12
Topic & Suggested Pacing Student Target Core MAFS.912.G-CO.1.1 Calculator: Neutral 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. 1.1, 1.2, 1.4, 1.5 MAFS.912.G-CO.4.12 Calculator: Neutral 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. 1.4 MAFS.912.G-GPE.2.7 Calculator: Neutral Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. 1.2, 1.3, 1.4 MAFS.912.G-MG.1.1 Calculator: Neutral Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). 1.6 • name and sketch geometric figures • use segment posulates to identify congruent segments • find lengths of segments in the coordinate plane • copy and bisect segments and angles using construction tools • use special angle relationships to find angle measures • classify polygons • name, measure, and classify angles FSQ Unit A August 18 - August 28 Identify Points, Lines, and Planes Use Segments and Congruence Use Midpoint and Distance Formulas Measure and Classify Angles Measure and Classify Angles Constructions Describe Angle Pair Relationships Classify Polygons Larson Geometry 1.1 1.2 1.3 1.4 & Constructions 1.5 1.6 The School District of Palm Beach County GEOMETRY HONORS Unit A: Essentials of Geometry 2015 - 2016 Standards Mathematics Florida Standards G-CO Geometry - Congruence G-GPE Geometry – Expressing Geometric Properties with Equations G-MG Geometry – Modeling Geometry G-GMD Geometry – Geometry Measurement & Dimension Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education

The School District of Palm Beach County GEOMETRY ... parts congruent • use theorems about isosceles and equilateral triangles • create an image congruent to a given triangle FSQ

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Page 1: The School District of Palm Beach County GEOMETRY ... parts congruent • use theorems about isosceles and equilateral triangles • create an image congruent to a given triangle FSQ

Topic & Suggested

PacingStudent Target Core

MAFS.912.G-CO.1.1

Calculator: Neutral

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.

1.1, 1.2, 1.4, 1.5

MAFS.912.G-CO.4.12

Calculator: Neutral

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.

1.4

MAFS.912.G-GPE.2.7

Calculator: Neutral

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the

distance formula.

1.2, 1.3, 1.4

MAFS.912.G-MG.1.1

Calculator: Neutral

Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a

human torso as a cylinder).

1.6

• name and sketch geometric

figures

• use segment posulates to identify

congruent segments

• find lengths of segments in the

coordinate plane

• copy and bisect segments and

angles using construction tools

• use special angle relationships to

find angle measures

• classify polygons

• name, measure, and classify

angles

FSQ Unit A

August 18 - August 28

Identify Points, Lines, and Planes

Use Segments and Congruence

Use Midpoint and Distance

Formulas

Measure and Classify Angles

Measure and Classify Angles

Constructions

Describe Angle Pair Relationships

Classify Polygons

Larson

Geometry

1.1

1.2

1.3

1.4 &

Constructions

1.5

1.6

The School District of Palm Beach County

GEOMETRY HONORS

Unit A: Essentials of Geometry

2015 - 2016

Standards

Mathematics Florida Standards

G-CO Geometry - Congruence G-GPE Geometry – Expressing Geometric Properties with EquationsG-MG Geometry – Modeling GeometryG-GMD Geometry – Geometry Measurement & Dimension

Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education

Page 2: The School District of Palm Beach County GEOMETRY ... parts congruent • use theorems about isosceles and equilateral triangles • create an image congruent to a given triangle FSQ

Topic & Suggested

PacingStudent Target Core

MAFS.912.G-CO.1.1

Calculator: Neutral

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.

2.2

MAFS.912.G-CO.3.9

Calculator: Neutral

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 segment’s endpoints.

2.2, 2.4, 2.5, 2.6, 2.7

FSQ Unit B

• write definitions as conditional

statements

• use postulates involving points,

lines, and planes

• use algebraic properties in logical

arguments

• write proofs using geometric

theorems

• use properties of special pairs of

angles

Standards

Mathematics Florida StandardsAugust 31 - September 9

Analyze Conditional Statements

Use Postulates and Diagrams

Reason Using Properties from

Algebra

Prove Statements about Segments

and Angles

Prove Angle Pair Relationships

Larson

Geometry

2.2

2.4

2.5

2.6

2.7

The School District of Palm Beach County

GEOMETRY HONORS

Unit B: Reasoning and Proof

2015 - 2016 G-CO Geometry - Congruence

Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education

Page 3: The School District of Palm Beach County GEOMETRY ... parts congruent • use theorems about isosceles and equilateral triangles • create an image congruent to a given triangle FSQ

Topic & Suggested

PacingStudent Target Core

MAFS.912.G-CO.1.1

Calculator: Neutral

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.

