Download Geometry - Lee County School District

THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan
Geometry (1206310)
Adopted Instructional Materials:
1-1
Transformations and Congruence
1-2
Lines, Angles, & Triangles
1-3 & 2-1
Triangles
Houghton Mifflin Harcourt Geometry
2-2
Quadrilaterals
2-3
Similarity
2-4 & 3-1
Trigonometry
2-4 & 3-1
Trigonometry
3-2
Circles
3-3
Solids
4-1
Probability
FLORIDA STATEWIDE ASSESSMENT
April 17–May 5, 2017
4-2
Polynomials (optional)
The fundamental purpose of the course in Geometry is to formalize and extend students’ geometric experiences from the middle grades. Students explore more complex geometric
situations and deepen their explanations of geometric relationships, moving towards formal mathematical arguments. Important differences exist between this Geometry course
and the historical approach taken in Geometry classes. For example, transformations are emphasized early in this course. Close attention should be paid to the introductory content
for the Geometry conceptual category found in the high school standards. The Standards for Mathematical Practice apply throughout each course and, together with the content
standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. The critical
areas, organized into five units are as follows.
Unit 1-Congruence, Proof, and Constructions: In previous grades, students were asked to draw triangles based on given measurements. They also have prior experience with rigid
motions: translations, reflections, and rotations and have used these to develop notions about what it means for two objects to be congruent. In this unit, students establish
triangle congruence criteria, based on analyses of rigid motions and formal constructions. They use triangle congruence as a familiar foundation for the development of formal
proof. Students prove theorems—using a variety of formats—and solve problems about triangles, quadrilaterals, and other polygons. They apply reasoning to complete geometric
constructions and explain why they work.
Unit 2- Similarity, Proof, and Trigonometry: Students apply their earlier experience with dilations and proportional reasoning to build a formal understanding of similarity. They
identify criteria for similarity of triangles, use similarity to solve problems, and apply similarity in right triangles to understand right triangle trigonometry, with particular attention
to special right triangles and the Pythagorean Theorem. Students develop the Laws of Sines and Cosines in order to find missing measures of general (not necessarily right) triangles,
building on students’ work with quadratic equations done in the first course. They are able to distinguish whether three given measures (angles or sides) define 0, 1, 2, or infinitely
many triangles.
Unit 3- Extending to Three Dimensions: Students’ experience with two-dimensional and three-dimensional objects is extended to include informal explanations of circumference,
area and volume formulas. Additionally, students apply their knowledge of two-dimensional shapes to consider the shapes of cross-sections and the result of rotating a twodimensional object about a line.
Unit 4- Connecting Algebra and Geometry Through Coordinates: Building on their work with the Pythagorean theorem in 8th grade to find distances, students use a rectangular
coordinate system to verify geometric relationships, including properties of special triangles and quadrilaterals and slopes of parallel and perpendicular lines, which relates back to
work done in the first course. Students continue their study of quadratics by connecting the geometric and algebraic definitions of the parabola.
Unit 5-Circles With and Without Coordinates: In this unit students prove basic theorems about circles, such as a tangent line is perpendicular to a radius, inscribed angle theorem,
and theorems about chords, secants, and tangents dealing with segment lengths and angle measures. They study relationships among segments on chords, secants, and tangents as
an application of similarity. In the Cartesian coordinate system, students use the distance formula to write the equation of a circle when given the radius and the coordinates of its
center. Given an equation of a circle, they draw the graph in the coordinate plane, and apply techniques for solving quadratic equations, which relates back to work done in the first
course, to determine intersections between lines and circles or parabolas and between two circles.
Page 1 of 28
Updated: June 8, 2016
State Assessment Information






FSA Portal
Training Tests Site
Calculator & Reference Sheet Policy
Reference Sheet Packet
Online Testing Scientific Calculator for FSA
Geometry FSA Test Item Specifications
Professional Development






Page 2 of 28
Math Practices by Grade Level
Build Relationships: Teach More Than ‘Just
Math’
Sorting Equations Video: Research shows that
formative assessments have a significant impact
on student learning gains. This video is just one
example of using formative assessment to inform
instruction.
CPALMS MFAS Training
Research around formative assessment shows
that students make greater learning gains when
they are accountable for their own learning and
the learning of their peers. The video, Facilitating
Peer Learning, is a good example of a math
classroom where students are engaged with one
another.
Five “Key Strategies” for Effective Formative
Assessment
Helpful Websites

Teaching Channel: Videos and Best Practices
https://www.teachingchannel.org/

Illustrative Mathematics: Performance Tasks
https://www.illustrativemathematics.org/

Inside Mathematics: Videos and Best Practices
http://www.insidemathematics.org/

Khan Academy: Practice by Grade Level Standards
https://www.khanacademy.org/commoncore/map

Shmoop: Math videos & Lesson Resources
http://www.shmoop.com/video/math-videos

CK12.org
http://www.ck12.org/

Math Open Reference
http://www.mathopenref.com/

Math Interactives (LearnAlberta)
http://www.learnalberta.ca/content/mejhm/index.html?l=0

