Youngstown City Schools - - GEOMETRY - CURRICULUM MAP (2014-2015)
Unit: #1
Name: Geometry Tools & Proofs Time: 20 days instruction 14 computer days 1 assessment day
CHAPTER/LESSON
Chapter 1 Tools of
Geometry
1.1 Points, Lines, Planes,
Rays, and Line Segments
1.2 Translating and
Constructing Line Segments
1.3 Midpoints and Bisectors
1.4 Translating and
Constructing Angles and
Angle Bisectors
1.5 Parallel and
Perpendicular Lines on the
Coordinate Plane
1.6 Constructing
Perpendicular Lines, Parallel
Lines, and Polygons
1.7 Points of Concurrency
Chapter 2 Tools of
Geometry
2.1 Foundations for Proof
2.2 Special Angles and
Postulates
2.3 Paragraph Proof, TwoColumn Proof, Construction
Proof, and Flow Chart Proof
2.4 Angle Postulates and
Theorems
2.5 Parallel Line Converse
MATH STANDARDS
MATH PRACTICES
. CCSS.MATH.CONTENT.HSG.CO.A.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.
1. Make sense of problems
and persevere in solving
them.
2. Reason abstractly and
quantitatively.
3. Construct viable
arguments and critique
the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools
strategically.
6. Attend to precision.
7. Look for and make use of
structure.
8. Look for and express
regularity in repeated
reasoning
CCSS.MATH.CONTENT.HSG.CO.A.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).
CCSS.MATH.CONTENT.HSG.CO.A.4
Develop definitions of rotations, reflections, and
translations in terms of angles, circles,
perpendicular lines, parallel lines, and line
segments.
CCSS.MATH.CONTENT.HSG.CO.A.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.
CCSS.MATH.CONTENT.HSG.CO.C.9
Prove theorems about lines and angles. Theorems
include: vertical angles are congruent; when a
6/3/2014
SPECIAL
EXPLANATIONS
Please note that the
time accounted for does
not include SLO pre test
assessment. The
assessment day if for
the unit only.
1.1 being in with
introduction to
vocabulary and
then practice
problems 1-5 take
your time with 1.1
and we estimated
that it would take 2
days so that the
students could be
introduced to the
concept of the book
and set up a
foundation.
1.2 We estimated this
would take 3 days
begin with
introduction to
vocabulary . The
warm up problem is
very good. You will
need to focus on
the distance
formula.
Youngstown City Schools – Math Map – Geometry 2014-2015 1
CHAPTER/LESSON
Theorems
MATH STANDARDS
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.
CCSS.MATH.CONTENT.HSG.CO.D.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.
CCSS.MATH.CONTENT.HSG.CO.D.13
Construct an equilateral triangle, a square, and a
regular hexagon inscribed in a circle.
CCSS.MATH.CONTENT.HSG.GPE.B.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).
CCSS.MATH.CONTENT.HSG.GPE.B.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).
6/3/2014
MATH PRACTICES
SPECIAL
EXPLANATIONS
1.3 We estimate 2 days
begin with
vocabulary focus
on the fact that the
midpoint is related
to the distance
formula in the fact
that the midpoint is
half the distance.
Be sure to do
Problem 3 on page
45 it is also a good
introduction to
proof.
1.4 We estimate 2 days
begin with
vocabulary focus
on constructions
using a
straightedge and
compass. Hint it is
hard to do
constructions in
book either make
copies of the page
or have the
students take the
pages out of the
text book.
1.5 We estimate 3 days
begin with
vocabulary. Be sure
to review slope,
and review linear
equations. You
may have to review
Youngstown City Schools – Math Map – Geometry 2014-2015 2
CHAPTER/LESSON
MATH STANDARDS
CCSS.MATH.CONTENT.HSG.GPE.B.6
Find the point on a directed line segment between
two given points that partitions the segment in a
given ratio.
CCSS.MATH.CONTENT.HSG.MG.A.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).*
CCSS.MATH.CONTENT.HSG.MG.A.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).*
MATH PRACTICES
SPECIAL
EXPLANATIONS
solving equations
and graphing lines
and.
1.6 We estimate 1 day
for this lesson, be
sure to review
vocabulary. Be sure
the students know
how to construct a
perpendicular
line/bisector.
