Download Geometry

Revised 7/5/10
Estimated Geometry Pacing Timeline
2010-2011 School Year
Revised 7/5/10
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.
Unit Name
Unit 0: B.O.Y Assessments, establishing procedures and
Algebra Review (5 days)
Estimated Timeframe for Instruction and Assessment
Unit 1: Tools of Geometry – Chapter 1 (16 days)
August 23 – September 14
Unit 2: Reasoning and Proof – Chapter 2 (9 days)
September 15 – September 27
Unit 3: Parallel and Perpendicular Lines – Chapter 3 (14 days)
September 28 – October 15
Unit 4: Congruent Triangles – Chapter 4 (14 days)
October 19 – November 5
Unit 5: Relationships Within Triangles - Chapter 5 (14 days)
November 8 – December 1
Unit 6: Polygons, Quadrilaterals – Chapter 6 and Exams (21
days)
December 2 – January 19
Unit 7: Similarity – Chapter 6 (10 days)
January 20– February 2
Unit 8:Right Triangles and Trigonometry – Chapter 8 (8 days)
February 3 – February 16
Unit 9: Transformations – Chapter 9 (10 days)
February 17 – March 3
Unit 10: Area – Chapter 10 (16 days)
March 4 – April 4
Unit 11: Surface Area and Volume – Chapter 11 (18 days)
April 5 – April 28
Unit 12: Circles – Chapter 12 (10 days)
May 2 – May 13
Unit 13: EOC Review and Test (12 days)
May 17 – May 31
August 16 – August 20
Page 1 of 40
Revised 7/5/10
Course Name:
Geometry, 2010-11
Unit Title:
(00)- Algebra Review
Number of Days:
5
Know:
Understand:
Do:
There are differences between equations
and expressions.
Many algebraic concepts are foundational
for the study of geometry.
Evaluate equations and simplify expressions.
Linear equations can be expressed
algebraically and graphically.
Unit conversions require the use of ratios
and proportions.
Taking the square root of a number is the
reverse process of squaring a number.
There are procedures to evaluate an
absolute value.
Solve and graph linear equations.
Set up and solve proportions to convert
units.
Use correct procedures for squaring
numbers and finding square roots.
Use correct procedures for finding
absolute value,
Page 2 of 40
Revised 7/5/10
Course Name:
Geometry, 2010-11
Unit Title:
(00) Algebra Review
Number of Days:
5
Key Learning:
Many algebraic concepts are foundational for the study of geometry.
Unit Essential Question: What algebraic concepts are foundational for the study of geometry?
Concept:
Evaluating and
Simplifying
Expressions
Benchmark(s):
MA.912.A.1.1
MA.912.A.1.4
MA.912.G.8.3
MA.912.G.8.2
Concept:
Benchmark(s):
Solving and Writing MA.912.A.3.10
Linear Equations
MA.912.A.3.9
MA.912.A.3.8
MA.912.G.8.2
Concept:
Benchmark(s):
Conversions and pg MA.912.A.1.5
826, Ratios
MA.912.A.5.1
Concept:
Benchmark(s):
Squares and
MA.912.A.1.4
Absolute Value
MA.912.A.1.1
MA.912.A.1.4.3
Lesson Essential Questions:
1. How are algebraic expressions evaluated and
simplified?
Textbook: Vocabulary:
1. Pg 858
algebraic expression
Lesson Essential Questions:
2. How are the properties of equality used to find
values of variables to satisfy equations?
Textbook: Vocabulary:
2. Pg 862 variable, linear
equation
Lesson Essential Questions:
3. How are unit conversions related to ratios?
Textbook:
3. Pg 859,
864
Textbook:
4. Pg 857,
860
Lesson Essential Questions:
4. What procedures are used when squaring numbers
and finding absolute value?
Vocabulary:
Ratio, unit
conversion
Vocabulary:
radical, exponent,
absolute value
Additional Information:
*During this week, you will be administrating the Differentiated Accountability (Core, K-12) assessment.
*Use flexibility with teaching algebraic concepts as needed. Resources are flexible.
Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook.
Page 3 of 40
Revised 7/5/10
Course Name:
Geometry, 2010-11
Unit Title:
(01) Tools of Geometry - Chapter 1
Number of Days:
16
Know:
Understand:
Do:
Geometric solids have nets.
Geometry is a subject consisting of many
symbols, rules, formulas and properties.
Identify, draw and describe regular, nonregular polyhedra and their nets.
Points, lines, planes, segments, angles, and
rays are foundations of geometry.
Segments and angles can be measured and
compared.
There are relationships between angle pairs.
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,
perimeter, and area for circles and
rectangles.
Define and compare points, lines, planes,
segments, angles, and rays.
Draw, measure, and classify angles and
segments.
Identify angle pairs and determine their
measures.
Use constructions to copy and bisect angles
and segments.