iXL Math practice (20 problems free per day)
http://www.ixl.com/standards/florida/math/high-school
Updated: June 8, 2016
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan
1-1
Geometry (1206310)
Adopted Instructional Materials:
Houghton Mifflin Harcourt Geometry
Big Idea: Transformations and Congruence
Standards
Math Content Standards
Suggested Literacy & English Language Standards
MAFS.912.G-CO.1: Experiment with transformations in the plane.
 MAFS.912.G-CO.1.1: Know precise definitions of angle, circle, perpendicular line, parallel
line, and line segment, based on the undefined notions of point, line, distance along a line,
and distance around a circular arc.
 MAFS.912.G-CO.1.2: Represent transformations in the plane using, e.g., transparencies
and geometry software; describe transformations as functions that take points in the plane
as inputs and give other points as outputs. Compare transformations that preserve
distance
 MAFS.912.G-CO.1.3: Given a rectangle, parallelogram, trapezoid, or regular polygon,
describe the rotations and reflections that carry it onto itself.
 MAFS.912.G-CO.1.4: Develop definitions of rotations, reflections, and translations in terms
of angles, circles, perpendicular lines, parallel lines, and line segments.
 MAFS.912.G-CO.1.5: Given a geometric figure and a rotation, reflection, or translation,
draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software.
Specify a sequence of transformations that will carry a given figure onto another.
MAFS.912.G-CO.2: Understand congruence in terms of rigid motions.
 MAFS.912.G-CO.2.6: Use geometric descriptions of rigid motions to transform figures and
to predict the effect of a given rigid motion on a given figure; given two figures, use the
definition of congruence in terms of rigid motions to decide if they are congruent.
 MAFS.912.G-CO.2.7: Use the definition of congruence in terms of rigid motions to show
that two triangles are congruent if and only if corresponding pairs of sides and
corresponding pairs of angles are congruent.
MAFS.912.G-CO.3: Prove geometric theorems.
 MAFS.912.G-CO.3.9: Prove theorems about lines and angles; use theorems about lines and
angles to solve problems. Theorems include: vertical angles are congruent; when a
transversal crosses parallel lines, alternate interior angles are congruent and corresponding
LAFS.910.WHST.1.1: Write arguments focused on disciplinespecific content.
a. Introduce precise claim(s), distinguish the claim(s) from
alternate or opposing claims, and create an organization that
establishes clear relationships among the claim(s),
counterclaims, reasons, and evidence.
b. Develop claim(s) and counterclaims fairly, supplying data and
evidence for each while pointing out the strengths and
limitations of both claim(s) and counterclaims in a disciplineappropriate form and in a manner that anticipates the
audience’s knowledge level and concerns.
c. Use words, phrases, and clauses to link the major sections of
the text, create cohesion, and clarify the relationships
between claim(s) and reasons, between reasons and
evidence, and between claim(s) and counterclaims.
d. Establish and maintain a formal style and objective tone while
attending to the norms and conventions of the discipline in
which they are writing.
e. Provide a concluding statement or section that follows from
or supports the argument presented.
Page 3 of 28
Suggested Mathematical Practice Standards
MAFS.K12.MP.5.1: Use appropriate tools strategically.
 What tools do you have available to make constructions?
 How do constructions help make sense of the problem?
Updated: June 8, 2016
angles are congruent; points on a perpendicular bisector of a line segment are exactly
those equidistant from the segments endpoints.
MAFS.912.G-CO.4: Make geometric constructions.
 MAFS.912.G-CO.4.12: Make formal geometric constructions with a variety of tools and
methods (compass and straightedge, string, reflective devices, paper folding, dynamic
geometric software, etc.). Copying a segment; copying an angle; bisecting a segment;
bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of
a line segment;
MAFS.912.G-GPE.2: Use coordinates to prove simple geometric theorems algebraically.
 MAFS.912.G-GPE.2.4: Use coordinates to prove simple geometric theorems algebraically.
For example, prove or disprove that a figure defined by four given points in the coordinate
plane is a rectangle; prove or disprove that the point
MAFS.912.G-MG.1: Apply geometric concepts in modeling situations.
 MAFS.912.G-MG.1.3: Apply geometric methods to solve design problems (e.g., designing
an object or structure to satisfy physical constraints or minimize cost; working with
typographic grid systems based on ratios). ★
MAFS.K12.MP.7.1: Look for and make use of structure.
 What information helps you determine how to solve the
problem?
 How can you use what you know to explain why this works?
 Are there any patterns in the problems you’re doing that help
you make generalizations?
Essential Outcome Question(s)


How can you use tools of the trade, or concepts, to describe the construction of geometric figures?
How do transformations help identify and prove congruent figures?
Aligned Learning Goals
District Adopted
Materials

Define and identify basic geometric concepts including, point, line, line segment, ray,
angle, plane, distance along a line, perpendicular lines, parallel lines, linear pair, bisect,
perpendicular bisector, and angle bisector
Houghton Mifflin
Modules
1, 2, & 3

Use various tools to create line segments and angles, including a ruler, compass, and
technology

Perform a formal geometric construction to copy and bisect a line segment and angle using
a variety of tools, which could include a compass and straightedge, string, reflective
devices, paper folding, and dynamic geometric software


Know and use midpoint formula and distance formula to locate points and find lengths on
a coordinate plane and apply these formulas when solving problems and writing
coordinate proofs
Know and use vocabulary associated with transformations, including transformation,
image, preimage, rotation, reflection, translation, dilation, clockwise, counterclockwise,
isometry, and rigid motion
Page 4 of 28
Supplemental
Resources
Strategies for
Differentiation
INTERVENTION
MAFS.912.GCO.1.1: Intro to
Plane Geometry
MAFS.912.GCO.1.1: Sage N
Scribe activity using
precise vocabulary
MAFS.912.GGPE.2.6: Lesson
plan segment
partitioning
MAFS.912.GCO.1.1: Angles
MAFS.912.GCO.2.6:
Transformations
Updated: June 8, 2016

Identify the properties of rigid motions

Describe transformations, both rigid and non-rigid, using coordinate notation

Understand and use inductive reasoning, deductive reasoning, counterexamples,
postulates, and conditional statements to write simple proofs about lines and angles

Use postulates and theorems about points, lines, planes, and angles to solve problems

Define and use vocabulary and notation associated with vectors, including vector, initial
point, and terminal point, to describe translations

Perform translations and reflections on a coordinate plane and apply knowledge of
translations and reflections to identify coordinates, translation vectors, a line of reflection,
center of rotation, location of a figure, image, and preimage on a coordinate plane

Perform rotations using various tools both on and off a coordinate plane and apply
knowledge to identify the center of rotation and angle of rotation

Use symmetry and related vocabulary, including line of symmetry, line symmetry, and
rotational symmetry, to describe and identify properties of transformed figures

Describe a series of rotations and reflections that will carry a figure onto itself

Apply two or more transformations, either rigid or non-rigid, to a given figure to draw a
transformed figure, and predict beforehand the effect of the transformation