1.7 We estimate 2 days
for this section
begin with the
vocabulary. This
lesson may be
more effective with
teacher created
notes and
exploration with
teacher using
Sketchpad or
Geogeba.
2.1 We estimate 1
day. Focus on
inductive and
deductive reasoning,
and hypotheses and
drawing diagrams.
2.2 We estimate 1
day. Focus on
supplementary and
complementary
angles and linear
pairs.
6/3/2014
Youngstown City Schools – Math Map – Geometry 2014-2015 3
CHAPTER/LESSON
MATH STANDARDS
MATH PRACTICES
SPECIAL
EXPLANATIONS
2.3 We estimate 1
day. Focus on
properties of equality
and using
construction proof.
2.4 We estimate 1
day. Focus on Writing
conjectures and
diagramming a proof.
2.5 We estimate 1
day. Focus on the
converse of
postulates.
6/3/2014
Youngstown City Schools – Math Map – Geometry 2014-2015 4
Youngstown City Schools - - CURRICULUM MAP – MATH - (2014-2015)
Unit: #2
Name: Geometric Shapes & Solids
Time: 15 days 10 computer days 1 assessment day
CHAPTER/LESSON
MATH STANDARDS
Chapter 3 Perimeter and Area
of Geometric Figures on the
Coordinate Plane
CCSS.MATH.CONTENT.HSG.CO.B.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.
3.1 Using Transformations to
Determine Area
3.2 Area and Perimeter of
Triangles on the Coordinate Plane
3.3 Area and Perimeter of
Parallelograms on the Coordinate
Plane
3.4 Area and Perimeter of
Trapezoids on the Coordinate
Plane
3.5 Area and Perimeter of
Composite Figures on the
Coordinate Plane
Chapter 4 Three-Dimensional
Figures
4.1 Rotating Two-Dimensional
Figures through Space
4.2 Translating and Stacking
Two-Dimensional Figures
4.4 Volume of Cones and
Pyamids
4.5 Volume of a Sphere
4.7 Cross Sections
4.8 Diagonals in Three
Dimensions
CCSS.MATH.CONTENT.HSG.GPE.B.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).
CCSS.MATH.CONTENT.HSG.GPE.B.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).
CCSS.MATH.CONTENT.HSG.GPE.B.7
Use coordinates to compute perimeters of polygons
and areas of triangles and rectangles, e.g., using the
distance formula.*
CCSS.MATH.CONTENT.HSG.GMD.A.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, Cavalieri's principle, and informal limit
arguments.
6/3/2014
MATH PRACTICES
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems
and persevere in solving
them.
Reason abstractly and
quantitatively.
Construct viable
arguments and critique the
reasoning of others.
Model with mathematics.
Use appropriate tools
strategically.
Attend to precision.
Look for and make use of
structure.
Look for and express
regularity in repeated
reasoning
SPECIAL
EXPLANATIONS
4.3 skip
4.6 skip
3.1 We estimate 1 day
Focus on the distance
formula and
transformations as it
relates to the coordinate
plane.
3.2 We estimate 2 days.
Focus on the determining
perimeter using distance
and slope.
3.3 We estimate 2 days.
Use what worked for your
students on 3.2 but focus
on parallelograms.
3.4 We estimate 1 day.
Use what worked for your
students on 3.3 but focus
of trapezoids.
3.5 We estimate 2 days.
Focus on breaking down
the composite figure and
making sure the students
understand.
4.1 We estimate 1 day
follow the spinner activity
in the book to save time
Youngstown City Schools – Math Map – Geometry 2014-2015 5
CHAPTER/LESSON
MATH STANDARDS
CCSS.MATH.CONTENT.HSG.GMD.A.3
Use volume formulas for cylinders, pyramids, cones,
and spheres to solve problems.*
CCSS.MATH.CONTENT.HSG.GMD.B.4
Identify the shapes of two-dimensional cross-sections
of three-dimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects.
CCSS.MATH.CONTENT.HSG.MG.A.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).*
CCSS.MATH.CONTENT.HSG.MG.A.2
Apply concepts of density based on area and volume
in modeling situations (e.g., persons per square mile,
BTUs per cubic foot).*
CCSS.MATH.CONTENT.HSG.MG.A.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).*
6/3/2014
MATH PRACTICES
SPECIAL
EXPLANATIONS
pre-make the spinners.