3.1

MAFS.912.G-CO.3.9

Calculator: Neutral

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 segment’s endpoints.

3.1, 3.2, 3.3, 3.6

MAFS.912.G-CO.4.12

Calculator: Neutral

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.

3.6

MAFS.912.G-GPE.2.5

Calculator: Neutral

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).

3.4, 3.5

USA Unit A, B, C

• identify angle pairs formed by

three intersecting lines

• use angles formed by parallel lines

and transversals

• use angle relationships to prove

that lines are parallel

• find and compare slopes of lines

• find equations of lines

• find the distance between a point

and a line

• construct parallel and

perpendicular lines

The School District of Palm Beach County

GEOMETRY HONORS

Unit C: Parallel and Perpendicular Lines

2015 - 2016

Standards

Mathematics Florida StandardsSeptember 10 - September 29

Identify Pairs of Lines and Angles

Use Parallel Lines & Transversals

Prove Lines are Parallel

Find and Use Slopes of Lines

Write and Graph Equations of

Lines

Prove Theorems About

Perpendicular Lines

Prove Theorems About

Perpendicular Lines

(Constructions)

Larson

Geometry

3.1

3.2

3.3

3.4

3.5

3.6 &

Constructions

G-CO Geometry - Congruence G-GPE Geometry – Expressing Geometric Properties with Equations

Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education

Page 4: The School District of Palm Beach County GEOMETRY ... parts congruent • use theorems about isosceles and equilateral triangles • create an image congruent to a given triangle FSQ

Topic & Suggested

PacingStudent Target Core

MAFS.912.G-CO.1.2

Calculator: Neutral

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 and angle to those that do not (e.g., translation versus horizontal

stretch).

4.3, 4.9

MAFS.912.G-CO.1.5

Calculator: Neutral

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.

4.9

MAFS.912.G-CO.2.6

Calculator: Neutral

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.

4.3, 4.9

MAFS.912.G-CO.2.7

Calculator: Neutral

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.

4.2, 4.3 *Not included on district assessment FSQ Unit D. Standard will be assessed on USA Unit D, E, F.

MAFS.912.G-CO.2.8

Calculator: Neutral

Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse Leg) follow from the definition

of congruence in terms of rigid motions.

4.4, 4.5, 4.6, 4.7

MAFS.912.G-CO.3.10

Calculator: Neutral

Prove theorems about triangles; use theorems about triangles to solve problems. Theorems include: measures

of interior angles of a triangle sum to 180°; triangle inequaliy 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.

4.1., 4.4, 4.5, 4.6, 4.7, 4.8

• classify triangles and find

measures of their angles

• identify congruent figures

• use transformations t show

congruence

• use the sides lengths to prove

triangles congruent

• use sides and angles to prove

congruence

• prove congruence through ASA

and AAS

• use congruent triangles to prove

corresponding parts congruent

• use theorems about isosceles and

equilateral triangles

• create an image congruent to a

given triangle

FSQ Unit D

The School District of Palm Beach County

GEOMETRY HONORS

Unit D: Congruent Triangles

2015 - 2016

Standards

Mathematics Florida StandardsOctober 5 - October 22

Apply Triangle Sum Properties

Apply Congruence and Triangles

Relate Transformations &

Congruence

Prove Triangles Congruent by SSS

Prove Triangles Congruent by SAS

& HL

Prove Triangles Congruent by ASA

and AAS

Use Congruent Triangles

Use Isosceles and Equilateral

Triangles

Perform Congruence

Transformations

Larson

Geometry

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

4.9

G-CO Geometry - Congruence

Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education

Page 5: The School District of Palm Beach County GEOMETRY ... parts congruent • use theorems about isosceles and equilateral triangles • create an image congruent to a given triangle FSQ

Topic & Suggested

PacingStudent Target Core

MAFS.912.G-CO.3.9

Calculator: Neutral

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 segment’s endpoints.

