Download The School District of Palm Beach County GEOMETRY REGULAR

The School District of Palm Beach County
GEOMETRY REGULAR
Unit A: Essentials of Geometry
2015 - 2016
Topic & Suggested
Pacing
Standards
G-CO Geometry - Congruence
G-GPE Geometry – Expressing
Geometric Properties with Equations
G-MG Geometry – Modeling Geometry
G-GMD Geometry – Geometry
Measurement & Dimension
Student Target
Core
Mathematics Florida Standards
August 18 - August 28
• name and sketch geometric
figures
Identify Points, Lines, and Planes • use segment posulates to
identify congruent segments
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string,
Use Segments and Congruence • find lengths of segments in
reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting
MAFS.912.G-CO.4.12
the coordinate plane
a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line
Use Midpoint and Distance
Calculator Neutral
• copy and bisect segments
segment; and constructing a line parallel to a given line through a point not on the line.
Formulas
and angles using construction
1.4
tools
Measure and Classify Angles
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance
• use special angle
MAFS.912.G-GPE.2.7
formula.
relationships to find angle
Calculator Neutral
Measure and Classify Angles
1.2, 1.3, 1.4
measures
Constructions
Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a
• classify polygons
MAFS.912.G-MG.1.1
human torso as a cylinder).
• name, measure, and classify
Calculator Neutral
Describe Angle Pair Relationships angles
1.6
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
Classify Polygons
FSQ Unit A
Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education
Larson
Geometry
1.1
1.2
1.3
1.4 &
Constructions
1.5
1.6
The School District of Palm Beach County
GEOMETRY REGULAR
Unit B: Reasoning and Proof
2015 - 2016
G-CO Geometry - Congruence
Topic & Suggested
Pacing
Standards
Mathematics Florida Standards
• write definitions as
conditional statements
• use postulates involving
Analyze Conditional Statements points, lines, and planes
• use algebraic properties in
Use Postulates and Diagrams logical arguments
• write proofs using geometric
Reason Using Properties from theorems
Algebra
• use properties of special
pairs of angles
Prove Statements about
Segments and Angles
Core
August 31 - September 9
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
Prove Angle Pair Relationships
FSQ Unit B
Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education
Student Target
Larson
Geometry
2.2
2.4
2.5
2.6
2.7
The School District of Palm Beach County
GEOMETRY REGULAR
Unit C: Parallel and Perpendicular Lines
2015 - 2016
Topic & Suggested
Pacing
Standards
Mathematics Florida Standards
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
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
MAFS.912.G-CO.4.12
a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line
Calculator: Neutral
segment; and constructing a line parallel to a given line through a point not on the line.
3.6
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
Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education
Student Target
• identify angle pairs formed
by three intersecting lines
• use angles formed by parallel
Identify Pairs of Lines and Angles lines and transversals
• use angle relationships to
Use Parallel Lines & Transversals prove that lines are parallel
• find and compare slopes of
Prove Lines are Parallel
lines
• find equations of lines
Find and Use Slopes of Lines
• find the distance between a
point and a line
Write and Graph Equations of • construct parallel and
Lines
perpendicular lines
Core
September 10 - September 29
MAFS.912.G-CO.1.1
Calculator: Neutral
MAFS.912.G-GPE.2.5
Calculator: Neutral
G-CO Geometry - Congruence
G-GPE Geometry – Expressing Geometric
Properties with Equations
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
The School District of Palm Beach County
GEOMETRY REGULAR
Unit D: Congruent Triangles
2015 - 2016
G-CO Geometry - Congruence
Topic & Suggested
Pacing
Standards
Mathematics Florida Standards
MAFS.912.G-CO.1.2
Calculator: Neutral
MAFS.912.G-CO.1.5
Calculator: Neutral
MAFS.912.G-CO.2.6
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
October 5 - October 22
Apply Triangle Sum Properties
Apply Congruence and Triangles
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph
Relate Transformations &
paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure
Congruence
onto another.
4.9
Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on Prove Triangles Congruent by SSS
a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are
Prove Triangles Congruent by SAS
congruent.
