.G.5.4
MA.912.G.8.3
MACC.912.GSRT.2.4
MACC.912.GSRT.3.8
Geometry, 2013-14
(H) Right Triangles and Trigonometry
10
Trigonometric ratios are developed as applications of right triangle geometry.
How are the trigonometric ratios used to find unknown lengths and angle measures in diagrams and real world
scenarios?
Lesson Essential Questions:
1.In what problems can I use the Pythagorean Theorem to solve for
missing sides of a triangle?
Vocabulary:
Pythagorean triple
Concept:
Benchmark(s):
Special Right Triangles MA.912.G.5.3
MA.912.G.5.4
MACC.912.GSRT.3.6
Lesson Essential Questions:
Vocabulary:
2. How are the properties of special right triangles (30-60-90, 45-4590) used to find missing sides?
Concept:
Trigonometry
Benchmark(s):
MA.912.G.5.3
MA.912.G.5.4
MACC.912.GSRT.3.6
MACC.912.GSRT.3.8
Lesson Essential Questions:
3. How are the sine, cosine, and tangent ratios applied to determine
missing sides and angles in right triangles? * see Additional
Information
Vocabulary:
trigonometric rations, sine, cosine, tangent,
cotangent, cosecant, cosine
Concept:
Angles of Elevation
and Depression
Benchmark(s):
MA.912.G.5.4
MA.912.T.2.1
MACC.912.GSRT.3.6
MACC.912.GSRT.3.8
Lesson Essential Questions:
4. How do you use angles of elevation and depression to solve
problems?
Vocabulary:
Angle of elevations, Angles of depression
Page 25 of 37
Revised 7/19/13
Additional Information:
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook. Textbook resources are 8-1 through 8-4.
*Use flexibility with teaching algebraic concepts as needed. Resources are flexible.
*Exposure to secant, cosecant and cotangent is covered on page 539 #16-21. MA.912.T.2.1. This is needed for the state Geometry End of Course Assessment
and the CORE K12 assessments.
Also included are:
Math Benchmark: MA.912.G.8.2
Page 26 of 37
Revised 7/19/13
Course Name:
Geometry, 2013-14
Unit Title:
(I) Area
Estimated Number of Days:
18
Know:
Understand:
Do:
There are formulas for circumference, perimeter, and The characteristics of two-dimensional figures Find the area and circumference of circles, and the area
area for circles, triangles, quadrilaterals, and regular can be used to calculate circumference,
and perimeter of triangles, quadrilaterals and regular
polygons.
perimeter and area.
polygons.
There is a relationship between area, sectors,
segments, central angles, intercepted arcs,
circumference and arc length in circles.
Define and identify: circumference, radius, diameter, arc,
arc length, chord, secant, and segment in circles.
Find the probability of events using geometric models.
Geometric models can be used to find the probability
of events.
There is an equation for any circle graphed on the
coordinate plane, which is based upon the distance
formula.
Page 27 of 37
Given the center and radius of a circle, find its equation
and sketch the circle on the coordinate plane.
Given the equation of a circle, find its radius and center.
Revised 7/19/13
Course Name:
Unit Title:
Estimated Number of Days:
Key Learning:
Unit Essential Question:
Concept:
Area of Triangles,
Parallelograms
Trapezoids, Rhombuses
and Kites
Geometry, 2013-14
(I) Area
18
The characteristics of two-dimensional figures can be used to calculate circumference, perimeter and area.
What properties of perimeter, area, and trigonometry can be applied in geometric situations?
Benchmark(s):
Lesson Essential Questions:
MA.912.G.2.5
1. How do I find the area of parallelograms, triangles, trapezoids,
MA.912.G.2.1
rhombuses and kites?