Use rigid motion to determine if two figures on a coordinate plane are congruent

Explain how CPCTC follows from figures being congruent and identify congruent parts of
congruent figures
MAFS.912.GCO.2.6: Lesson
transformations by
rigid motion
MAFS.912.GCO.4.12:
Constructions
ENRICHMENT
MAFS.912.GCO.2.6: Exploring
rigid
transformations
MAFS.K12.MP.3.1:
Deductive
Arguments
Formative Assessment Options:
MFAS Tasks G-CO.1.1:
 Definition of Angle
 Definition of
Perpendicular Lines
 Definition of Parallel
Lines
 Definition of Line
Segment
 Definition of a Circle
Page 5 of 28
MFAS Tasks G-CO.1.3:
 Transformations of
Parallelograms and
Rhombi
 Transformations of
Rectangles and Squares
 Transformations of
Regular Polygons
 Transformations of
Trapezoids
MFAS Tasks G-CO.1.4:
 Define a Reflection
 Define a Rotation
 Define a Translation
MFAS Tasks G-CO.2.6:
 Repeated Reflections and
Rotations
 Transform This
Congruent Trapezoids
MFAS Tasks G-CO.2.7:
 Basketball Goal
 Congruence Implies
 Congruent Corresponding
Parts
 Proving Congruence Using
Corresponding Parts
Updated: June 8, 2016
FSA Item Specifications:
MAFS.912.GCO.1.1
Page 6 of 28
MAFS.912.GCO.1.2
MAFS.912.GCO.1.5
MAFS.912.GCO.2.6
MAFS.912.GCO.3.9
MAFS.912.GCO.4.12
MAFS.912.GGPE.2.4
MAFS.912.GMG.1.3
Updated: June 8, 2016
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan
1-2
Geometry (1206310)
Adopted Instructional Materials:
Houghton Mifflin Harcourt Geometry
Big Idea: Lines, Angles, & Triangles
Standards
Math Content Standards
Suggested Literacy & English Language Standards
MAFS.912.G-CO.2: Understand congruence in terms of rigid motions.
 MAFS.912.G-CO.2.7: Use the definition of congruence in terms of rigid motions to show
that two triangles are congruent if and only if corresponding pairs of sides and
corresponding pairs of angles are congruent.
 MAFS.912.G-CO.2.8: Explain how the criteria for triangle congruence (ASA, SAS, SSS, and
Hypotenuse-Leg) follow from the definition of congruence in terms of rigid motions.
MAFS.912.G-CO.3: Prove geometric theorems.
 MAFS.912.G-CO.3.9: Prove theorems about lines and angles; use theorems about lines
and angles to solve problems. Theorems include: vertical angles are congruent; when a
transversal crosses parallel lines, alternate interior angles are congruent and
corresponding angles are congruent; points on a perpendicular bisector of a line segment
are exactly those equidistant from the segments endpoints.
MAFS.912.G-CO.4: Make geometric constructions.
 MAFS.912.G-CO.4.12: Make formal geometric constructions with a variety of tools and
methods (compass and straightedge, string, reflective devices, paper folding, dynamic
geometric software, etc.). Copying a segment; copying an angle; bisecting a segment;
bisecting an angle; constructing perpendicular lines, including the perpendicular bisector
of a line segment; and constructing a line parallel to a given line through a point not on
the line.
 MAFS.912.G-CO.4.13: Construct an equilateral triangle, a square, and a regular hexagon
inscribed in a circle.
MAFS.912.G-GPE.2: Use coordinates to prove simple geometric theorems algebraically.
 MAFS.912.G-GPE.2.5: Prove the slope criteria for parallel and perpendicular lines and use
them to solve geometric problems (e.g., find the equation of a line parallel or
perpendicular to a given line that passes through a given point).
MAFS.912.G-SRT.2: Prove theorems involving similarity.
 MAFS.912.G-SRT.2.5: Use congruence and similarity criteria for triangles to solve
LAFS.910.SL.1.2: Integrate multiple sources of information
presented in diverse media or formats (e.g., visually,
quantitatively, orally) evaluating the credibility and accuracy of
each source.
LAFS.910.RST.3.7: Translate quantitative or technical information
expressed in words in a text into visual form (e.g., a table or chart)
and translate information expressed visually or mathematically
(e.g., in an equation) into words.
Page 7 of 28
ELD.K12.ELL.SI.1: English language learners communicate for
social and instructional purposes within the school setting.
Suggested Mathematical Practice Standards
MAFS.K12.MP.3.1: Construct viable arguments and critique the
reasoning of others.
 Do you agree with that answer? Explain.
 Repeat what he/she said in your own words.
 How do you know what you are saying is true?
MAFS.K12.MP.2.1: Reason abstractly and quantitatively.
 What does the given information in the problem represent?
 How does the information help to solve the problem?
Updated: June 8, 2016
problems and to prove relationships in geometric figures.
Essential Outcome Question(s)
How does algebraic knowledge of lines help to solve problems about geometric concepts?
Aligned Learning Goals

Identify and define various angle pairs, including complementary, supplementary, vertical,
adjacent, and linear pair

Apply theorems about lines and angles to solve mathematical and real world problems

Identify angle pairs formed by a transversal intersecting two coplanar lines, including
corresponding angles, alternate interior angles, and same-side interior angles

Use properties and theorems of angles formed by a transversal intersecting parallel lines
to solve mathematical and real world problems

Write proofs justifying congruent angle pairs and parallel lines

Perform formal geometric constructions of parallel line, perpendicular lines, and
perpendicular bisectors and explain/justify each step in a proof

Prove perpendicular bisector theorem and theorems about right angles

Identify properties and make generalizations for the slopes of parallel and perpendicular
lines

Find the equation of a line parallel or perpendicular to a given line and solve geometric
problems involving parallel and perpendicular lines

Use rigid motion and congruent parts of congruent triangles (CPCTC) to prove triangles
are congruent

Know and apply the triangle postulates (SSS, SAS, ASA, AAS and HL) and use to prove two
triangles congruent

Solve mathematical and real world problems using congruence theorems for triangles
Page 8 of 28
District Adopted
Materials
Supplemental
Resources
Houghton Mifflin
Modules
4, 5, & 6
MAFS.912.GGPE.2.5: Parallel
Lines
Strategies for
Differentiation
ENRICHMENT
MAFS.912.GGPE.2.5: Parallel &
Perpendicular Lines
Investigation
MAFS.912.GCO.4.12:
Constructions
MAFS.912.GCO.2.7: Congruence
Updated: June 8, 2016
Formative Assessment Options:
MFAS Tasks G-CO.2.8:
 Justifying SSS Congruence
 Justifying SAS Congruence
 Justifying ASA Congruence
MFAS Tasks G-CO.3.9:
 Proving Vertical Angles Congruent
 Proving Alternate Interior Angles
Congruent
 Equidistant Points
MFAS Tasks G-CO.4.12:
 Constructing a Congruent Segment
 Constructing a Congruent Angle
 Bisecting a Segment and Angle
 Constructions for Parallel Lines
 Constructions for Perpendicular
Lines
MAFS.912.G-CO.4.12
MAFS.912.G-GPE.2.5
MFAS Tasks G-GPE.2.5:
 Proving the Slope Criterion for
Parallel Lines 1
 Proving Slope Criterion for Parallel
Lines 2
 Proving the Slope Criterion for
Perpendicular Lines 1
 Proving the Slope Criterion for
Perpendicular Lines 2
 Writing Equations for Parallel Lines
 Writing Equations for Perpendicular
Lines
FSA Item Specifications:
MAFS.912.G-CO.3.9
Page 9 of 28
MAFS.912.G-SRT.2.5
Updated: June 8, 2016
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan
1-3 & 2-1
Geometry (1206310)
Adopted Instructional Materials:
Houghton Mifflin Harcourt Geometry
Big Idea: Triangles
Standards
Math Content Standards
MAFS.912.G-CO.3: Prove geometric theorems.
 MAFS.912.G-CO.3.10: Prove theorems about triangles; use theorems about triangles to
solve problems. Theorems include: measures of interior angles of a triangle sum to 180°
triangle inequality theorem; base angles of isosceles triangles are congruent; the segment
joining midpoints of two sides of a triangle is parallel to the third side and half the length;
the medians of a triangle meet at a point.
MAFS.912.G-CO.4: Make geometric constructions.
 MAFS.912.G-CO.4.12: Make formal geometric constructions with a variety of tools and
methods (compass and straightedge, string, reflective devices, paper folding, dynamic
geometric software, etc.). Copying a segment; copying an angle; bisecting a segment;
bisecting an angle; constructing perpendicular lines, including the perpendicular bisector
of a line segment; and constructing a line parallel to a given line through a point not on
the line.
MAFS.912.G-SRT.2: Prove theorems involving similarity.
 MAFS.912.G-SRT.2.5: Use congruence and similarity criteria for triangles to solve
problems and to prove relationships in geometric figures.
MAFS.912.G-C.1: Understand and apply theorems about circles.
 MAFS.912.G-C.1.3: Construct the inscribed and circumscribed circles of a triangle, and
prove properties of angles for a quadrilateral inscribed in a circle.
MAFS.912.G-GPE.2: Use coordinates to prove simple geometric theorems algebraically.
 MAFS.912.G-GPE.2.4: Use coordinates to prove simple geometric theorems algebraically.
For example, prove or disprove that a figure defined by four given points in the coordinate
plane is a rectangle; prove or disprove that the point (1, 3) lies on the circle centered at the
origin and containing the point (0, 2).
Page 10 of 28
Suggested Literacy & English Language Standards
LAFS.910.SL.2.4: Present information, findings, and supporting
evidence clearly, concisely, and logically such that listeners can
follow the line of reasoning and the organization, development,
substance, and style are appropriate to purpose, audience, and
task.
Suggested Mathematical Practice Standards
MAFS.K12.MP.6.1: Attend to precision.
 What labels do you need to help make sense of the
model/diagram?
 What information is needed in order to answer the problem
accurately?
MAFS.K12.MP.1.1: Make sense of problems and persevere in
solving them.
 What is this problem asking?
 Could someone else understand how to solve the problem
based on your explanation?
Updated: June 8, 2016