4.2 We estimate 2 days.
Exploring translating a
two dimensional figure to
make a 3 dimensional
figure and staking of
congruent figures.
4.4 We estimate 1 day if
your students are doing
well with the advanced
thinking have them
quickly do the activity for
cones with the pyramid
being homework. IF they
are not doing well pick
and choose the problems
they will understand best.
This is a parcc tested
topic
4.5 We estimate 1 day. If
they did well with the
cone please use the book
text. If you simplified
please simplify in a
similar manner for a
spere.
4.7 We estimate 1 day
Look at the warm up
activity. Relate the
information to cutting a
solid what would be left.
4.8 We estimate 1 day. A
good hands on activity
Youngstown City Schools – Math Map – Geometry 2014-2015 6
CHAPTER/LESSON
MATH STANDARDS
MATH PRACTICES
SPECIAL
EXPLANATIONS
would be to use dental
floss to cut foam
rectangles to see the
diagonal cross section.
6/3/2014
Youngstown City Schools – Math Map – Geometry 2014-2015 7
Youngstown City Schools - - CURRICULUM MAP – MATH (2014-2015)
UNIT: # 3
NAME: Properties of Triangles
CHAPTER/LESSON
Chapter 5 Properties of
Triangles
5.1 Classifying Triangles on
the Coordinate Plane
5.2 Triangle Sum, Exterior
Angle, and Exterior Angle
Inequality Theorems
5.3 The Triangle Inequality
Theorem
5.4 Properties of a 45°–45°–
90° Triangle
5.5 Properties of a 30°–60°–
90° Triangle
TIME: 5days instruction 4 days computer 1 day assessment
MATH STANDARDS
MATH PRACTICES
CCSS.MATH.CONTENT.HSG.MG.A.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).*
1. Make sense of problems and
persevere in solving them.
2. Reason abstractly and
quantitatively.
3. Construct viable arguments and
critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools
strategically.
6. Attend to precision.
7. Look for and make use of
structure.
8. Look for and express regularity in
repeated reasoning
CCSS.MATH.CONTENT.HSG.GPE.B.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).
CCSS.MATH.CONTENT.HSG.CO.C.10
Prove theorems about triangles. Theorems
include: measures of interior angles of a
triangle sum to 180°; 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.
6/3/2014
SPECIAL EXPLANATIONS
5.1 We estimate 1 day
5.2 We estimate 1 day
5.3 We estimate 1 day
5.4 We estimate 1 day
5.5 We estimate 1 day
Youngstown City Schools – Math Map – Geometry 2014-2015 8
Youngstown City Schools - - CURRICULUM MAP – MATH (2014-2015)
UNIT:4
NAME: Geometric Transformations
CHAPTER/LESSON
TIME: 20 days instruction 14 days computer 1 day assessment
MATH STANDARDS
Through CCSS.MATH.CONTENT.HSG.SRT.A.1
Verify experimentally the properties of dilations given by a
center and a scale factor:
6.1. Dilating Triangles to Create
Similar Triangles
CCSS.MATH.CONTENT.HSG.SRT.A.1.A
6.2 Similar Triangle Theorems
A dilation takes a line not passing through the center of the
6.3 Theorems About
dilation to a parallel line, and leaves a line passing through
Proportionality
the center unchanged.
6.4 More Similar Triangles
6.5 Proving the Pythagorean
CCSS.MATH.CONTENT.HSG.SRT.A.1.B
Theorem and the Converse of the The dilation of a line segment is longer or shorter in the
Pythagorean Theorem
ratio given by the scale factor.
6.6 Application of Similar
Triangles
CCSS.MATH.CONTENT.HSG.SRT.A.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
Chapter 7Congruence Through
similarity for triangles as the equality of all corresponding
Transformations
pairs of angles and the proportionality of all corresponding
7.1 Translating, Rotating, and
pairs of sides.
Reflecting Geometric Figures
7.2 Congruent Triangles
CCSS.MATH.CONTENT.HSG.SRT.A.3
7.3 Side-Side-Side Congruence
Use the properties of similarity transformations to establish
Theorem
the AA criterion for two triangles to be similar.
7.4 Side-Angle-Side Congruence
Theorem
CCSS.MATH.CONTENT.HSG.SRT.B.4
7.5 Angle-Side-Angle
Prove theorems about triangles. Theorems include: a line
Congruence Theorem
parallel to one side of a triangle divides the other two
7.6 Angle-Angle-Side
proportionally, and conversely; the Pythagorean Theorem
Congruence Theorem
proved using triangle similarity.