MACC.912.G-CO.3.10
MACC.912.G-CO.3.11
MACC.912.G-MG.1.1
MACC.912.G-MG.1.3
Concept:
Benchmark(s):
Area of Regular Polygons MA.912.G.2.5
MA.912.G.2.7
Lesson Essential Questions:
2. How can I find the area of a regular polygon?
Vocabulary:
base, altitude and height of a
parallelogram and triangle, height of
trapezoid
Vocabulary:
radius of a regular polygon, apothem
Concept:
Perimeter and Areas of
Similar Figures
Benchmark(s):
Lesson Essential Questions:
MA.912.G.2.7
3. How can I find perimeters and areas of similar polygons?
MACC.912.G-SRT.1.2
MACC.912.G-MG.1.1
Concept:
Trigonometry and Area
Benchmark(s):
Lesson Essential Questions:
Vocabulary:
MA.912.G.2.5
4. How can I use trigonometry to find the area of regular polygons and
MA.912.T.2.1
triangles?
MACC.912.G-CO.3.10
MACC.912.G-SRT.3.8
MACC.912.G-MG.1.1
Concept:
Circles and Arcs
Benchmark(s):
MA.912.G.6.2
MA.912.G.6.4
MA.912.G.6.5
MACC.912.G-CO.1.1
MACC.912.C-C.1.2
Page 28 of 37
Lesson Essential Questions:
5. What is the relationship between central angles, arc length, and
circumference?
* see Additional Information
Vocabulary:
scale factor, ratio of perimeters, ratio
of areas
Vocabulary:
circle, center, radius, congruent
circles, diameter, central angle,
semicircle, minor arc, major arc,
adjacent arcs, circumference, pi,
concentric circles, arc length,
congruent arcs
Revised 7/19/13
Concept:
Areas of Circle and
Sectors
Concept:
Geometric Probability
Benchmark(s):
Benchmark(s):
MA.912.G.2.7
MA.912.G.6.5
MACC.912.C-C.1.2
MACC.912.C-C.2.5
MACC.912.GGMD.1.1
MA.912.G.2.5
MA.912.G.6.5
Concept:
Benchmark(s):
Circles in the Coordinate MA.912.G.1.1
Plane
MA.912.G.6.6
MA.912.G.6.7
MACC.912.GGPE.1.1
Lesson Essential Questions:
6. How do I find the area of circle, sector and segment?
Vocabulary:
sector of a circle, segment of a circle
Lesson Essential Questions:
7. What geometric models can be used to find the probability of
events?
Vocabulary:
geometric probability
Lesson Essential Questions:
8. How is the distance formula applied in the formula for the
equation of a circle in the coordinate plane?
Vocabulary:
standard form of an equation of a
circle
Additional Information:
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook. Textbook resources are 10-1 through 10-8 and 12-5.
*use Concept Byte: Circle Graphs on page 687 with lesson 10-6.
*Lesson 12-5 Circles in the Coordinate Plane has been moved into this chapter in order to make sure it is covered before the
CORE K12 EOY and State Geometry EOC Assessment.
Also included are:
Math Benchmark: MA.912.G.8.2
Page 29 of 37
Revised 7/19/13
Course Name:
Geometry, 2012-13
Unit Title:
(J) Surface Area and Volume
Estimated Number of Days:
13
Know:
Understand:
Do:
Euler's formula relates the numbers of faces, vertices, Surface area and volume may be calculated for
and edges of a polyhedron.
geometric solids.
Find the number of faces, edges and vertices of
polyhedra using Euler's Formula.
There are formulas for finding the lateral area, surface
area and volume of prisms, cylinders, cones, and
pyramids.
Use formulas to find lateral area, surface area and
volume of solids.
There are formulas for finding the surface area and
volume of spheres.
Changing the dimensions of a geometric solid affects
the surface area and volume.
Page 30 of 37
Determine how changes in the dimensions affect the
surface area and volume of common geometric
solids.
Revised 7/19/13
Course Name:
Geometry, 2013-14
Unit Title:
Estimated Number of Days:
(J) Surface Area and Volume
13
Key Learning:
Surface area and volume are some of the measurements used to describe geometric solids.
Unit Essential Question:
How do I calculate the surface area and volume of geometric solids?