MAFS.912.G-GPE.2.5: Prove the slope criteria for parallel and perpendicular lines and use
them to solve geometric problems (e.g., find the equation of a line parallel or
perpendicular to a given line that passes through a given point).
Essential Outcome Question(s)
How do triangle properties assist in solving real world problems?
Aligned Learning Goals
District Adopted
Materials

Understand and demonstrate conceptually that the interior angles of a triangle add to
180o and this information can be used to find the interior angles of any polygons

Use theorems about triangles to solve problems involving missing interior and exterior
angle measures, missing side lengths, and possible side lengths
Houghton Mifflin
Modules
7&8

Construct midsegments in triangles, and use the midsegment theorem to solve problems
about triangle side lengths

Fluently use vocabulary associated with triangles and other polygons, including vertex,
side, base angle, base, leg, isosceles, equilateral, and regular

Use constructions to make sense of theorems about triangles


Supplemental
Resources
INTERVENTION
MAFS.912.GCO.3.10: Triangles
MAFS.912.GCO.3.10: Lesson
Intersecting
medians and
resulting ratios
o
Prove theorems about triangles, including, interior angles sum to 180 , the triangle
inequality theorem, exterior angle theorem, isosceles triangle theorem, equilateral
triangle theorem, and base angles of isosceles triangles are congruent
Understand and define vocabulary associated with inscribing and circumscribing a circle
about a polygon, including circumscribed, inscribed, circumcircle, circumcenter, incircle,
and incenter

Describe the relationship between a circumscribed or inscribed circle and special
segments’ point of concurrency

Create formal geometric constructions of a circumscribed circle about a triangle and an
inscribed circle within a triangle

Create formal geometric constructions of a triangle’s perpendicular bisectors, angle
bisectors, medians, and altitudes and describe their relationship to a point of concurrency,
centroid, or orthocenter
Page 11 of 28
Strategies for
Differentiation
MAFS.912.GCO.3.10: Lesson
Midsegments
MAFS.912.GCO.4.12:
Perpendicular
Bisectors
MAFS.912.G-C.1.3:
Triangle
Circumcenter
MAFS.912.G-C.1.3:
Triangle Incenter
MAFS.912.GCO.4.12:
Constructions
ENRICHMENT
MAFS.912.GCO.3.10: Centroid
of a Triangle
Updated: June 8, 2016
Formative Assessment Options:
MFAS Tasks G-CO.3.10:
 Triangle Sum Proof
 Isosceles Triangle Proof
 Triangle Midsegment Proof
 Median Concurrency Proof
MFAS Tasks G-SRT.2.5:
 Basketball Goal
 County Fair
 Similar Triangles 1
 Prove Rhombus Diagonals Bisect Angles
 Similar Triangles 2
MFAS Tasks G-C.1.3:
 Circumscribed Circle Construction
 Inscribed Circle Construction
 Inscribed Quadrilaterals
MAFS.912.G-SRT.2.5
MAFS.912.G-GPE.2.4
FSA Item Specifications:
MAFS.912.G-CO.3.10
Page 12 of 28
MAFS.912.G-CO.4.12
MAFS.912.G-C.1.3
MAFS.912.G-GPE.2.5
Updated: June 8, 2016
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan
2-2
Geometry (1206310)
Adopted Instructional Materials:
Houghton Mifflin Harcourt Geometry
Big Idea: Quadrilaterals
Standards
Math Content Standards
Suggested Literacy & English Language Standards
MAFS.912.G-CO.3: Prove geometric theorems.
 MAFS.912.G-CO.3.11: Prove theorems about parallelograms; use theorems about
parallelograms to solve problems. Theorems include: opposite sides are congruent,
opposite angles are congruent, the diagonals of a parallelogram bisect each other, and
conversely, rectangles are parallelograms with congruent diagonals.
MAFS.912.G-SRT.2: Prove theorems involving similarity.
 MAFS.912.G-SRT.2.5: Use congruence and similarity criteria for triangles to solve problems
and to prove relationships in geometric figures.
MAFS.912.G-GPE.2: Use coordinates to prove simple geometric theorems algebraically.
 MAFS.912.G-GPE.2.4: Use coordinates to prove simple geometric theorems algebraically.
For example, prove or disprove that a figure defined by four given points in the coordinate
plane is a rectangle; prove or disprove that the point (1, 3) lies on the circle centered at the
origin and containing the point (0, 2).
 MAFS.912.G-GPE.2.5: Prove the slope criteria for parallel and perpendicular lines and use
them to solve geometric problems (e.g., find the equation of a line parallel or
perpendicular to a given line that passes through a given point).
 MAFS.912.G-GPE.2.7: Use coordinates to compute perimeters of polygons and areas of
triangles and rectangles, e.g., using the distance formula.
LAFS.910.RST.1.3: Follow precisely a complex multistep
procedure when carrying out experiments, taking measurements,
or performing technical tasks, attending to special cases or
exceptions defined in the text.
ELD.K12.ELL.MA.1: English language learners communicate
information, ideas and concepts necessary for academic success
in the content area of Mathematics.
Suggested Mathematical Practice Standards
MAFS.K12.MP.7.1: Look for and make use of structure.
 How can you use what you know to explain why this works?
 What patterns do you see?
MAFS.K12.MP.6.1: Attend to precision.
 How are you showing the meaning of the quantities in the
problem?
 How could you test your solution to see if your answer is
accurate?
Essential Outcome Question(s)
How can you determine the similarities and differences between various quadrilaterals?
Page 13 of 28
Updated: June 8, 2016
Aligned Learning Goals
District Adopted
Materials

Identify properties of parallelograms’ sides, angles, and diagonals and use when solving
problems about parallelograms, verifying parallelograms, and when identifying
quadrilaterals
Houghton Mifflin
Modules
9 & 10

Define and identify by their properties and special conditions, rectangle, rhombus, and
square and explain how they are related to one another and to the larger group,
parallelograms

Define and use associated vocabulary and symbols when sketching, identifying, and
describing parallelograms, trapezoids, and kites

Prove theorems about parallelograms, including opposite sides are congruent, opposite
angles are congruent, diagonals bisect each other, rectangle diagonals are congruent, and
diagonals of a rhombus are perpendicular using slope and/or distance formula when
necessary

Define and identify by their properties and special conditions, kites, trapezoids, and
isosceles trapezoids, and explain how they are related to the larger group, quadrilaterals

Use properties of special quadrilaterals to solve problems

Prove parallel lines have the same slope and perpendicular lines have slopes that are
opposite reciprocals