Chapter 6 Similarity
Transformations
6/3/2014
MATH PRACTICES
SPECIAL
EXPLANATIONS
1. Make sense of
problems and
persevere in solving
them.
2. Reason abstractly
and quantitatively.
3. Construct viable
arguments and
critique the reasoning
of others.
4. Model with
mathematics.
5. Use appropriate
tools strategically.
6. Attend to precision.
7. Look for and make
use of structure.
8. Look for and express
regularity in repeated
reasoning
6.1 We estimate 1 day
6.2 We estimate 2 days
6.3 We estimate 2 days
6.4 We estimate 1 day
6.5 We estimate 2 days
6.6 We estimate 1 day
7.1 We estimate 1 day
7.2 We estimate 1 day
7.3 We estimate 2 days
7.4 We estimate 1 day
7.5 We estimate 2 days
7.6 We estimate 2 days
7.7 We estimate 2 days
Youngstown City Schools – Math Map – Geometry 2014-2015 9
CHAPTER/LESSON
MATH STANDARDS
MATH PRACTICES
7.7 Using Congruent Triangles
CCSS.MATH.CONTENT.HSG.SRT.B.5
Use congruence and similarity criteria for triangles to solve
problems and to prove relationships in geometric figures.
SPECIAL
EXPLANATIONS
CCSS.MATH.CONTENT.HSG.CO.A.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).
CCSS.MATH.CONTENT.HSG.CO.A.3
Given a rectangle, parallelogram, trapezoid, or regular
polygon, describe the rotations and reflections that carry it
onto itself.
CCSS.MATH.CONTENT.HSG.CO.A.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.
CCSS.MATH.CONTENT.HSG.CO.B.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.
CCSS.MATH.CONTENT.HSG.CO.B.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.
6/3/2014
Youngstown City Schools – Math Map – Geometry 2014-2015 10
CHAPTER/LESSON
MATH STANDARDS
MATH PRACTICES
SPECIAL
EXPLANATIONS
CCSS.MATH.CONTENT.HSG.CO.B.8
Explain how the criteria for triangle congruence (ASA,
SAS, and SSS) follow from the definition of congruence in
terms of rigid motions.
CCSS.MATH.CONTENT.HSG.CO.C.9
Prove theorems about lines and angles. 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.
CCSS.MATH.CONTENT.HSG.CO.C.10
Prove theorems about triangles. Theorems include:
measures of interior angles of a triangle sum to 180°; 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.
CCSS.MATH.CONTENT.HSG.CO.D.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.
CCSS.MATH.CONTENT.HSG.MG.A.1
Use geometric shapes, their measures, and their properties
to describe objects (e.g., modeling a tree trunk or a human
6/3/2014
Youngstown City Schools – Math Map – Geometry 2014-2015 11
CHAPTER/LESSON
MATH STANDARDS
MATH PRACTICES
SPECIAL
EXPLANATIONS
torso as a cylinder).*
6/3/2014
Youngstown City Schools – Math Map – Geometry 2014-2015 12
Youngstown City Schools - - CURRICULUM MAP – MATH
UNIT: #5
NAME: Triangle Theorems & Trigonometry
CHAPTER/LESSON
Chapter 8 Using Congruence
Theorems
8.1 Right Triangle
Congruence Theorems
8.2 Corresponding Parts of
Congruent Triangles are
Congruent
8.3 Isosceles Triangle
Theorems
8.4 Inverse, Contrapositive,
Direct Proof, and Indirect
Proof
Chapter 9 Trigonometry
9.1 Introduction to
Trigonometry
9.2 Tangent Ratio, Cotangent
Ratio, and Inverse Tangent
9.3 Sine Ratio, Cosecant
Ratio, and Inverse Sine
9.4 Cosine Ratio, Secant
Ratio, and Inverse Cosine
9.5 Complement Angle
Relationships
9.6 Deriving the Triangle
Area Formula, the Law of
Sines, and the Law of Cosines
MATH STANDARDS
CCSS.MATH.CONTENT.HSG.CO.B.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.
CCSS.MATH.CONTENT.HSG.CO.B.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.