& HL
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
Prove Triangles Congruent by ASA
and AAS
Use Congruent Triangles
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
MAFS.912.G-CO.3.10
congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length;
Calculator: Neutral
the medians of a triangle meet at a point.
4.1., 4.4, 4.5, 4.6, 4.7, 4.8
FSQ Unit D
Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education
Use Isosceles and Equilateral
Triangles
Perform Congruence
Transformations
Student Target
• 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
Core
Larson
Geometry
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
The School District of Palm Beach County
GEOMETRY REGULAR
Unit E: Relationships within Triangles
2015 - 2016
Topic & Suggested
Pacing
Standards
Mathematics Florida Standards
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
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
Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education
Student Target
• use properties of
midsegments and write
coordinate proofs
Midsegment Theorem and
• use perpendicular bisectors
Coordinate Proof
to solve problems
• use angle bisectors to find
Use Perpendicular Bisectors
distance relationships
• use medians and altitudes of
Use Angle Bisectors of Triangles triangles
• find possbile side lengths of
Use Medians and Altitudes
triangles
• use inequalities to make
Use Inequalities in a Triangle comparisons in two triangles
Core
October 26 – November 6
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
MAFS.912.G-CO.3.10
congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length;
Calculator: Neutral
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
G-CO Geometry - Congruence
G-GPE Geometry – Expressing
Geometric Properties with Equations
Inequalities in Two Triangles and
Indirect Proof
Larson
Geometry
5.1
5.2
5.3
5.4
5.6
The School District of Palm Beach County
GEOMETRY REGULAR
Unit F: Similarity
2015 - 2016
Standards
Mathematics Florida Standards
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
MAFS.912.G-SRT.1.1
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
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
Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education
G-CO Geometry - Congruence
G-GPE Geometry – Expressing Geometric Properties
with Equations
G-MG Geometry - Modeling Geometry
Topic & Suggested
Pacing
Student Target
Core
November 9 – November 24
• use proportions to identify
similar polygons
Larson
Use Similar Polygons
• identify similarity
Geometry
transformations called
6.1
Relate Transformations and
dilations
6.2
Similarity
• explain what it means for
two figures to be similar
6.3
Prove Triangles Similar by AA • use the AA Similarity
6.4
Posulate to show two triangles
6.5
Prove Triangles Similar by SSS and similar
SAS
• use the SSS and SAS Similarity
6.6
Theorems to show to triangle
6.6
Use Proportionality Theorems similar
• use proprotions with a
Extension
Perform Similarity
triangle or parallel lines
Transformations
• perform dilations
Blender
• find a point on a directed line
Supplmental
Partition Segments
segment that partitions the
segment in a given ratio
Lessons
OCG 5-3
OCG 8-3
The School District of Palm Beach County
GEOMETRY REGULAR
Unit G: Right Triangles and Trigonometry
2015 - 2016
Topic & Suggested
Pacing
Standards
Mathematics Florida Standards
MAFS.912.G-MG.1.1
Calculator: Neutral
MAFS.912.G-SRT.2.4
Calculator: Neutral
MAFS.912.G-SRT.2.5
Calculator: Neutral
MAFS.912.G-SRT.3.6
Calculator: Neutral
MAFS.912.G-SRT.3.7
Calculator: Neutral
MAFS.912.G-SRT.3.8
Calculator: Neutral
Student Target
Core
• use the Pythagorean
Theoerm to find the side
Larson
lengths in right triangles
Geometry
Apply the Pythagorean Theorem • use the converse of the
7.1
Pythagorean Theorem to
7.2
Use the Converse of the
determine if a triangle is a right
Pythagorean Theorem
triangle
7.3
• use properties of the altitude
7.4
Use Similar Right Triangles
of a right triangle
7.5
• use the relationships among
Special Right Triangles
the sides in special right
7.6
triangles
7.6
Apply the Tangent Ratio
• use the tangent ratio for
Additional
indirect measurment
Apply the Sine and Cosine Ratios • use the sine and cosine ratios Lesson AL 2
• explain the relationships
3
Trig Ratios of Complementary between the sine and cosine of
Angles
complementary angles
7.7
• use the inverse tangent, sine,
Solve Right Triangles
and cosine ratios
January 5 – January 20
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.