Concept:
Space Figures and
Cross-Sections
Concept:
Surface Area of
Geometric Solids
Benchmark(s):
Lesson Essential Questions:
MA.912.G.7.2
1. How can I identify and analyze 3-D figures (geometric solids) and
MACC.912.Gtheir cross sections?
GMD.2.4
Benchmark(s):
Lesson Essential Questions:
MA.912.G.7.1
2. How do I calculate surface area of geometric solids?
MA.912.G.7.5
MA.912.G.7.7
MACC.912.G-SRT.3.8
MACC.912.G-MG.1.1
Concept:
Volume of Geometric
Solids
Benchmark(s):
Lesson Essential Questions:
MA.912.G.7.5
3. How do I calculate volume of geometric solids?
MA.912.G.7.7
MACC.912.GGMD.1.1
MACC.912.GGMD.1.3
MACC.912.GGMD.2.4
MACC.912.G-MG.1.1
Concept:
Surface Area and
Volume of Spheres
Benchmark(s):
Lesson Essential Questions:
MA.912.G.7.4
4. How do I calculate the surface area and volume of a sphere?
MA.912.G.7.5
MA.912.G.7.7
MACC.912.GGMD.1.3
MACC.912.GGMD.2.4
MACC.912.G-MG.1.2
Page 31 of 37
Vocabulary:
cross section, polyhedron, face, edge,
vertex, net, Euler’s Formula
Vocabulary:
prism, bases, lateral faces, altitude,
height, lateral area, surface area, right
prism, oblique prism, cylinder, right
cylinder, oblique cylinder, pyramid,
cone, slant height, right cone, regular
pyramid
Vocabulary:
volume, composite space figure,
pyramids, cones
Vocabulary:
sphere, center, radius, diameter,
circumference of a sphere, great circle,
hemisphere
Revised 7/19/13
Concept:
Areas and Volumes of
similar solids
Benchmark(s):
Lesson Essential Questions:
MA.912.G.7.6
5. How are the areas and volumes of similar solids related?
MACC.912.GGMD.1.3
MACC.912.G-MG.1.1
MACC.912.G-MG.1.2
Additional Information:
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook. Textbook resources are 11-1 through 11-7.
*Use flexibility with teaching algebraic concepts as needed. Resources are flexible.
Also included are:
Math Benchmark: MA.912.G.8.2
Page 32 of 37
Vocabulary:
similar solids
Revised 7/19/13
Course Name:
Geometry, 2013-14
Unit Title:
(K) Circles
Estimated Number of Days:
9
Know:
Understand:
There is a relationship between segments and angles The study of circles involves many aspects of
formed by chords, secants and tangents of circles.
geometry including lines, segments, arcs and
angles.
Do:
Define and identify diameters, arcs and chords in
circles.
Determine and use measures of arcs and related
angles.
Page 33 of 37
Revised 7/19/13
Course Name:
Geometry, 2013-14
Unit Title:
Estimated Number of Days:
(K) Circles
9
Key Learning:
The study of circles involves many aspects of geometry including lines, segments, arcs, and angles.
Unit Essential Question:
What are the properties of circles and the lines, segments, arcs and angles involved with them?
Concept:
Tangent Lines
Lesson Essential Questions:
1. What causes a line to be tangent to a circle?
Vocabulary:
tangent to a circle, point of tangency,
inscribed in, circumscribed about
Lesson Essential Questions:
2. How are a circle's chords and arcs related to each other?
Vocabulary:
Chord, arc
Concept:
Chords and Arcs
Benchmark(s):
MA.912.G.6.2
MACC.912.GSRT.3.8
MACC.912.C-C.1.2
Benchmark(s):
MA.912.G.6.2
MACC.912.C-C.1.2
Concept:
Inscribed Angles
Benchmark(s):
Lesson Essential Questions:
Vocabulary:
MA.912.G.6.4
3. What is the relationship between an inscribed angle and its intercepted inscribed angle, intercepted arc
MACC.912.C-C.1.2 arc?