CCSS.MATH.CONTENT.HSG.CO.B.8
Explain how the criteria for triangle congruence
(ASA, SAS, and SSS) follow from the definition
of congruence in terms of rigid motions.
TIME: 12 days 8 days computer 1 day assessment
MATH PRACTICES
1. Make sense of problems and
persevere in solving them.
2. Reason abstractly and
quantitatively.
3. Construct viable arguments and
critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools
strategically.
6. Attend to precision.
7. Look for and make use of
structure.
8. Look for and express regularity
in repeated reasoning
SPECIAL
EXPLANATIONS
8.1 We estimate 1 day
8.2 We estimate 1 day
8.3 We estimate 1 day
8.4 We estimate 1 day
9.1 We estimate 2 days
9.2 We estimate 1 day
9.3 We estimate 1 day
9.4 We estimate 1 day
9.5 We estimate 1 day
9.6 We estimate 2 days
CCSS.MATH.CONTENT.HSG.CO.C.10
Prove theorems about triangles. Theorems
include: measures of interior angles of a triangle
sum to 180°; 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.
CCSS.MATH.CONTENT.HSG.CO.D.12
Make formal geometric constructions with a
variety of tools and methods (compass and
6/3/2014
Youngstown City Schools – Math Map – Geometry 2014-2015 13
CHAPTER/LESSON
MATH STANDARDS
MATH PRACTICES
SPECIAL
EXPLANATIONS
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.
CCSS.MATH.CONTENT.HSG.SRT.A.3
Use the properties of similarity transformations to
establish the AA criterion for two triangles to be
similar.
CCSS.MATH.CONTENT.HSG.SRT.B.5
Use congruence and similarity criteria for
triangles to solve problems and to prove
relationships in geometric figures.
CCSS.MATH.CONTENT.HSG.SRT.C.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.
CCSS.MATH.CONTENT.HSG.SRT.C.7
Explain and use the relationship between the sine
and cosine of complementary angles.
CCSS.MATH.CONTENT.HSG.SRT.C.8
Use trigonometric ratios and the Pythagorean
Theorem to solve right triangles in applied
problems.*
CCSS.MATH.CONTENT.HSG.SRT.D.9
(+) Derive the formula A = 1/2 ab sin(C) for the
6/3/2014
Youngstown City Schools – Math Map – Geometry 2014-2015 14
CHAPTER/LESSON
MATH STANDARDS
MATH PRACTICES
SPECIAL
EXPLANATIONS
area of a triangle by drawing an auxiliary line
from a vertex perpendicular to the opposite side.
CCSS.MATH.CONTENT.HSG.SRT.D.10
(+) Prove the Laws of Sines and Cosines and use
them to solve problems.
CCSS.MATH.CONTENT.HSG.SRT.D.11
(+) 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).
CCSS.MATH.CONTENT.HSG.MG.A.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).*
6/3/2014
Youngstown City Schools – Math Map – Geometry 2014-2015 15
Youngstown City Schools - - CURRICULUM MAP – MATH - (2014-2015)
Unit: #6 Name: Quadrilaterals
CHAPTER/LESSON
Chapter 10Properties of
Quadrilaterals
10.1 Properties of Squares and
Rectangles
10.2Properties of
Parallelograms and Rhombi
10.3 Properties of Kites and
Trapezoids
10.4 Sum of the Interior Angle
Measures of a Polygon
10.5 Sum of the Exterior
Angle Measures of a Polygon
10.6 Categorizing
Quadrilaterals Based on Their
Properties
10.7Classifying Quadrilaterals
on the Coordinate Plane
Time:14 days 10 days computer 1 day assessment
MATH STANDARDS
CCSS.MATH.CONTENT.HSG.CO.C.9
Prove theorems about lines and
angles. 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.
MATH PRACTICES
SPECIAL EXPLANATIONS
10.1 We estimate 2 days
10.2 We estimate 2 days
10.3 We estimate 2 days
10.4 We estimate 2 days
10.5 We estimate 2 days
10.6 We estimate 2 days
10.7 We estimate 2 days
CCSS.MATH.CONTENT.HSG.CO.C.11
Prove theorems about
parallelograms. 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.
CCSS.MATH.CONTENT.HSG.CO.D.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.