Apply formulas when finding the distance
and midpoint of lines or segments in the
coordinate plane.
Find the area, perimeter and circumference
of circles, rectangles and irregular shapes.
Page 4 of 40
Revised 7/5/10
Course Name:
Geometry, 2010-11
Unit Title:
(01) Tools of Geometry - Chapter 1
Number of Days:
16
Key Learning:
Geometry is a subject consisting of many building blocks including symbols, rules and properties.
Unit Essential Question: What are the building blocks of geometry?
Concept:
Nets and Drawings
for Visualizing
Geometry
Benchmark(s):
MA.912.G.7.1
Concept:
Points, lines and
Planes
Benchmark(s):
MA.912.G.8.1
Lesson Essential Questions:
Textbook: Vocabulary:
1. How can I represent three-dimensional figures with 1. PH 1-1
net, isometric
a two-dimensional drawing?
drawing,
orthographic
drawing
Lesson Essential Questions:
Textbook: Vocabulary:
2. What are the relationships between points, lines,
2. PH 1-2
point, space, line,
rays, segments and planes?
collinear points,
plane, coplanar, ray,
opposite ray,
postulate, axiom
Page 5 of 40
Revised 7/5/10
Concept:
Benchmark(s):
Measuring segments MA.912.G.1.1
and angles
MA.912.G.1.3
Concept:
Benchmark(s):
Exploring angle Pairs MA.912.G.4.2
Lesson Essential Questions:
2. How are segments and angles measured ?
Textbook: Vocabulary:
3. PH 1-3, coordinate, distance,
PH 1-4
congruent segments,
segment bisector,
midpoint, acute
angle, right angle,
obtuse angle,
straight angle,
congruent angles,
angle (vertex, sides)
Lesson Essential Questions:
Textbook: Vocabulary:
4. What are the different ways to describe different 4. PH 1-5
vertical angles,
kinds of angle pairs?
adjacent angles,
complementary
angles,
supplementary
angles, linear pair,
angle bisector
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
Lesson Essential Questions:
5. How are angles and segments copied and bisected
using construction techniques?
Concept:
Midpoint and
Distance in the
Coordinate Plane
Benchmark(s):
MA.912.G.1.1
Lesson Essential Questions:
6. How do I use the distance and midpoint formulas?
Textbook: Vocabulary:
5. PH 1-6
construction,
straightedge,
compass,
perpendicular lines,
perpendicular
bisector
Textbook: Vocabulary:
6. PH 1-7
Distance Formula,
Midpoint Formula
Page 6 of 40
Revised 7/5/10
Concept:
Perimeter,
Circumference and
Area
Benchmark(s):
MA.912.G.2.5
MA.912.G.6.5
Lesson Essential Questions:
7. How do I calculate the perimeter, circumference,
and area of basic shapes?
Course Name:
Geometry, 2010-11
Unit Title:
(02) Reasoning and Proof - Chapter 2
Number of Days:
13
Know:
Understand:
Textbook: Vocabulary:
7. PH 1-8
perimeter,
circumference, area,
irregular shapes
Do:
Additional Information:
Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook
Page 7 of 40
Revised 7/5/10
Logic and truth tables involve conditional
statements, converses, biconditionals,
definitions, negations, inverses and
contrapositives.
Logical statements have symbolic forms.
Mathematical reasoning concepts are used Find the converse, inverse, and
to make conclusions in algebra, geometry, contrapositive of a conditional statement.
and real world situations.
Identify and use symbolic forms of logical
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.
Angles that are equal in measure are
congruent.
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.
Course Name:
Geometry, 2010-11
Unit Title:
(02) Reasoning and Proof - Chapter 2 - Chapter 2
Number of Days:
9
Mathematical reasoning concepts are used to make conclusions in algebra, geometry, and real-world
situations.
Key Learning:
Page 8 of 40
Revised 7/5/10
Unit Essential Question: What are the key elements of reasoning?
Concept:
Patterns and
Inductive Reasoning
Concept:
Logic and Truth
Tables
Benchmark(s): Lesson Essential Questions:
Textbook: Vocabulary:
MA.912.G.8.4
1. How is inductive reasoning used to find patterns? 2. PH 2-1 inductive reasoning,
conjecture, counterexample
Benchmark(s): Lesson Essential Questions:
Textbook: Vocabulary:
MA.912.D.6.1
2. How is logical reasoning used in geometry?
conditional, hypothesis,
MA.912.D.6.2
2. PH 2-2, conclusion, truth value,
MA.912.D.6.3
2-3, 2-4
converse, biconditional,
MA.912.D.6.4
negation, inverse,
MA.912.G.8.1
contrapositive, equivalent
statements, indirect
reasoning, indirect proof, Law
of Detachment, Law of
Syllogism, deductive
reasoning
Concept:
Benchmark(s): Lesson Essential Questions:
Textbook: Vocabulary:
Reasoning in Algebra MA.912.D.6.4
3. How is reasoning used to construct a formal
3.PH 2-5
reflexive property,
MA.912.G.8.5
algebraic proof?
symmetric property,
transitive property, proof,
two-column proof
Concept:
Benchmark(s): Lesson Essential Questions:
Textbook: Vocabulary:
Proving Angles
MA.912.D.6.4
4. How can angle relationships be identified, solved 4. PH 2-6 theorem, paragraph proof
Congruent
MA.912.G.8.1
and proved?