5.2

MAFS.912.G-CO.3.10

Calculator: Neutral

Prove theorems about triangles; use theorems about triangles to solve problems. Theorems include: measures

of interior angles of a triangle sum to 180°; triangle inequaliy 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.

5.1, 5.3, 5.4, 5.6

MAFS.912.G-GPE.2.4

Calculator: Neutral

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, ) lies on

the circle centered at the origin and containing the point (0, 2).

5.1

FSQ Unit E

• use properties of midsegments

and write coordinate proofs

• use perpendicular bisectors to

solve problems

• use angle bisectors to find

distance relationships

• use medians and altitudes of

triangles

• find possbile side lengths of

triangles

• use inequalities to make

comparisons in two triangles

The School District of Palm Beach County

GEOMETRY HONORS

Unit E: Relationships within Triangles

2015 - 2016

Standards

Mathematics Florida StandardsOctober 26 – November 6

Midsegment Theorem and

Coordinate Proof

Use Perpendicular Bisectors

Use Angle Bisectors of Triangles

Use Medians and Altitudes

Use Inequalities in a Triangle

Inequalities in Two Triangles and

Indirect Proof

Larson

Geometry

5.1

5.2

5.3

5.4

5.6

G-CO Geometry - CongruenceG-GPE Geometry – Expressing Geometric Properties with Equations

Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education

Page 6: The School District of Palm Beach County GEOMETRY ... parts congruent • use theorems about isosceles and equilateral triangles • create an image congruent to a given triangle FSQ

Topic & Suggested

PacingStudent Target Core

MAFS.912.G-C.1.1

Calculator: Neutral

Prove that all circles are similar.

6.2

MAFS.912.G-CO.1.2

Calculator: Neutral

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 and angle to those that do not (e.g., translation versus horizontal

stretch).

6.6 *Not included on district assessment for this unit. Standard will be assessed elsewhere as appropriate.

MAFS.912.G-GPE.2.4

Calculator: Neutral

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, ) lies on

the circle centered at the origin and containing the point (0, 2).

6.6

MAFS.912.G-GPE.2.6

Calculator: Neutral

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

6.5, 6.6 Extension

MAFS.912.G-MG.1.3

Calculator: Neutral

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).

6.5

MAFS.912.G-SRT.1.1

Calculator: Neutral

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.

6.2, 6.6

MAFS.912.G-SRT.1.2

Calculator: Neutral

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 the proportionality of all corresponding pairs of sides.

6.2 *Not included on district assessment for this unit. Standard will be assessed elsewhere as appropriate.

MAFS.912.G-SRT.1.3

Calculator: Neutral

Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

6.3

MAFS.912.G-SRT.2.4

Calculator: Neutral

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.

6.4, 6.5 *Not included on district assessment for this unit. Standard will be assessed elsewhere as

appropriate.

MAFS.912.G-SRT.2.5

Calculator: Neutral

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric

figures.

6.1, 6.5

USA Unit E, F

• use proportions to identify similar

polygons

• identify similarity transformations

called dilations

• explain what it means for two

figures to be similar

• use the AA Similarity Posulate to

show two triangles similar

• use the SSS and SAS Similarity

Theorems to show to triangle

similar

• use proprotions with a triangle or

parallel lines

• perform dilations

• find a point on a directed line

segment that partitions the

segment in a given ratio

The School District of Palm Beach County

GEOMETRY HONORS

Unit F: Similarity

2015 - 2016

Standards

November 9 – November 24

Use Similar Polygons

Relate Transformations and

Similarity

Prove Triangles Similar by AA

Prove Triangles Similar by SSS and

SAS

Use Proportionality Theorems

Perform Similarity

Transformations

Partition Segments

Mathematics Florida Standards

Larson

Geometry

6.1

6.2

6.3

6.4

6.5

6.66.6 Extension

Blender

Supplmental

Lessons

OCG 5-3

OGC 8-3

G-CO Geometry - CongruenceG-GPE Geometry – Expressing Geometric Properties with EquationsG-MG Geometry - Modeling Geometry

Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education

Page 7: The School District of Palm Beach County GEOMETRY ... parts congruent • use theorems about isosceles and equilateral triangles • create an image congruent to a given triangle FSQ

Topic & Suggested

PacingStudent Target Core

MAFS.912.G-MG.1.1

Calculator: Neutral

Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a

human torso as a cylinder).