Use coordinate geometry to solve problems involving polygons, including find the
perimeter of polygons and area of triangles and quadrilaterals

Understand and demonstrate how to write a coordinate proof
Supplemental
Resources
Strategies for
Differentiation
INTERVENTION
MAFS.912.GCO.3.11:
Quadrilateral Quest
MAFS.912.GMG.1.3: Lesson
linking geometry to
real-life problem
solving
Formative Assessment Options:
MFAS Tasks G-CO.3.11:
 Proving Parallelogram Side Congruence
 Proving Parallelogram Angle Congruence
 Proving Parallelogram Diagonals Bisect
 Proving A Rectangle A Parallelogram
 Proving Congruent Diagonals
MFAS Tasks G-GPE.2.4:
 Describe the Quadrilateral
 Diagonals of a Rectangle
 Midpoints of Sides of a Quadrilateral
 Type of Triangle
MFAS Tasks G-GPE.2.7:
 Pentagon’s Perimeter
 Perimeter and Area of a Rectangle
 Perimeter and Area of a Right Triangle
Perimeter and Area of an Obtuse Triangle
FSA Item Specifications:
MAFS.912.G-CO.3.11
Page 14 of 28
MAFS.912.G-SRT.2.5
MAFS.912.G-GPE.2.4
MAFS.912.G-GPE.2.5
MAFS.912.G-GPE.2.7
Updated: June 8, 2016
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan
2-3
Geometry (1206310)
Adopted Instructional Materials:
Houghton Mifflin Harcourt Geometry
Big Idea: Similarity
Standards
Math Content Standards
Suggested Literacy & English Language Standards
MAFS.912.G-SRT.1: Understand similarity in terms of similarity transformations.
 MAFS.912.G-SRT.1.1: Verify experimentally the properties of dilations given by a center
and a scale factor:
a. 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.
b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
 MAFS.912.G-SRT.1.2: Given two figures, use the definition of similarity in terms of
similarity transformations to decide if they are similar; explain using similarity
transformations the meaning of similarity for triangles as the equality of all corresponding
pairs of angles and proportionality of all corresponding pairs of sides.
 MAFS.912.G-SRT.1.3: Use the properties of similarity transformations to establish the AA
criterion for two triangles to be similar.
MAFS.912.G-SRT.2: Prove theorems involving similarity.
 MAFS.912.G-SRT.2.4: Prove theorems about triangles. Theorems include: a line parallel to
one side of a triangle divides the other two proportionally, and conversely; the Pythagorean
Theorem proved using triangle similarity.
 MAFS.912.G-SRT.2.5: Use congruence and similarity criteria for triangles to solve problems
and to prove relationships in geometric figures.
MAFS.912.G-GPE.2: Use coordinates to prove simple geometric theorems algebraically.
 MAFS.912.G-GPE.2.6: Find the point on a directed line segment between two given points
that partitions the segment in a given ratio. ★
MAFS.912.G-C.1: Understand and apply theorems about circles.
 MAFS.912.G-C.1.1: Prove that all circles are similar.
MAFS.912.G-CO.4: Make geometric constructions.
 MAFS.912.G-CO.4.12: Make formal geometric constructions with a variety of tools and
methods (compass and straightedge, string, reflective devices, paper folding, dynamic
LAFS.910.RST.2.4: Determine the meaning of symbols, key
terms, and other domain-specific words and phrases as they are
used in a specific scientific or technical context relevant to
grades 9–10 texts and topics.
Page 15 of 28
ELD.K12.ELL.SI.1: English language learners communicate for
social and instructional purposes within the school setting.
Suggested Mathematical Practice Standards
MAFS.K12.MP.5.1: Use appropriate tools strategically.
 What math tools are available for finding the solution?
MAFS.K12.MP.8.1: Look for and express regularity in repeated
reasoning.
 Is this always true, sometimes true, or never true?
 What generalizations can you make?
Updated: June 8, 2016
geometric software, etc.).
Essential Outcome Question(s)
How can you determine if two figures are similar?
Aligned Learning Goals
District Adopted
Materials

Define and use vocabulary associated with dilations, including dilation, center of dilation,
and scale factor

Understand and explain how a dilation (along with reflections, translations, and rotations)
is a similarity transformation

Know the properties of a dilation and use them when solving problems and writing proofs
involving dilations and similar figures

Demonstrate how to find the center of dilation and scale factor for a given dilation


Dilate polygons and line segments
Identify corresponding parts of similar figures



Show/prove two figures are similar by identifying their similarity transformations
Prove that all circles are similar
Use transformations to explain why the AA criterion is sufficient to show two triangles are
similar
Use similarity criteria to set up proportions and solve algebraic problems involving
similarity




Supplemental
Resources
Houghton Mifflin
Modules
11 & 12
Strategies for
Differentiation
INTERVENTION
MAFS.912.GSRT.1.1: Dilations
MAFS.912.GGPE.2.7: Lesson
distance and
Pythagorean
Theorem
ENRICHMENT
MAFS.912.GSRT.1.1: Dilating a
Line
MAFS.912.GGPE.2.6:
Partitioning a
segment
MAFS.912.GSRT.1.1: Dilations
Use properties of similar triangles to prove the triangle proportionality theorem, the
geometric mean theorems, and the Pythagorean Theorem
Partition a segment on a coordinate plane into a given ratio, and determine the point that
partitions a segment in a given ratio
Determine the missing endpoint when given a ratio, one endpoint, and a point on a
partitioned line segment
Formative Assessment Options:
MFAS Tasks G-SRT.2.4:
 Converse of the Triangle
Proportionality Theorem
Page 16 of 28
MFAS Tasks G-GPE.2.6:
 Partitioning a Segment
MFAS Tasks G-SRT.1.1:
 Dilation of a Line: Factor of Two
 Dilation of a Line Segment
MFAS Tasks G-SRT.1.3:
 Describe the AA Similarity Theorem
Updated: June 8, 2016




Pythagorean Theorem Proof
Triangle Proportionality Theorem
Dilation of a Line: Center on the Line
Dilation of a Line: Factor of One Half


Justifying a Proof of the AA
Similarity Theorem
Prove the AA Similarity Theorem
FSA Item Specifications:
MAFS.912.G-SRT.1.1
Page 17 of 28
MAFS.912.G-SRT.1.2
MAFS.912.G-SRT.1.3
MAFS.912.G-SRT.2.5
MAFS.912.GGPE.2.6
MAFS.912.G-C.1.1
MAFS.912.GCO.4.12
Updated: June 8, 2016
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan
2-4 & 3-1
Geometry (1206310)
Adopted Instructional Materials:
Houghton Mifflin Harcourt Geometry
Big Idea: Trigonometry
Standards
Math Content Standards
Suggested Literacy & English Language Standards
MAFS.912.G-SRT.3: Define trigonometric ratios and solve problems involving right triangles.
 MAFS.912.G-SRT.3.6: Understand that by similarity, side ratios in right triangles are
properties of the angles in the triangle, leading to definitions of trigonometric ratios for
acute angles.
 MAFS.912.G-SRT.3.7: Explain and use the relationship between the sine and cosine of
complementary angles.
 MAFS.912.G-SRT.3.8: Use trigonometric ratios and the Pythagorean Theorem to solve right
triangles in applied problems. ★
MAFS.912.G-GPE.2: Use coordinates to prove simple geometric theorems algebraically.
 MAFS.912.G-GPE.2.7: Use coordinates to compute perimeters of polygons and areas of
triangles and rectangles, e.g., using the distance formula.
LAFS.910.WHST.3.9: Draw evidence from informational texts to
support analysis, reflection, and research.
ELD.K12.ELL.MA.1: English language learners communicate
information, ideas and concepts necessary for academic success
in the content area of Mathematics.
Suggested Mathematical Practice Standards
MAFS.K12.MP.2.1: Reason abstractly and quantitatively.
 What does the given information in the problem represent?
 How does the information help to solve the problem?
MAFS.K12.MP.4.1: Model with mathematics.
 What other ways could you use to model the situation
mathematically?
 What connections can you make between different
representations of the situation?
Essential Outcome Question(s)
How can you find a missing side or angle of a triangle?
Aligned Learning Goals
District Adopted
Materials
Supplemental
Resources
Strategies for
Differentiation