MA.912.G.8.5
Concept:
Benchmark(s): Lesson Essential Questions:
Textbook: Vocabulary:
Concept:
Benchmark(s): Lesson Essential Questions:
Textbook: Vocabulary:
Page 9 of 40
Revised 7/5/10
Additional Information:
Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook.
Course Name:
Geometry, 2010-11
Unit Title:
(03) Lines and Angles - Chapter 3
Number of Days:
14
Know:
Understand:
Do:
Page 10 of 40
Revised 7/5/10
Angles are formed from intersecting lines.
Angle relationships can be used to prove
whether or not lines are parallel.
Parallel and perpendicular line properties
lead to several angle relationships.
Lines in the coordinate plane can be
expressed algebraically.
The Triangle-Angle-Sum theorem is used to
determine missing angle measures in a
triangle.
Classify angles formed from various types
of intersecting lines.
Prove lines parallel given angle relationships.
Analyze linear equations to determine
whether they are parallel, perpendicular or
neither.
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.
Construct parallel and perpendicular lines
given specific constraints.
Course Name:
Geometry, 2010-11
Unit Title:
(03) Lines Angles - Chapter 3
Number of Days:
14
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?
Page 11 of 40
Revised 7/5/10
Concept:
Lines and Angles
Benchmark(s):
MA.912.G.7.2
Concept:
Benchmark(s):
Properties of Parallel MA.912.G.1.3
lines
MA.912.G.8.5
Concept:
Benchmark(s):
Proving Lines are
MA.912.G.1.3
Parallel and
MA.912.G.8.5
Perpendicular
Concept:
Benchmark(s):
Parallel lines and
MA.912.G.2.2
triangles
MA.912.G.4.1
MA.912. G.8.5
Concept:
Constructing Parallel
and Perpendicular
lines
Concept:
Equations of lines in
the coordinate plane
Benchmark(s):
MA.912.G.1.2
MA.912.G.4.1
Benchmark(s):
MA.912.G.3.3
Lesson Essential Questions:
1. What relationships exist between lines, planes and
angles in space?
Textbook: Vocabulary:
1. PH 3-1
parallel lines, skew
lines, parallel planes,
transversal,
alternate interior
angles, same-side
interior angles,
corresponding
angles, alternate
exterior angles
Lesson Essential Questions:
Textbook: Vocabulary:
2. What are the relationships between pairs of angles 2. PH 3-2
formed by parallel lines and transversals?
Lesson Essential Questions:
Textbook: Vocabulary:
3. What are the different ways to prove lines parallel 3. PH 3-3, flow proof
or perpendicular?
3-4
Lesson Essential Questions:
4. What is unique about the measures of angles in
triangles?
Textbook: Vocabulary:
4. PH 3-5 auxiliary line,
exterior angle of a
polygon, remote
interior angle
Lesson Essential Questions:
Textbook: Vocabulary:
5. How is a parallel or perpendicular lines constructed 5. PH 3-6
using only a compass and a straightedge?
Lesson Essential Questions:
6. How are lines on the coordinate plane expressed
algebraically?
Textbook: Vocabulary:
6. PH 3-7 slope, slopeintercept form,
point-slope form
Page 12 of 40
Revised 7/5/10
Concept:
Benchmark(s):
Slopes of parallel and MA. 912.G.3.3
perpendicular lines
Lesson Essential Questions:
7. What are the relationships between slopes of
parallel and perpendicular lines?
Textbook: Vocabulary:
7. PH 3-8
Additional Information:
Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook.
Course Name:
Geometry, 2010-11
Unit Title:
(04) Congruent Triangles - Chapter 4
Number of Days:
14
Page 13 of 40
Revised 7/5/10
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-Side-Angle (ASA), AngleAngle-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.
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.
Isosceles, equilateral and right triangles
have specific theorems to prove triangles
congruent.