7.3 *Not included on district assessment for this unit. Standard will be assessed elsewhere as appropriate.

MAFS.912.G-SRT.2.4

Calculator: Neutral

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.

7.1, 7.3

MAFS.912.G-SRT.2.5

Calculator: Neutral

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric

figures.

7.3

MAFS.912.G-SRT.3.6

Calculator: Neutral

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.

7.4, 7.5

MAFS.912.G-SRT.3.7

Calculator: Neutral

Explain and use the relationship between the sine and cosine of complementary angles.

7.6

MAFS.912.G-SRT.3.8

Calculator: Neutral

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

7.1, 7.2, 7.5, 7.6, 7.7

MAFS.912.G-SRT.4.10

Calculator: Neutral

Prove the Laws of Sines and Cosines and use them to solve problems.

7.7 Extension *Not included on district assessment for this unit.

MAFS.912.G-SRT.4.11

Calculator: Neutral

Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in

right and non-right triangles (e.g., surveying problems, resultant forces).

7.7 Extension *Not included on district assessment for this unit.

• use the Pythagorean Theoerm to

find the side lengths in right

triangles

• use the converse of the

Pythagorean Theorem to determine

if a triangle is a right triangle

• use properties of the altitude of a

right triangle

• use the relationships among the

sides in special right triangles

• use the tangent ratio for indirect

measurment

• use the sine and cosine ratios

• explain the relationships between

the sine and cosine of

complementary angles

• use the inverse tangent, sine, and

cosine ratios

• use trigonometry with acute and

obtuse triangles

FSQ Unit G

The School District of Palm Beach County

GEOMETRY HONORS

Unit G: Right Triangles and Trigonometry

2015 - 2016

Standards

January 5 – January 20

Apply the Pythagorean Theorem

Use the Converse of the

Pythagorean Theorem

Use Similar Right Triangles

Special Right Triangles

Apply the Tangent Ratio

Apply the Sine and Cosine Ratios

Trig Ratios of Complementary

Angles

Solve Right Triangles

Law of Sines and Cosines

Larson

Geometry

7.1

7.2

7.3

7.4

7.5

7.67.6 Additional

Lesson AL 2 - 3

7.77.7 Extension

Mathematics Florida Standards

G-GPE Geometry – Expressing Geometric Properties with EquationsG-MG Geometry - Modeling Geometry

Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education

Page 8: The School District of Palm Beach County GEOMETRY ... parts congruent • use theorems about isosceles and equilateral triangles • create an image congruent to a given triangle FSQ

Topic & Suggested

PacingStudent Target Core

MAFS.912.G-CO.3.11

Calculator: Neutral

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.

8.2, 8.3, 8.4, 8.6

MAFS.912.G-GPE.2.4

Calculator: Neutral

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, ) lies on

the circle centered at the origin and containing the point (0, 2).

8.5

MAFS.912.G-GPE.2.7

Calculator: Neutral

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the

distance formula.

8.4 *Not included on district assessment for this unit. Standard will be assessed elsewhere as appropriate.

MAFS.912.G-MG.1.1

Calculator: Neutral

Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a

human torso as a cylinder).

8.1 *Not included on district assessment for this unit. Standard will be assessed elsewhere as appropriate.

MAFS.912.G-SRT.2.5

Calculator: Neutral

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric

figures.

8.2, 8.3, 8.4, 8.5 *Not included on district assessment for this unit. Standard will be assessed elsewhere as

appropriate.

• find angle measures in polygons

• find angle and side measures in

parallelograms

• know the diagonal properties in

parallelograms

• use properties to identify

parallelgrams

• use properties of rhombuses,

rectangles, and squares

• use the properties of trapezoids

and kites

• identify special quadrilaterals

Mathematics Florida Standards

FSQ Unit H

January 21 – February 5

Find Angle Measures in Polygons

Use Properties of Parallelograms

Sides and Angles of Parallelograms

Show that a Quadrilateral is a

Parallelogram

Properties of Rhombuses, Rec-

tangles, and Squares

Special Parallelograms

Use Properties of Trapezoids and

Kites

Identify Special Quadrilaterals

Larson

Geometry

8.1

8.2

8.3

8.4

8.5

8.6

Blender

Supplemental

Lessons

8.2 Part 2

OCG 4-2 & 3

8.4 Part 2

OCG 4-5

The School District of Palm Beach County

GEOMETRY HONORS

Unit H: Quadrilateral

2015 - 2016

Standards

G-CO Geometry - CongruenceG-GPE Geometry – Expressing Geometric Properties with EquationsG-MG Geometry - Modeling Geometry

Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education

Page 9: The School District of Palm Beach County GEOMETRY ... parts congruent • use theorems about isosceles and equilateral triangles • create an image congruent to a given triangle FSQ

Topic & Suggested

PacingStudent Target Core

MAFS.912.G-CO.1.2

Calculator: Neutral

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 and angle to those that do not (e.g., translation versus horizontal

stretch).

9.3, 9.5, 9.7

MAFS.912.G-CO.1.3

Calculator: Neutral

Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry

it onto itself.

9.6

MAFS.912.G-CO.1.4

Calculator: Neutral

Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines,

parallel lines, and line segments.

9.1, 9.3, 9.4

MAFS.912.G-CO.1.5

Calculator: Neutral

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.

9.1, 9.3, 9.4, 9.5, 9.6, 9.7

MAFS.912.G-SRT.1.1

Calculator: Neutral

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.

9.7 *Not included on district assessment for this unit. Standard will be assessed elsewhere as appropriate.

MAFS.912.G-SRT.1.2

Calculator: Neutral

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 the proportionality of all corresponding pairs of sides.

9.7

USA Unit G, H, I

The School District of Palm Beach County

GEOMETRY HONORS

Unit I: Properties of Transformations

2015 - 2016

Standards

Mathematics Florida Standards• use a vector to translate a figure

• reflect a figure in any given line

• rotate figures about a point

• carry a polygon onto itself through

rotations and reflections

• perform combinations of two or

more transformations

• identify line and rotational

symmetries of a figure

• use drawing tools to draw

dilations

Larson

Geometry

9.1

9.3

9.4

9.5

9.6

9.7

Blender

Supplemental

Lessons

Supplement

Rotations &

Reflections

February 8 – February 22

Translate Figures and Use Vectors

Perform Reflections

Perform Rotations

Rotations & Reflections - Carry a

Polygom onto Itself

Apply Compositions of

Transformations

Identify Symmetry

Identify and Perform Dilations

G-CO Geometry - Congruence

Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education

Page 10: The School District of Palm Beach County GEOMETRY ... parts congruent • use theorems about isosceles and equilateral triangles • create an image congruent to a given triangle FSQ

Topic & Suggested

PacingStudent Target Core

MAFS.912.G-C.1.2

Calculator: Neutral

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.

10.1, 10.3, 10.4, 10.5, 10.6

MAFS.912.G-C.1.3

Calculator: Neutral

Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral

inscribed in a circle.

10.3, 10.4, 10.6 Part 2

MAFS.912.G-C.2.5

Calculator: Neutral

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.

10.4, 10.5 *Not included on district assessment FSQ Unit J. Standard will be assessed on USA Unit J, K.

MAFS.912.G-CO.1.1

Calculator: Neutral

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.

10.1, 10.2

MAFS.912.G-CO.1.2

Calculator: Neutral

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 and angle to those that do not (e.g., translation versus horizontal

stretch).

10.1 *Not included on district assessment for this unit. Standard will be assessed elsewhere as appropriate.

MAFS.912.G-CO.4.12

Calculator: Neutral

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.

10.3 *Not included on district assessment for this unit. Standard will be assessed elsewhere as appropriate.

MAFS.912.G-CO.4.13

Calculator: Neutral

Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

10.4, 10.6 Part 2

MAFS.912.G-GPE.1.1

Calculator: Neutral

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.

10.7

MAFS.912.G-GPE.1.2

Calculator: Neutral

Derive the equations of ellipses and hyperbolas given the foci and directrices.10.7 Part 2 AL 14 - 17 *Honors only. Not included on district assessment for this unit.