CCSS.MATH.CONTENT.HSG.SRT.C.8
Use trigonometric ratios and the Pythagorean
Theorem to solve right triangles in applied
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Youngstown City Schools – Math Map – Geometry 2014-2015 16
CHAPTER/LESSON
MATH STANDARDS
MATH PRACTICES
SPECIAL EXPLANATIONS
problems.*
CCSS.MATH.CONTENT.HSG.GPE.B.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).
CCSS.MATH.CONTENT.HSG.GPE.B.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).
CCSS.MATH.CONTENT.HSG.MG.A.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).*
CCSS.MATH.CONTENT.HSG.MG.A.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).*
6/3/2014
Youngstown City Schools – Math Map – Geometry 2014-2015 17
Youngstown City Schools - - CURRICULUM MAP – MATH - Geometry
Unit: 7
Name: Circles
Time: 23 days instruction 16 days computer 1 day assessment
CHAPTER/LESSON
MATH STANDARDS
MATH PRACTICES
SPECIAL EXPLANATIONS
Chapter 11 Circles
11.1 Introduction to Circles
11.2Central Angles,
Inscribed Angles, and
Intercepted Arcs
11.3 Measuring Angles
Inside and Outside of
Circles
11.4 Chords
11.5 Tangents and
Secants
CCSS.MATH.CONTENT.HSG.CO.A.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.
1. Make sense of problems and
persevere in solving them.
2. Reason abstractly and
quantitatively.
3. Construct viable arguments and
critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools
strategically.
6. Attend to precision.
7. Look for and make use of
structure.
8. Look for and express regularity in
repeated reasoning
PLEASE NOT THAT THIS
UNIT IS A PARCC PLUS
STANDARD. Ie NOT TESTED
ON PARCC GEOMETRY
WOULD MAKE A GOOD UNIT
IF YOU HAVE ADVANCED
STUDNDETS.
Chapter 12 Arcs and
Sectors of Circles
12.1 Inscribed and
Circumscribed Triangles
and Quadrilaterals
12.2 Arc Length
12.3 Sectors and Segments
of a Circle
12.4 Circle Problems
Chapter 13 Circles and
Parabolas
13.1 Circles and Polygons
on the Coordinate Plane
CCSS.MATH.CONTENT.HSG.C.A.1
Prove that all circles are similar.
CCSS.MATH.CONTENT.HSG.C.A.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.
CCSS.MATH.CONTENT.HSG.C.A.3
Construct the inscribed and circumscribed
circles of a triangle, and prove properties of
angles for a quadrilateral inscribed in a
circle.
CCSS.MATH.CONTENT.HSG.C.A.4
(+) Construct a tangent line from a point
outside a given circle to the circle.
CCSS.MATH.CONTENT.HSG.C.B.5
Derive using similarity the fact that the
length of the arc intercepted by an angle is
6/3/2014
13.4 Skip
13.5 Skip
11.1 We estimate 1 day
11.2 We estimate 2 days
11.3 We estimate 2 days
11.4 We estimate 2 days
11.5 We estimate 2 days
12.1 WE estimate 2 days
12.2 We estimate 2 days
12.3 We estimate 2 days
12.4 We estimate 2 days
131 We estimate 2 days
13.2 We estimate 2 days
13.3 We estimate 2 days.
Youngstown City Schools – Math Map – Geometry 2014-2015 18
CHAPTER/LESSON
13.2 Deriving the Equation
for a Circle
13.3 Determining Points on
a Circle
MATH STANDARDS
MATH PRACTICES
SPECIAL EXPLANATIONS
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.
CCSS.MATH.CONTENT.HSG.GPE.A.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.
CCSS.MATH.CONTENT.HSG.GPE.B.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).
CCSS.MATH.CONTENT.HSG.GPE.B.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).
CCSS.MATH.CONTENT.HSG.SRT.C.8
Use trigonometric ratios and the
Pythagorean Theorem to solve right
triangles in applied problems.*
CCSS.MATH.CONTENT.HSG.MG.A.1
Use geometric shapes, their measures, and
their properties to describe objects (e.g.,
modeling a tree trunk or a human torso as a
6/3/2014
Youngstown City Schools – Math Map – Geometry 2014-2015 19
CHAPTER/LESSON
MATH STANDARDS
MATH PRACTICES
SPECIAL EXPLANATIONS
cylinder).*
CCSS.MATH.CONTENT.HSG.MG.A.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).*
6/3/2014
Youngstown City Schools – Math Map – Geometry 2014-2015 20