Course Name:
Geometry, 2010-11
Unit Title:
(04) Congruent Triangles - Chapter 4
Number of Days:
14
Page 14 of 40
Revised 7/5/10
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):
MA.912.G.2.4
Ma.912.G.4.6
Concept:
Benchmark(s):
Methods of Proving MA.912.G.4.3
Triangles Congruent MA.912G.4.6
Concept:
Using Congruent
Triangles: CPCTC
Benchmark(s):
MA.912.G.2.3
MA.912.G.4.4
MA.912.G.4.6
Concept:
Benchmark(s):
Isosceles and
MA.912.G.4.1
Equilateral Triangles
Lesson Essential Questions:
Textbook: Vocabulary:
1. What are the characteristics of congruent figures? 1. PH 4-1
congruent polygons,
corresponding parts
Lesson Essential Questions:
Textbook: Vocabulary:
2. What are the methods used to prove triangles are 2. PH 4-2, SSS (Side-Sidecongruent?
4-3
Side), SAS (SideAngle-Side), ASA
(Angle-Side-Angle),
AAS (Angle-AngleSide)
Lesson Essential Questions:
Textbook: Vocabulary:
3. What conclusions can I draw about triangles based 3.
CPCTC
on congruency statements?
PH 4-4
(Corresponding Parts
of Congruent
Triangles are
Congruent)
Lesson Essential Questions:
Textbook: Vocabulary:
4. How are the congruence properties used with
4.
legs of an isosceles
isosceles and equilateral triangles?
PH 4-5
triangle, base of an
isosceles triangle,
vertex angle of an
isosceles triangle,
base angles of an
isosceles triangle,
corollary
Page 15 of 40
Revised 7/5/10
Concept:
Benchmark(s):
Congruence in Right MA.912.G.4.6
Triangles
MA.912.G.5.4
Lesson Essential Questions:
Textbook: Vocabulary:
5. What relationships of right triangles help me prove 5.
hypotenuse, legs of
triangles congruent?
PH 4-6
a right triangle, HL
(Hypotenuse-Leg)
theorem
Concept:
Benchmark(s):
Congruence in
MA.912.G.4.6
Overlapping Triangles
Lesson Essential Questions:
6. How do you identify congruency in overlapping
triangles?
Textbook: Vocabulary:
6.
overlapping
PH 4-7
Additional Information:
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 the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook
Page 16 of 40
Revised 7/5/10
Course Name:
Geometry, 2010-11
Unit Title:
(05) Relationships Within Triangles - Chapter 5
Number of Days:
14
Know:
Understand:
Do:
Midsegments, angle bisectors, perpendicular Important segment and angle relationships Identify various segments and their points
bisectors, altitudes, and medians exist in
exist within triangles.
of concurrency within triangles.
triangles.
Prove the Triangle Midsegment Theorem
Coordinate geometry can be used to prove
using coordinate geometry.
various geometric properties.
Find the center of a circle using coordinate
The are four points of concurrency that are
geometry.
formed by segments within triangles (
circumcenter, incenter, centroid, and
Apply properties related to the segments
orthocenter).
within triangles.
Triangle inequalities involve angles and sides
of 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 17 of 40
Revised 7/5/10
Course Name:
Geometry, 2010-11
Unit Title:
(05) Relationships Within Triangles - Chapter 5
Number of Days:
14
Key Learning:
Important segment and angle relationships exist within triangles.
Unit Essential Question: How are segments and angles formed within triangles related?
Concept:
Midsegments of
Triangles
Concept:
Perpendicular and
Angle Bisectors
Benchmark(s):
MA.912.G.1.1
MA.912.G.4.5
Benchmark(s):
MA. 912.G.4.2
Lesson Essential Questions:
1. How do I locate a triangle's midsegment?
Concept:
Points of
Concurrency in
Triangles
Benchmark(s):
MA.912.G.1.1
MA.912.G.4.2
MA.912.G.4.5
Lesson Essential Questions:
3. What are the properties of the four points of
concurrency in a triangle?
Concept:
Indirect Proof
Benchmark(s):
MA.912.G.8.5
Lesson Essential Questions:
4. How is indirect reasoning used in proofs?
Concept:
Inequalities in
Triangles
Benchmark(s):
MA.912.G.4.7
Lesson Essential Questions:
5. How are angles and sides of triangles related?
Lesson Essential Questions:
2. What observations can be made about angle
bisectors and perpendicular bisectors?
Textbook: Vocabulary:
1. PH 5-1
midsegment,
coordinate proof
Textbook: Vocabulary:
2. PH 5-2 Equidistant,
distance from a
point to a line
Textbook: Vocabulary:
3. PH 5-3, concurrent, point of
5-4
concurrency,
circumcenter of a
triangle,
circumscribed
about, incenter of a
triangle, inscribed
in, median of a
triangle, centroid,
altitude,
orthocenter
Textbook: Vocabulary:
4. PH 5-5 indirect reasoning,
indirect proofs
Textbook: Vocabulary:
5. PH 5-6
PH 5-7
Page 18 of 40
Revised 7/5/10
Additional Information:
Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook.
Page 19 of 40
Revised 7/5/10
Course Name:
Geometry, 2010-11
Unit Title:
(06) Polygons and Quadrilaterals - Chapter 6
Number of Days:
22
Know:
Understand:
Polygons have interior and exterior angle
sums.