MACC.912.C-C.1.3
Concept:
Angle Measures and
Segment Lengths
Benchmark(s):
Lesson Essential Questions:
Vocabulary:
MA.912.G.6.2
4. What is the relationship between segments and angles formed by chords, secant
MA.912.G.6.4
secants, and tangents of circles?
MACC.912.C-C.1.2
Additional Information:
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook. Textbook resources 12-1 through 12-4.
*Use flexibility with teaching algebraic concepts as needed. Resources are flexible.
Note: 12-5 was moved to unit I with Chapter 10.
Also included are:
Math Benchmark: MA.912.G.8.2
Page 34 of 37
Revised 7/19/13
Course Name:
Geometry, 2013-14
Unit Title:
(L) Transformations
Estimated Number of Days:
10
Know:
Understand:
Do:
Two-dimensional objects can be reflected, translated, Transformations can be performed on tworotated or dilated on a plane.
dimensional shapes.
Perform transformations (translations, reflections,
dilations and scale size change) on polygons.
Transformations that result in congruent images and
pre-images are isometries.
Determine the congruence, similarity, and symmetry
between images and pre-images.
Some polygons can tessellate on a plane.
Create and verify tessellations of polygons on a
plane.
Page 35 of 37
Revised 7/19/13
Course Name:
Geometry, 20113-14
Unit Title:
Estimated Number of Days:
(L) Transformations
10
Key Learning:
Transformations can be performed on two-dimensional shapes.
Unit Essential Question:
What are the transformations in geometry?
Concept:
Reflections,
Translations,
Rotations
Concept:
Symmetry
Concept:
Dilations
Benchmark(s):
Lesson Essential Questions:
MA.912.G.2.4
1. How are objects reflected, translated, rotated?
MACC.912.G-CO.1.2
MACC.912.G-CO.1.3
MACC.912.G-CO.1.4
MACC.912.G-CO.1.5
MACC.912.G-CO.2.6
Benchmark(s):
Lesson Essential Questions:
MA.912.G.2.4
2. How can I identify the types of symmetry in a figure?
MACC.912.G-CO.1.2
MACC.912.G-CO.1.3
MACC.912.G-CO.1.4
MACC.912.G-CO.1.5
MACC.912.G-CO.2.6
Vocabulary:
symmetry, reflectional symmetry, line
symmetry, rotational symmetry, point
symmetry
Benchmark(s):
Lesson Essential Questions:
Vocabulary:
MA.912.G.2.4
3. How can I apply dilations and scale factors to polygons to determine dilation, center of dilation, scale factor of
MACC.912.G-CO.1.2 similarity?
dilation, enlargement, reductions
MACC.912.GSRT.1.1
MACC.912.GSRT.1.2
Concept:
Benchmark(s):
Lesson Essential Questions:
Compositions
MA.912.G.2.4
4. How are compositions and reflections in figures used in graphing?
and Reflections MACC.912.G-CO.1.2
MACC.912.G-CO.1.4
MACC.912.G-CO.1.5
MACC.912.G-CO.2.6
Page 36 of 37
Vocabulary:
transformation, pre-image, image, isometry,
reflection, line of reflection, translation,
composition, rotation (center, angle), center of
a regular polygon
Vocabulary:
glide reflection
Revised 7/19/13
Concept:
Tessellations
Benchmark(s):
Lesson Essential Questions:
MA.912.G.2.4
5. How can I identify symmetry and transformations in polygons that
MACC.912.G-CO.1.2 have been tessellated?
MACC.912.G-CO.1.5
MACC.912.G-CO.2.6
Additional Information:
*Use flexibility with teaching algebraic concepts as needed. Resources are flexible.
Also included are:
Math Benchmark: MA.912.G.8.2
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook. Textbook resources 9-1 though 9-7.
Page 37 of 37
Vocabulary:
tessellation, translational symmetry, glide
reflection symmetry