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
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric
figures.
7.3
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
Explain and use the relationship between the sine and cosine of complementary angles.
7.6
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
7.1, 7.2, 7.5, 7.6, 7.7
FSQ Unit G
Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education
G-GPE Geometry – Expressing
Geometric Properties with Equations
G-MG Geometry - Modeling
Geometry
-
The School District of Palm Beach County
GEOMETRY REGULAR
Unit H: Quadrilateral
2015 - 2016
G-CO Geometry - Congruence
G-GPE Geometry – Expressing Geometric Properties
with Equations
G-MG Geometry - Modeling Geometry
Topic & Suggested
Pacing
Standards
Student Target
Core
• find angle measures in
Larson
polygons
Geometry
• find angle and side measures
8.1
Prove theorems about parallelograms; use theorems about parallelograms to solve problems. Theorems include:
Find Angle Measures in Polygons in parallelograms
MAFS.912.G-CO.3.11 opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and
8.2
• know the diagonal properties
Calculator: Neutral conversely, rectangles are parallelograms with congruent diagonals.
Use Properties of Parallelograms in parallelograms
8.3
8.2, 8.3, 8.4, 8.6
• use properties to identify
8.4
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure
Sides and Angles of
parallelgrams
MAFS.912.G-GPE.2.4 defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, ) lies on the
8.5
Parallelograms
• use properties of rhombuses,
Calculator: Neutral circle centered at the origin and containing the point (0, 2).
rectangles, and squares
8.6
8.5
Show that a Quadrilateral is a • use the properties of
Parallelogram
trapezoids and kites
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance
Blender
MAFS.912.G-GPE.2.7
• identify special quadrilaterals
formula.
Supplemental
Calculator: Neutral
Properties of Rhombuses, Rec8.4 *Not included on district assessment for this unit. Standard will be assessed elsewhere as appropriate.
Lessons
tangles, and Squares
Mathematics Florida Standards
January 21 – February 5
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.
FSQ Unit H
Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education
Special Parallelograms
Use Properties of Trapezoids and
Kites
Identify Special Quadrilaterals
8.2 Part 2
OCG 4-2 & 3
8.4 Part 2
OCG 4-5
The School District of Palm Beach County
GEOMETRY REGULAR
Unit I: Properties of Transformations
2015 - 2016
Topic & Suggested
Pacing
Standards
MAFS.912.G-CO.1.3
Calculator: Neutral
MAFS.912.G-CO.1.4
Calculator: Neutral
MAFS.912.G-CO.1.5
Calculator: Neutral
MAFS.912.G-SRT.1.1
Calculator: Neutral
MAFS.912.G-SRT.1.2
Calculator: Neutral
Student Target
• use a vector to translate a
figure
• reflect a figure in any given
Represent transformations in the plane using, e.g., transparencies and geometry software; describe
Translate Figures and Use Vectors line
transformations as functions that take points in the plane as inputs and give other points as outputs. Compare
• rotate figures about a point
transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
Perform Reflections
• carry a polygon onto itself
9.3, 9.5, 9.7
through rotations and
Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it
Perform Rotations
reflections
onto itself.
• perform combinations of two
9.6
Rotations & Reflections - Carry a or more transformations
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel
Polygom onto Itself
• identify line and rotational
lines, and line segments.
symmetries of a figure
9.1, 9.3, 9.4
Apply Compositions of
• use drawing tools to draw
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph
Transformations
dilations
paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure
onto another.
Identify Symmetry
9.1, 9.3, 9.4, 9.5, 9.6, 9.7
Identify and Perform Dilations
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.