Classification techniques and proofs can be Identify and describe convex, concave,
used to identify quadrilaterals.
regular, equilateral and equiangular
polygons.
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.
Do:
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.
Page 20 of 40
Revised 7/5/10
Course Name:
Geometry, 2010-11
Unit Title:
(06) Polygons and quadrilaterals - Chapter 6
Number of Days:
22
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:
Polygon Angle-Sum
Theorem
Benchmark(s):
MA.912.G.2.2
Concept:
Properties of
Parallelogram
Benchmark(s):
MA.912.G.3.1
MA.912.G.3.4
MA.912.G.4.5
MA.912.G.8.5
Concept:
Properties of
Rhombuses,
Rectangles and
Squares
Concept:
Trapezoids and Kites
Benchmark(s):
MA.912.G.3.1
MA.912.G.3.2
MA.912.G.3.4
Benchmark(s):
MA.912.G.3.1
MA.912.G.3.2
MA.912.G.3.4
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
Lesson Essential Questions:
2. How are properties of parallelograms used in
proofs?
Textbook: Vocabulary:
1. PH 6-1
equilateral polygon,
equiangular polygon,
regular polygon
Textbook: Vocabulary:
2. PH 6-2, parallelogram,
6-3
opposite sides,
opposite angles,
consecutive angles,
diagonal
Lesson Essential Questions:
Textbook: Vocabulary:
3. What are the similarities and differences between 3. PH 6-4, rhombus, square,
squares, rectangles, and rhombuses?
6-5
rectangles
Lesson Essential Questions:
4. What are the unique properties of trapezoids and
kites?
Textbook: Vocabulary:
4. PH 6-6 trapezoid, base, leg,
base angle, isosceles
trapezoid,
midsegment of a
trapezoid, kite
Page 21 of 40
Revised 7/5/10
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.4.8
MA.912.G.8.5
Lesson Essential Questions:
5. How can you use coordinates to identify special
figures? See Additional Information
Textbook: Vocabulary:
5. PH 6-7 coordinate proof
6-8, 6-9
Additional Information:
*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, K-12) and semester testing.
Algebra review on simplifying radicals 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 the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook.
Page 22 of 40
Revised 7/5/10
Course Name:
Geometry, 2010-11
Unit Title:
(07) Similarity - Chapter 7
Number of Days:
10
Know:
Understand:
Do:
Proportions are formed by ratios and are
used in unit conversions.
The concepts of ratios, proportions and
Set up ratios and proportions and solve
similarity are strongly interrelated and
using the cross-product property.
necessary for solving problems with similar
Similar triangles and other similar polygons figures.
Use similarity properties to identify similar
have congruent angles and proportional
triangles and other polygons.
sides.
Find missing sides and segments of
There are specific theorems that describe
triangles using triangle proportion
the proportions in triangle measurements.
theorems.
Page 23 of 40
Revised 7/5/10
Course Name:
Geometry, 2010-11
Unit Title:
(07) Similarity - Chapter 7
Number of Days:
10
The concepts of ratios, proportions and similarity are strongly interrelated and necessary for solving
Key Learning:
problems with similar figures.
Unit Essential Question: How do ratios and proportions enable the solving of problems involving similar polygons?
Concept:
Ratios and
Proportions
Benchmark(s):
MA.912.G.2.3
MA.912.G.4.4
Concept:
Similar Polygons
Benchmark(s):
MA.912.G.2.3
Concept:
Proving Triangles
Similar
Concept:
Similarity in Right
Triangles
Benchmark(s):
MA.912.G.4.5
MA.912.G.4.6
Benchmark(s):
MA.912.G.8.3
MA.912.G.5.2
Lesson Essential Questions:
1. How do I write and evaluate proportions using
ratios?
Textbook: Vocabulary:
1. PH 7-1
proportion, ratio,
means, extremes,
extended ratio,
cross products
property
Lesson Essential Questions:
Textbook: Vocabulary:
2. What are similar polygons?
2. PH 7-2 similar figures,
similar polygons,
extended
proportion,
similarity ratio,
scale factor, golden
rectangle, golden
ratio
Lesson Essential Questions:
Textbook: Vocabulary:
3. How can I prove triangles similar?
3. PH 7-3 indirect
measurement
Lesson Essential Questions:
Textbook: Vocabulary:
4. How does the altitude drawn to the hypotenuse of a 4. PH 7-4 geometric means
right triangle demonstrate the use of a geometric
mean?
Page 24 of 40
Revised 7/5/10
Concept:
Golden Ratio
Benchmark(s):
MA.912.D.11.5
Lesson Essential Questions:
5. What is the Golden Ratio and how can I relate the
Golden Ratio to the Fibonacci Sequence
Concept:
Proportions in
Triangles
Benchmark(s):
MA.912.G.4.5
Lesson Essential Questions:
5. How do I apply the side-splitter theorem and the
triangle-angle bisector theorem in order to find
missing sides of a triangle?