• use properties of a tangent to a

circle

• use angle measures to find arc

measures

• use relationships of arcs and

chords in a circle

• use inscribed angles of circles

• find the measures of angles

interior and exterior a circle

• construct equilateral triangle,

regular hexagon, square in a circle

• find segment lengths in circles

• construct a circle that

circumscribes a triangle

• write equations of circles in the

coordinate plane

• explain how the Pythagorean

Theorem can be used to derive the

equation of a circle

• write the equation of a parabola

given a focus and directrx

FSQ Unit J

February 29 – March 16

Use Properties of Tangents

Find Arc Measures

Apply Properties of Chords

Use Inscribed Angles and Polygons

Use Inscribed Angles and

Polygons(Constructions)

Apply Other Angle Relationships in

Circles

Find Segment Lengths in Circles

Constructing Circumscribed Circles

Write and Graph Equations of

Circles

Equation of a Parabola

Larson

Geometry

10.1

10.2

10.3

10.4 &

Constructions

10.5

10.6

10.7AL 14 - 17

Blender

Supplemental

Lessons

10.6 Part 2

OCG 7-2, 7-

3, 7-6

Standards

The School District of Palm Beach County

GEOMETRY HONORS

Unit J: Properties of Circles

2015 - 2016

Mathematics Florida Standards

G-C Geometry - CirclesG-CO Geometry - CongruenceG-GPE Geometry – Expressing Geometric Properties

Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education

Page 11: The School District of Palm Beach County GEOMETRY ... parts congruent • use theorems about isosceles and equilateral triangles • create an image congruent to a given triangle FSQ

Topic & Suggested

PacingStudent Target Core

MAFS.912.G-C.2.5

Calculator: Neutral

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.

11.1, 11.1 Extension, 11.2

MAFS.912.G-CO.4.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

11.3

MAFS.912.G-GMD.1.1

Calculator: Neutral

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, Cavalieri’s principle, and informal limit arguments.

11.1, 11.7

MAFS.912.G-GMD.1.3

Calculator: Neutral

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

11.6, 11.7, 11.8, 11.9

MAFS.912.G-GMD.2.4

Calculator: Neutral

Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-

dimensional objects generated by rotations of two-dimensional objects.

11.5, 11.7 Extension

MAFS.912.G-MG.1.2

Calculator: Neutral

Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs

per cubic foot).

11.6 Extension

MAFS.912.G-MG.1.3

Calculator: Neutral

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).

11.7 *Not included on district assessment for this unit. Standard will be assessed elsewhere as appropriate.

MAFS.912.G-SRT.3.8

Calculator: Neutral

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

11.3 *Not included on district assessment for this unit. Standard will be assessed elsewhere as appropriate.

USA Unit J, K

• find arc lengths and other

measures

• find the radian measure of an

angle

• find the areas of circles and

sectors

• fine the areas of regular polygons

inscribed in circles

• identify solids

• find the volume of prisms and

cylinders

• use density to solve problems

• find the volume of pyramids and

cones

• describe solids produced by

rotating two-dimensional firgures

around an axis in space

• find the surface area and volume

of spheres

• use properties of similar solids

Standards

Mathematics Florida StandardsMarch 28 – April 11

Circumference and Arc Length

Measure Angles in Radians

Areas of Circles and Sectors

Areas of Regular Polygons

Explore Solids

Volume of Prisms and Cylinders

Density

Volume of Pyramids and Cones

Solids of Revolution

Surface Area and Volume of

Spheres

Similar Solids

Larson

Geometry

11.111.1 Extension

11.2

11.3

11.4

11.5

11.611.6 Extension

11.7

11.8

11.9

Blender

Supplemental

Lessons

OCA2 8-1

The School District of Palm Beach County

GEOMETRY HONORS

Unit K: Measurement of Figures and Solids

2015 - 2016

G-C Geometry - CirclesG-CO Geometry - CongruenceG-GMD Geometry - Geometry Measurement & DimensionG-MG Geometry - Modeling GeometryG-SRT Geometry - G-SRT Geometry -

Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education

Page 12: The School District of Palm Beach County GEOMETRY ... parts congruent • use theorems about isosceles and equilateral triangles • create an image congruent to a given triangle FSQ

Topic & Suggested

PacingStudent Target Core

MAFS.912.G-GPE.1.3 Derive the equations of ellipses and hyperbolas given the foci and directrices.

Supplement

Post Assessment • derive the equation of ellipses and

hyperbolas given a focus and

directrx

Supplement

Standards

The School District of Palm Beach County

GEOMETRY HONORS

Unit L: Post Assessment Content

2015 - 2016

Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education