Mathematics Florida Standards
MAFS.912.G-CO.1.2
Calculator: Neutral
G-CO Geometry - Congruence
February 8 – February 22
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
Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education
Core
Larson
Geometry
9.1
9.3
9.4
9.5
9.6
9.7
Blender
Supplemental
Lessons
Supplement
Rotations &
Reflections
The School District of Palm Beach County
GEOMETRY REGULAR
Unit J: Properties of Circles
2015 - 2016
Standards
Mathematics Florida Standards
MAFS.912.G-C.1.2
Calculator: Neutral
MAFS.912.G-C.1.3
Calculator: Neutral
MAFS.912.G-C.2.5
Calculator: Neutral
MAFS.912.G-CO.1.1
Calculator: Neutral
MAFS.912.G-CO.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
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
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.
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
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.
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
MAFS.912.G-CO.4.12
a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line
Calculator: Neutral
segment; and constructing a line parallel to a given line through a point not on the line.
10.4 *Not included on district assessment for this unit. Standard will be assessed elsewhere as appropriate.
MAFS.912.G-CO.4.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Calculator: Neutral 10.4, 10.6 Part 2
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to
MAFS.912.G-GPE.1.1
find the center and radius of a circle given by an equation.
Calculator: Neutral
10.7
FSQ Unit J
Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education
G-C Geometry - Circles
G-CO Geometry - Congruence
G-GPE Geometry – Expressing Geometric Properties
Topic & Suggested
Pacing
Student Target
Core
• use properties of a tangent
to a circle
Larson
• use angle measures to find
Geometry
Use Properties of Tangents
arc measures
10.1
• use relationships of arcs and
10.2
Find Arc Measures
chords in a circle
• use inscribed angles of circles
10.3
Apply Properties of Chords
• find the measures of angles
10.4 &
interior and exterior a circle
Use Inscribed Angles and
• construct equilateral triangle, Constructions
Polygons
regular hexagon, square in a
circle
Use Inscribed Angles and
• find segment lengths in
Polygons(Constructions)
circles
• construct a circle that
Apply Other Angle Relationships circumscribes a triangle
Blender
in Circles
• write equations of circles in
Supplemental
the coordinate plane
Lessons
Find Segment Lengths in Circles • explain how the Pythagorean
Theorem can be used to derive
10.6 Part 2
Constructing Circumscribed
the equation of a circle
OCG 7-2, 7Circles
February 29 – March 16
10.5
10.6
10.7
3, 7-6
Write and Graph Equations of
Circles
The School District of Palm Beach County
GEOMETRY REGULAR
Unit K: Measurement of Figures and Solids
2015 - 2016
Topic & Suggested
Pacing
Standards
Mathematics Florida Standards
Student Target
Core
• find arc lengths and other
measures
Larson
• find the radian measure of an
Geometry
Circumference and Arc Length angle
• find the areas of circles and
Measure Angles in Radians
sectors
11.1 Extension
• fine the areas of regular
Areas of Circles and Sectors
polygons inscribed in circles
• identify solids
Areas of Regular Polygons
• find the volume of prisms
and cylinders
Explore Solids
• use density to solve problems
• find the volume of pyramids
Volume of Prisms and Cylinders and cones
• describe solids produced by
11.6 Extension
Density
rotating two-dimensional
firgures around an axis in space
Volume of Pyramids and Cones • find the surface area and
volume of spheres
Solids of Revolution
• use properties of similar
solids
Surface Area and Volume of
Blender
Spheres
Supplemental
Lessons
Similar Solids
March 28 – April 11
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.
Calculator: Neutral 11.3
MAFS.912.G-C.2.5
Calculator: Neutral
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder,
MAFS.912.G-GMD.1.1
pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
Calculator: Neutral
11.1, 11.7
MAFS.912.G-GMD.1.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Calculator: Neutral 11.6, 11.7, 11.8, 11.9
Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional
MAFS.912.G-GMD.2.4
objects generated by rotations of two-dimensional objects.
Calculator: Neutral
11.5, 11.7 Extension
Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per
MAFS.912.G-MG.1.2
cubic foot).
Calculator: Neutral
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
Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education
G-C Geometry - Circles
G-CO Geometry - Congruence
G-GMD Geometry - Geometry Measurement &
Dimension
G-MG Geometry - Modeling Geometry
G-SRT Geometry - G-SRT Geometry - Similarity,
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
OCA2 8-1