Textbook:
5. Concept
Byte:
Golden
Ration
Textbook:
5. PH 7-5
Vocabulary:
Golden Ratio,
Fibonacci sequence
Vocabulary:
Side-splitter
Theorem, Triangleangle Bisector
Theorem
Additional Information:
Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook
Page 25 of 40
Revised 7/5/10
Course Name:
Geometry, 2010-11
Unit Title:
(08) Right Triangles and Trigonometry - Chapter 8
Number of Days:
10
Know:
Understand:
Do:
Special right triangles are defined as 30-60- Trigonometric ratios are developed as
90 degree or 45-45-90 degree triangles.
applications of right triangle geometry.
Prove and apply the Pythagorean Theorem
and its 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).
Use special right triangles to solve
problems.
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.
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.
Angles of elevation and depression have
many real-world applications.
Page 26 of 40
Revised 7/5/10
Course Name:
Geometry, 2010-11
Unit Title:
(08) Right Triangles and Trigonometry - Chapter 10
Number of Days:
10
Key Learning:
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
Unit Essential Question:
world scenarios?
Concept:
The Pythagorean
Theorem and its
Converse
Concept:
Special Right
Triangles
Concept:
Trigonometry
Benchmark(s):
MA.912.G.5.1
MA.912.G.5.4
MA.912.G.8.3
Benchmark(s):
MA.912.G.5.3
MA.912.G.5.4
Benchmark(s):
MA.912.G.5.3
MA.912.G.5.4
Concept:
Angles of Elevation
and Depression
Concept:
Vectors
Benchmark(s):
MA.912.G.5.4
MA.912.T.2.1
Benchmark(s):
MA.912.D.9.3
Lesson Essential Questions:
Textbook: Vocabulary:
1.What problems can I use the Pythagorean Theorem 1. PH 8-1
Pythagorean triple
to solve for missing sides of a triangle?
Lesson Essential Questions:
2. How are the properties of special right triangles
(30-60-90, 45-45-90) used to find missing sides?
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
Lesson Essential Questions:
4. How do you use angles of elevation and depression
to solve problems?
Lesson Essential Questions:
4. How are vectors used to model motion and
directions?
Textbook: Vocabulary:
2. PH 8-2
Textbook: Vocabulary:
3. PH 8-3 trigonometric
rations, sine, cosine,
tangent, cotangent,
cosecant, cosine
Textbook: Vocabulary:
4. PH 8-4 Angle of elevations,
Angles of depression
Textbook: Vocabulary:
4. PH 8-5 vector, magnitude,
initial point, terminal
point, resultant
Page 27 of 40
Revised 7/5/10
Additional Information:
*Exposure to cosine, cosecant and cotangent is covered on page 539 #16-21. MA.912.T.2.1. This maybe needed for the state End of
Course Exam.
Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook
Page 28 of 40
Revised 7/5/10
Course Name:
Geometry, 2010-11
Unit Title:
(09) Transformations - Chapter 9
Number of Days:
10
Know:
Understand:
Two dimensional objects can be reflected,
translated, rotated or dilated on a plane.
Transformations can be performed on two- Perform transformations (translations,
dimensional shapes.
reflections, dilations and scale size change)
on polygons.
Transformations that result in congruent
images and pre-images are isometries.
Some polygons can tessellate on a plane.
Do:
Determine the congruence, similarity, and
symmetry between images and pre-images.
Create and verify tessellations of polygons
on a plane.
Page 29 of 40
Revised 7/5/10
Course Name:
Geometry, 2010-11
Unit Title:
(09) Transformations - Chapter 9
Number of Days:
10
Key Learning:
Transformations can be performed on two-dimensional shapes.
Unit Essential Question: What are the transformations in geometry?
Concept:
Reflections,
Translations,
Rotations
Benchmark(s):
MA.912.G.2.4
Lesson Essential Questions:
1. How are objects reflected, translated, rotated?
Concept:
Symmetry
Benchmark(s):
MA.912.G.2.4
Lesson Essential Questions:
2. How can I identify the types of symmetry in a
figure?
Concept:
Dilations
Benchmark(s):
MA.912.G.2.4
Lesson Essential Questions:
3. How can I apply dilations and scale factors to
polygons to determine similarity?
Concept:
Compositions and
Reflections
Benchmark(s):
MA.912.G.2.4
Lesson Essential Questions:
4. How are compositions and reflections in figures
used in graphing?