Understand and explain the connection between similar right triangles and sine, cosine,
and tangent ratios
Identify the sides of a right triangle that are opposite and adjacent to a given acute angle.
MAFS.912.GSRT.3.8:
Trigonometry
INTERVENTION

Houghton Mifflin
Module
13
Page 18 of 28
Updated: June 8, 2016

Identify and use trigonometric ratios needed to find missing sides of right triangles and the
inverse of trigonometric ratios to find missing angle measures

Explain the relationship between the sine and cosine of complementary angles (sin A = Cos
B and Sin B = Cos A)

Discover relationships in special right triangles, 45° − 45° − 90° and 30° − 60° − 90°

Use the Pythagorean Theorem, trigonometric ratios, and special right triangle relationships
to solve mathematical and real world problems involving right triangles

Derive the formula for the area of any triangle with a missing height using trigonometric
ratios and use the area formula to solve problems
MAFS.912.GSRT.3.8: Intro to
Trigonometry
MAFS.912.GSRT.3.8: Trig
Functions
MAFS.912.GSRT.3.7: 45-45-90
Triangles
MAFS.912.GSRT.3.7: 30-60-90
Triangles
ENRICHMENT
MAFS.912.GSRT.3.8: Trig Mini
Golf
Formative Assessment Options:
MFAS Tasks G-SRT.3.6:
 The Sine of 57
 The Cosine Ratio
MFAS Tasks G-SRT.3.7:
 Patterns in the 30-60-90 Table
 Finding Sine
 Right Triangle Relationships
 Sine and Cosine
MFAS Tasks G-SRT.3.8:
 Will It Fit?
 TV Size
 River Width
 Washington Monument




Holiday Lights
Step Up
Perilous Plunge
Lighthouse Keeper
FSA Item Specifications:
MAFS.912.G-SRT.3.8
Page 19 of 28
MAFS.912.G-GPE.2.7
Updated: June 8, 2016
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan
3-2
Geometry (1206310)
Adopted Instructional Materials:
Houghton Mifflin Harcourt Geometry
Big Idea: Circles
Standards
Math Content Standards
Suggested Literacy & English Language Standards
MAFS.912.G-C.1: Understand and apply theorems about circles.
 MAFS.912.G-C.1.2: Identify and describe relationships among inscribed angles, radii, and
chords. Include the relationship between central, inscribed, and circumscribed angles;
inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the
tangent where the radius intersects the circle.
 MAFS.912.G-C.1.3: Construct the inscribed and circumscribed circles of a triangle, and
prove properties of angles for a quadrilateral inscribed in a circle. MAFS.912.G-C.2: Find
arc lengths and areas of sectors of circles.
 MAFS.912.G-C.2.5: Derive using similarity the fact that the length of the arc intercepted by
an angle is proportional to the radius, and define the radian measure of the angle as the
constant of proportionality; derive the formula for the area of a sector.
MAFS.912.G-GMD.1: Explain volume formulas and use them to solve problems.
 MAFS.912.G-GMD.1.1: Give an informal argument for the formulas for the circumference
of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection
arguments, Cavalieris principle, and informal limit arguments.
MAFS.912.G-MG.1: Apply geometric concepts in modeling situations.
 MAFS.912.G-MG.1.1: Use geometric shapes, their measures, and their properties to
describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). ★
MAFS.912.G-GPE.1: Translate between the geometric description and the equation for a
conic section.
 MAFS.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.
MAFS.912.G-CO.4: Make geometric constructions.
 MAFS.912.G-CO.4.13: Construct an equilateral triangle, a square, and a regular hexagon
inscribed in a circle.
LAFS.910.SL.1.1: Initiate and participate effectively in a range of
collaborative discussions (one-on-one, in groups, and teacher-led)
with diverse partners on grades 9–10 topics, texts, and issues,
building on others’ ideas and expressing their own clearly and
persuasively.
a. Come to discussions prepared, having read and researched
material under study; explicitly draw on that preparation by
referring to evidence from texts and other research on the
topic or issue to stimulate a thoughtful, well-reasoned
exchange of ideas.
b. Work with peers to set rules for collegial discussions and
decision-making (e.g., informal consensus, taking votes on
key issues, presentation of alternate views), clear goals and
deadlines, and individual roles as needed.
c. Propel conversations by posing and responding to questions
that relate the current discussion to broader themes or larger
ideas; actively incorporate others into the discussion; and
clarify, verify, or challenge ideas and conclusions.
Page 20 of 28
Suggested Mathematical Practice Standards
MAFS.K12.MP.3.1: Construct viable arguments and critique the
reasoning of others.
 Do you agree with ______’s answer?
Updated: June 8, 2016
Essential Outcome Question(s)
How can similarity and proportion be used to describe relationships among geometric figures related to circles?
Aligned Learning Goals



District Adopted
Materials
Define and identify vocabulary associated with circles, including inscribed angle, radius,
diameter, arc, major arc, minor arc, adjacent arcs, intercepted arc, semicircle, central
angle, inscribed angle, circumscribed angle, tangent, point of tangency, secant, chord,
radian measure, and concentric circles
Houghton Mifflin
Modules
15, 16, & 17
Identify relationships among segments in a circle, such as radius and an inscribed angle or
a radius and tangent segment
Houghton Mifflin
Know and apply the Inscribed Angle Theorem, Circumscribed Angle Theorem, Chord-Chord
Product Theorem, Secant-Secant Product Theorem, Secant-Tangent Product Theorem,
Intersecting Chords Angle Measure Theorem, Tangent-Secant Interior Angle Theorem,
Tangent-Secant Exterior Angle Theorem, and Tangent-Radius Theorem to solve problems
with circles

Prove and apply the Inscribed Quadrilateral Theorem to solve problems involving
quadrilaterals inscribed in circles

Construct a circle inscribed in a triangle

Construct a circle circumscribed about a triangle and a quadrilateral

Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle

Construct a tangent line from a point outside a given circle to the circle.