Textbook: Vocabulary:
1. PH 9-1, 9- transformation,
2, 9-3
preimage, image,
isometry, reflection,
line of reflection,
translation,
composition,
rotation (center,
angle), center of a
regular polygon
Textbook: Vocabulary:
2. PH 9-4 symmetry,
reflectional
symmetry, line
symmetry, rotational
symmetry, point
symmetry
Textbook: Vocabulary:
3. PH 9-5 dilation, center of
dilation, scale factor
of dilation,
enlargement,
reductions
Textbook: Vocabulary:
4. PH 9-6 glide reflection
Page 30 of 40
Revised 7/5/10
Concept:
Tessellations
Benchmark(s):
MA.912.G.2.4
Lesson Essential Questions:
5. How can I identify symmetry and transformations
in polygons that have been tessellated?
Textbook: Vocabulary:
5. PH 9-7 tessellation,
translational
symmetry, glide
reflection symmetry
Additional Information:
Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook.
Page 31 of 40
Revised 7/5/10
Course Name:
Geometry, 2010-11
Unit Title:
(10) Area - Chapter 10
Number of Days:
16
Know:
Understand:
Do:
There are formulas for circumference,
perimeter, and area for circles, triangles,
quadrilaterals, and regular polygons.
The characteristics of two-dimensional
figures can be used to calculate
circumference, perimeter and area.
Find the area, perimeter and circumference
of circles, triangles, quadrilaterals and
regular polygons.
There is a relationship between area,
sectors, segments, central angles,
intercepted arcs, circumference and arc
length in circles.
Geometric models can be used to find the
probability of events.
Define and identify: circumference, radius,
diameter, arc, arc length, chord, secant,
and segment in circles.
Find the probability of events using
geometric models.
Page 32 of 40
Revised 7/5/10
Course Name:
Geometry, 2010-11
Unit Title:
(10) Area - Chapter 10
Number of Days:
16
The characteristics of two-dimensional figures can be used to calculate circumference, perimeter and
Key Learning:
area.
Unit Essential Question: What properties of perimeter, area, and trigonometry can be applied in geometric situations?
Concept:
Area of Triangles,
Parallelograms
Trapezoids,
Rhombuses and Kites
Concept:
Area of Regular
Polygons
Concept:
Perimeter and Areas
of Similar Figures
Concept:
Trigonometry and
Area
Concept:
Circles and Arcs
Concept:
Areas of Circle and
Sectors
Benchmark(s): Lesson Essential Questions:
MA.912.G.2.5 1. How do I find the area of a parallelograms,
triangles, trapezoids, rhombuses and kites?
Benchmark(s):
MA.912.G.2.5
MA.912.G.2.7
Benchmark(s):
MA.912.G.2.7
Textbook: Vocabulary:
1. PH 10-1 base, altitude and height of a
10-2
parallelogram and triangle,
height of trapezoid
Lesson Essential Questions:
2. How can I find the area of a regular polygon?
Textbook: Vocabulary:
2. PH 10-3 radius of a regular polygon,
apothem
Lesson Essential Questions:
Textbook: Vocabulary:
3. How can I find perimeters and areas of similar 3. PH 10-4 scale factor, ratio of
polygons?
perimeters, ratio of areas
Benchmark(s): Lesson Essential Questions:
Textbook: Vocabulary:
MA.912.G.2.5 4. How can I use trigonometry to find the area of 4. PH 10-5
MA.912.G.2.1 regular polygons and triangles?
Benchmark(s): Lesson Essential Questions:
Textbook: Vocabulary:
MA.912.G.6.2 5. What is the relationship between central angles, 5. PH 10-6 circle, center, radius, congruent
MA.912.G.6.4 arc length, and circumference?
circles, diameter, central angle,
MA.912.G.6.5 * see Additional Information
semicircle, minor arc, major
arc, adjacent arcs,
circumference, pi, concentric
circles, arc length, congruent
arcs
Benchmark(s): Lesson Essential Questions:
Textbook: Vocabulary:
MA.912.G.2.7 6. How do I find the area of circle, sector and
6. PH 10-7 sector of a circle, segment of a
MA.912.G.6.5 segment?
circle
Page 33 of 40
Revised 7/5/10
Concept:
Geometric
Probability
Benchmark(s): Lesson Essential Questions:
Textbook: Vocabulary:
MA.912.G.2.5 7. What geometric models can be used to find the 7. PH 10-8 geometric probability
MA.912.G.6.5 probability of events?
Additional Information:
*use Concept Byte: Circle Graphs on page 687 with lesson 10-6.
*You may want to do 12-5 Circles in the Coordinate Plane after 10-6 as it may be on the State EOC Exam and needs to be covered
early.
Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook.
Page 34 of 40
Revised 7/5/10
Course Name:
Geometry, 2010-11
Unit Title:
(11) Surface Area and Volume - Chapter 10
Number of Days:
18
Know:
Understand:
Euler's formula relates the numbers of
faces and vertices a polyhedron has to its
edges.
Surface area and volume may be calculated Find the faces, edges and vertices of
for geometric solids.
polyhedra using Euler's Formula.
There are formulas for finding the lateral
area, surface area and volume of prisms,
cylinders, cones, and pyramids.
There are formulas for finding the surface
area and volume of spheres.
Do:
Use formulas to find lateral area, surface
area and volume of solids.
Determine how changes in the dimensions
affect the surface area and volume of
common geometric solids.
Changing the dimensions of a geometric solid
affects the surface area and volume.
Page 35 of 40
Revised 7/5/10
Course Name:
Geometry, 2010-11
Unit Title:
(11) Surface Area and Volume - Chapter 11
Number of Days:
18
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
Benchmark(s):
MA.912.G.7.2
Lesson Essential Questions:
1. How can I identify and analyze 3-D figures
(geometric solids) and their cross sections?
Concept:
Surface Area of
Geometric Solids
Benchmark(s):
MA.912.G.7.1
MA.912.G.7.5
MA.912.G.7.7
Lesson Essential Questions:
2. How do I calculate surface area of geometric
solids?
Concept:
Benchmark(s):
Volume of Geometric MA.912.G.7.5
Solids
MA.912.G.7.7
Lesson Essential Questions:
3. How do I calculate volume of geometric solids?
Textbook: Vocabulary:
1. PH 11-1 cross section,
polyhedron, face,
edge, vertex, net,
Euler’s Formula
Textbook: Vocabulary:
2. PH 11-2, prism, bases, lateral
11-3
faces, altitude,
height, lateral area,
surface area, right
prism, oblique prism,
cylinder, right
cylinder, oblique
cylinder, pyramid,
cone, slant height,
right cone, regular
pyramid
Textbook: Vocabulary:
3. PH 11-4, volume, composite
11-5
space figure,
pyramids, cones
Page 36 of 40
Revised 7/5/10
Concept:
Surface Area and
Volume of Spheres
Benchmark(s):
MA.912.G.7.4
MA.912.G.7.5
MA.912.G.7.7
Concept:
Areas and Volumes
of similar solids
Benchmark(s):
MA.912.G.7.6
Lesson Essential Questions:
Textbook: Vocabulary:
4. How do I calculate the surface area and volume of a 4. PH 11-6 sphere, center,
sphere?
radius, diameter,
circumference of a
sphere, great circle,
hemisphere
Lesson Essential Questions:
Textbook: Vocabulary:
5. How are the areas and volumes of similar solids
5. PH 11-7 similar solids
related?
Additional Information:
Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook.
Page 37 of 40
Revised 7/5/10
Course Name:
Geometry, 2010-11
Unit Title:
(12) Circles - Chapter 12
Number of Days:
22
Know:
Understand:
Do:
There is a relationship between segments
and angles formed by chords, secants and
tangents of circles.
The study of circles involves many aspects Define and identify diameters, arc and
of geometry including lines, segments, arcs chords in circles.
and angles.
Determine and use measures of arcs and
There is an equation for any circle graphed
related angles
on the coordinate plane, which is based upon
the distance formula.
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, name its
radius and center.
Page 38 of 40
Revised 7/5/10
Course Name:
Geometry, 2010-11
Unit Title:
(12) Circles - Chapter 12
Number of Days:
22
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
Benchmark(s):
MA.912.G.6.2
Concept:
Chords and Arcs
Benchmark(s):
MA.912.G.6.2
Concept:
Inscribed Angles
Benchmark(s):
MA.912.G.6.4
Concept:
Benchmark(s):
Angle Measures and MA.912.G.6.2
Segment Lengths
MA.912.G.6.4
Concept:
Circles in the
Coordinate Plane
Benchmark(s):
MA.912.G.1.1
MA.912.G.6.6
MA.912.G.6.7
Lesson Essential Questions:
1. What causes a line to be tangent to a circle?
Textbook: Vocabulary:
1. PH 12-1 tangent to a circle,
point of tangency,
inscribed in,
circumscribed about
Lesson Essential Questions:
Textbook: Vocabulary:
2. How are a circle's chords and arcs related to each 2. PH 12-2 Chord, arc
other?
Lesson Essential Questions:
Textbook: Vocabulary:
3. What is the relationship between an inscribed angle 3. PH 12-3 inscribed angle,
and its intercepted arc?
intercepted arc
Lesson Essential Questions:
Textbook: Vocabulary:
4. What is the relationship between segments and
4. PH 12-4 secant
angles formed by chords, secants, and tangents of
circles?
Lesson Essential Questions:
Textbook: Vocabulary:
5. How is the distance formula applied in the formula 5. PH 12-5 standard form of an
for the equation of a circle in the coordinate plane?
equation of a circle
Page 39 of 40
Revised 7/5/10
Additional Information:
Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5
*You may want to do 12-5 Circles in the Coordinate Plane earlier as it may be on the state EOC Exam.
Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook.
Page 40 of 40