Justify and apply the formulas for the circumference and area of a circle

Derive the formula for arc length and apply it in problem solving

Convert the measure of a central angle in degrees to radian measure and vice versa

Identify the constant of proportionality when converting degrees to radian measure

Derive the formula for the area of a sector and use it to solve problems

Derive the equation of a circle using the Pythagorean Theorem and use it to graph and
solve problems

Find the center and radius of a circle by completing the square
Page 21 of 28
Supplemental
Resources
INTERVENTION
(omit 17.2)
Ancillary Material
Ellipses & Hyperbolas
Strategies for
Differentiation
MAFS.912.GCO.4.13: Lesson
Inscribing Regular
Polygons in a Circle
Lesson
MAFS.912.GCO.4.13: Lesson
Inscribing Hexagons
and Equilateral
Triangles in a Circle
Lesson
MAFS.912.GCO.4.13: Lesson
inscribing polygons
in a circle
MAFS.912.GGPE.1.1: Equation
for a circle using the
Pythagorean
Theorem
MAFS.912.G-C.1.3:
Geometric
constructions
MAFS.912.G-C.1.1:
Proving circles
similar
MAFS.912.GGPE.1.3: Ellipses
MAFS.912.G-C.1.3:
Lesson circles and
triangles
MAFS.912.G-C.1.3:
Lesson inscribing
and circumscribing
right triangles
Updated: June 8, 2016

Derive the equation of a parabola given a focus and directrix.

Derive the equations of ellipses and hyperbolas given the foci and directrices.
MAFS.912.GGPE.1.1: Lesson
equation of a circle
MAFS.912.G-C.2.5:
Lesson sector area
MAFS.912.GGMD.1.1: Lesson
area and
circumference
Formative Assessment Options:
MFAS Tasks G-C.1.2:
 Central and Inscribed Angles
 Circles with Angles
 Inscribed Angle on Diameter
 Tangent Line and Radius
MFAS Tasks G-C.1.3:
 Inscribed Circle Construction
 Circumscribed Circle Construction
 Inscribed Quadrilaterals
MFAS Tasks G-C.2.5:
 Arc Length
 Sector Area
 Arc Length and Radians
 Deriving the Sector Area
Formula
MFAS Tasks G-GPE.1.1:
 Complete the Square for Center-Radius
 Complete the Square for Center-Radius 2
 Derive the Circle - General Points
 Derive the Circle - Specific Points
FSA Item Specifications:
MAFS.912.G-C.1.2
Page 22 of 28
MAFS.912.G-C.2.5
MAFS.912.G-GMD.1.1
MAFS.912.G-GPE.1.1
MAFS.912.G-MG.1.1
MAFS.912.G-C.1.3
Updated: June 8, 2016
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan
3-3
Geometry (1206310)
Adopted Instructional Materials:
Houghton Mifflin Harcourt Geometry
Big Idea: Solids
Standards
Math Content Standards
Suggested Literacy & English Language Standards
MAFS.912.G-GMD.1: Explain volume formulas and use them to solve problems.
 MAFS.912.G-GMD.1.1: Give an informal argument for the formulas for the circumference
of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection
arguments, Cavalieris principle, and informal limit arguments.
 MAFS.912.G-GMD.1.3: Use volume formulas for cylinders, pyramids, cones, and spheres to
solve problems. ★
MAFS.912.G-GMD.2: Visualize relationships between two-dimensional and threedimensional objects.
 MAFS.912.G-GMD.2.4: Identify the shapes of two-dimensional cross-sections of threedimensional objects, and identify three-dimensional objects generated by rotations of twodimensional objects.
MAFS.912.G-MG.1: Apply geometric concepts in modeling situations.
 MAFS.912.G-MG.1.1: Use geometric shapes, their measures, and their properties to
describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). ★
 MAFS.912.G-MG.1.2: Apply concepts of density based on area and volume in modeling
situations (e.g., persons per square mile, BTUs per cubic foot). ★
 MAFS.912.G-MG.1.3: Apply geometric methods to solve design problems (e.g., designing
an object or structure to satisfy physical constraints or minimize cost; working with
typographic grid systems based on ratios).★
MAFS.912.G-GPE.2: Use coordinates to prove simple geometric theorems algebraically.
 MAFS.912.G-GPE.2.7: Use coordinates to compute perimeters of polygons and areas of
triangles and rectangles, e.g., using the distance formula.
LAFS.910.WHST.2.4: Produce clear and coherent writing in which
the development, organization, and style are appropriate to task,
purpose, and audience.
ELD.K12.ELL.S.1: English language learners communicate for
social and instructional purposes within the school setting.
Suggested Mathematical Practice Standards
MAFS.K12.MP.4.1: Model with mathematics.
 What do you already know about the problem?
 What information is important in solving this problem?
 What other ways could you use to model the situation
mathematically?
Essential Outcome Question(s)
How can you use three-dimensional geometric figures to model real-world objects and to solve real-world problems?
Page 23 of 28
Updated: June 8, 2016
Aligned Learning Goals

Define vocabulary associated with three-dimensional figures, including net, prism,
pyramid, cylinder, right prism, right cylinder, oblique prism, oblique cylinder, cone, base of
a figure, height, sphere, cross-section, lateral area, lateral surface, slant height, and volume

Explain how to derive the formula for the volume of a cylinder, pyramid, sphere, and cone

Find and use volume of prisms, pyramids, cones, spheres, and cylinders to solve problems,
including finding a missing dimension, finding dimensions when volume changes, and
volume of composite figures

Explain Cavalieri’s Principle and apply it when finding volume

Identify the shape of a two-dimensional cross-section from a three-dimensional object and
explain that the shape will depend on how the cross-section was taken (vertical,
horizontal, etc.)

Demonstrate how to generate a three-dimensional figure from rotating a two-dimensional
figure or composite figure and identify figures generated

Understand and demonstrate how to find the surface area of prisms, cylinders, cones, and
pyramids, including composite figures, for the purpose of solving real-world problems

Understand and explain density and population density and apply these concepts to
geometry and real-world problem solving

Understand constraints and apply geometric methods to solve real-world design problems
District Adopted
Materials
Supplemental
Resources
Strategies for
Differentiation
Houghton Mifflin
Modules
18, 19, & 20
MAFS.912.GGMD.1.2:
Cavalieri’s Principle
Video/Visual
INTERVENTION
MAFS.912.GGMD.2.4: Solids
MAFS.912.GMG.1.2: Lesson
apply concepts of
density
MAFS.G-GMD.2.4:
cross-sections and
three dimensional
objects
Formative Assessment Options:
MFAS Tasks G-GMD.1.1:
 Volume of a Cone
 Volume of a Cylinder
 Volume of a Pyramid
MFAS Tasks G-GMD.1.3:
 Sports Drinks
 Snow Cones
 Do Not Spill the Water!
 The Great Pyramid
MFAS Tasks G-GMD.2.4:
 2D Rotations of Triangles
 2D Rotations of Rectangles
 Working Backwards – 2D Rotations
 Slice It
 Slice of a Cone
 Inside the Box
MFAS Tasks G-MG.1.2:
 How Many Trees?
 Mudslide
 Population of Utah
MFAS Tasks G-MG.1.3:
 Land for the Twins
 The Sprinters’ Race
 Softball Complex
 The Duplex
MAFS.912.G-GPE.2.7
MAFS.912.G-GMD.2.4
FSA Item Specifications:
MAFS.912.G-GMD.1.1
Page 24 of 28
MAFS.912.G-MG.1.1
MAFS.912.G-MG.1.2
MAFS.912.G-MG.1.3
Updated: June 8, 2016
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan
4-1
Geometry (1206310)
Adopted Instructional Materials:
Houghton Mifflin Harcourt Geometry
Big Idea: Probability (Optional: Preparing for the Next Level)
Standards
Math Content Standards








MAFS.912.S-CP.1.1: Describe events as subsets of a sample space (the set of outcomes)
using characteristics (or categories) of the outcomes, or as unions, intersections, or
complements of other events (“or,” “and,” “not”). ★
MAFS.912.S-CP.1.2: Understand that two events A and B are independent if the
probability of A and B occurring together is the product of their probabilities, and use this
characterization to determine if they are independent. ★
MAFS.912.S-CP.1.3: Understand the conditional probability of A given B as P(A and
B)/P(B), and interpret independence of A and B as saying that the conditional probability
of A given B is the same as the probability of A, and the conditional probability of B given
A is the same as the probability of B. ★
MAFS.912.S-CP.1.4: Construct and interpret two-way frequency tables of data when two
categories are associated with each object being classified. Use the two-way table as a
sample space to decide if events are independent and to approximate conditional
probabilities. For example, collect data from a random sample of students in your school
on their favorite subject among math, science, and English. Estimate the probability that a
randomly selected student from your school will favor science given that the student is in
tenth grade. Do the same for other subjects and compare the results. ★
MAFS.912.S-CP.1.5: Recognize and explain the concepts of conditional probability and
independence in everyday language and everyday situations. For example, compare the
chance of having lung cancer if you are a smoker with the chance of being a smoker if you
have lung cancer. ★
MAFS.912.S-CP.2.6: Find the conditional probability of A given B as the fraction of B’s
outcomes that also belong to A, and interpret the answer in terms of the model. ★
MAFS.912.S-CP.2.7: Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and
interpret the answer in terms of the model. ★
MAFS.912.S-CP.2.8: Apply the general Multiplication Rule in a uniform probability model,
P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. ★
Page 25 of 28
Suggested Literacy & English Language Standards
LAFS.910.SL.1.3: Evaluate a speaker’s point of view, reasoning,
and use of evidence and rhetoric, identifying any fallacious
reasoning or exaggerated or distorted evidence.
ELD.K12.ELL.MA.1: English language learners communicate
information, ideas and concepts necessary for academic success
in the content area of Mathematics.
Suggested Mathematical Practice Standards
MAFS.K12.MP.8.1: Look for and express regularity in repeated
reasoning.
 Is this always true, sometimes true, or never true?
 What generalizations can you make?
Updated: June 8, 2016

MAFS.912.S-CP.2.9: Use permutations and combinations to compute probabilities of
compound events and solve problems. ★
Essential Outcome Question(s)
How can you use probability to judge the likelihood of events occurring in real life and make fair decisions?
Aligned Learning Goals

Understand and use vocabulary and symbols associated with set notation, including set,
element, universal set, empty set, Venn diagram, union, intersection, subset, compliment

Find the theoretical probability and conditional probability of an event

Describe the Fundamental Counting Principle and use it to solve problems

Define and find permutations and use factorials to find permutations when using
permutations to find probability

Find a probability using combinations

Find a probability of mutually exclusive events and overlapping events

Find a probability from a two-way table

Find the probability of independent and dependent events

Use probability to make a fair decision

Analyze decisions using probability
Page 26 of 28
District Adopted
Materials
Supplemental
Resources
Strategies for
Differentiation
Houghton Mifflin
Modules
21, 22, & 23
Updated: June 8, 2016
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan
4-2
Geometry (1206310)
Adopted Instructional Materials:
McGraw-Hill Algebra 1
Big Idea: Polynomials (Optional: Preparing for Algebra 2)
Standards
Math Content Standards
Suggested Literacy & English Language Standards
MAFS.912.A-APR.1: Perform arithmetic operations on polynomials.
 MAFS.912.A-APR.1.1: Understand that polynomials form a system analogous to the
integers, namely, they are closed under the operations of addition, subtraction, and
multiplication; add, subtract, and multiply polynomials.
MAFS.912.A-APR.2: Understand the relationship between zeros and factors of polynomials.
 MAFS.912.A-APR.2.3: Identify zeros of polynomials when suitable factorizations are
available, and use the zeros to construct a rough graph of the function defined by the
polynomial.
MAFS.912.A-SSE.1: Interpret the structure of expressions.
 MAFS.912.A-SSE.1.1: Interpret expressions that represent a quantity in terms of its
context.
a. Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a single
entity. For example, interpret as the product of P and a factor not depending on P.
 MAFS.912.A-SSE.1.2: Use the structure of an expression to identify ways to rewrite it. For
example, see 𝑥 4 − 𝑦 4 as (𝑥²)² – (𝑦²)², thus recognizing it as a difference of squares that
can be factored as (𝑥² – 𝑦²)(𝑥² + 𝑦²).
MAFS.912.A-SSE.2: Write expressions in equivalent forms to solve problems.
 MAFS.912.A-SSE.2.3: Choose and produce an equivalent form of an expression to reveal
and explain properties of the quantity represented by the expression.
a. Factor a quadratic expression to reveal the zeros of the function it defines.
MAFS.912.F-IF.3: Analyze functions using different representations.
 MAFS.912.F-IF.3.8: Write a function defined by an expression in different but equivalent
forms to reveal and explain different properties of the function.
a. Use the process of factoring and completing the square in a quadratic function to
show zeros, extreme values, and symmetry of the graph, and interpret these in terms
of a context.
LAFS.910.WHST.2.4: Produce clear and coherent writing in which
the development, organization, and style are appropriate to task,
purpose, and audience.
ELD.K12.ELL.MA.1: English language learners communicate
information, ideas and concepts necessary for academic success
in the content area of Mathematics.
Page 27 of 28
Suggested Mathematical Practice Standards
MAFS.K12.MP.7.1: Look for and make use of structure.
 What patterns do you see?
 Can you look at the individual parts/terms of the polynomials
to help solve the problem?
MAFS.K12.MP.8.1: Look for and express regularity in repeated
reasoning.
 Are there generalizations you can make about multiplying
binomials?
 Why are some products of binomials referred to as special
cases?
Updated: June 8, 2016
Essential Outcome Question(s)
When can a polynomial function be used to model and solve a real-world problem?
Aligned Learning Goals

Identify parts of polynomial expressions

Perform operations on polynomial expressions

Use polynomial identities to rewrite quadratic expressions

Solve quadratic equations by factoring
District Adopted
Materials
McGraw-Hill
Algebra 1
Chapter 8, including
all Exploration
Algebra Labs
Supplemental
Resources
Strategies for
Differentiation
INTERVENTION
MAFS.912.AAPR.1.1: Math Is
Fun Polynomial
Review
MAFS.912.AAPR.1.1: Adding,
Subtracting,
Multiplying,
Dividing Prezi
ENRICHMENT
MAFS.912.F-IF.3.8:
Teach Me How to
Factor Math Rap
Page 28 of 28
Updated: June 8, 2016