COMPLETE GEOMETRY PACING CHART HIGHSCHOOLMATHTEACHERS.COM@2018
COMPLETE GEOMETRY PACING CHART
HIGHSCHOOLMATHTEACHERS.COM@2018
Contents
Unit 1 Geometric Transformation ........................................................................................................................................................... 2
Unit 2 Angles and Line ........................................................................................................................................................................... 7
Unit 3 Triangles .................................................................................................................................................................................... 11
Unit 4 Triangle Congruence.................................................................................................................................................................. 15
Unit 5 Similarity Transformation.......................................................................................................................................................... 19
Unit 6 Right Triangle Relationships and Trigonometry ....................................................................................................................... 23
Unit 7 Quadrilaterals ............................................................................................................................................................................. 27
Unit 8 Circles ........................................................................................................................................................................................ 31
Unit 9 Geometric Modeling in Two Dimensions ................................................................................................................................. 36
Unit 10 Understanding and Modeling Three Dimensional Figures ...................................................................................................... 41
Unit 1 Pacing Chart
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Unit 1 Unit Week Day CCSS Standards Objective I Can Statements
Unit 1 Geometric
Transformations
Week 1 – Definitions
1
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.
Know precise definitions of angle, based on the undefined notions of
point, line, distance along a line, and distance around a circular arc. Give types the basic types of angles
that are not described using any form algebra.
I can define an angle I can identify situations or cases where angles
appear in day to day life
Unit 1 Geometric
Transformations
Week 1 – Definitions
2
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.
Know precise definitions of circle and line segment based on the
undefined notions of point, line, distance along a line, and distance
around a circular arc. Parts of circles; types of circles when in
groups.
I can define and identify line segment
I can define and identify a circle
I can identify lines and segments found in a
circle I can identify situations or cases where circles are applied in real life
situation
Unit 1 Geometric
Transformations
Week 1 – Definitions
3
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.
Know precise definitions of perpendicular line based on the undefined notions of point, line,
distance along a line, and distance around a circular arc.
I can define and identify perpendicular line
I can be able to identify a case where
perpendicular lines have been used in a classroom
Unit 1 Pacing Chart
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Unit 1 Geometric
Transformations
Week 1 – Definitions
4
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.
Know precise definitions of parallel lines based on the undefined
notions of point, line, distance along a line, and distance around a
circular arc.
I can define and identify parallel lines
I can be able to identify a case where parallel lines
have been used in a classroom
Unit 1 Geometric
Transformations
Week 1 – Definitions
5 Assessment Assessment Assessment
Unit 1 Geometric
Transformations
Week 2 – Rotations,
Reflections, and
Translations
6
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).
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.
Give short and precise definitions of transformations (translation, reflection, rotation, dilation).
Compare transformations that preserve distance and angle to
those that do not (e.g., translation versus horizontal stretch).
I can define what a transformation and state
a few common transformations.
I can briefly say what these transformations
are I can describe
transformation as functions having inputs
and outputs I can compare
transformations that preserve distance and
angle with those that do not
Unit 1 Pacing Chart
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Unit 1 Geometric
Transformations
Week 2 – Rotations,
Reflections, and
Translations
7
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.
Given a rectangle, parallelogram, trapezoid, or regular polygon,
describe the rotations and reflections that carry it onto itself.
I can describe the rotations and reflections
that carry a rectangle, parallelogram, trapezoid, or regular polygon into
itself
Unit 1 Geometric
Transformations
Week 2 – Rotations,
Reflections, and
Translations
8
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.
Develop definitions of rotations, reflections, and translations in
terms of angles, circles, perpendicular lines, parallel lines,
and line segments.
I can develop definitions of rotations, reflections, and translations in terms
of angles, circles, perpendicular lines,
parallel lines, and line segments.
Unit 1 Geometric
Transformations
Week 2 – Rotations,
Reflections, and
Translations
9
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.
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.
I can draw the transformed figure (using graph paper,
tracing paper, or geometry software)
under rotation, reflection, or translation
given the object (original) figure
I can specify a sequence of transformations that will carry a given figure
onto another.
Unit 1 Pacing Chart
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Unit 1 Geometric
Transformations
Week 2 – Rotations,
Reflections, and
Translations
10 Assessment Assessment Assessment
Unit 1 Geometric
Transformations
Week 3 – Congruence
11
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.
Use geometric descriptions of rigid motions to transform figures (2d-
figures)
I can use geometric descriptions of rigid
motions to transform figures (2d- figures)
Unit 1 Geometric
Transformations
Week 3 – Congruence
12
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.
Given two figures,the image and the object, identify the
transformation(s) involved.
I can identify the transformation(s)
involved from one figure to another (image to an
object)
Unit 1 Geometric
Transformations
Week 3 – Congruence
13
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.
Use geometric descriptions of rigid motion to predict the effect of a
given rigid motion on a given figure
I can use geometric descriptions of rigid
motion to predict the effect of a given rigid
motion on a given figure
Unit 1 Pacing Chart
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Unit 1 Geometric
Transformations
Week 3 – Congruence
14
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.
Given two figures, use the definition of congruence in terms of rigid motions to decide if they are
congruent.
Given two figures, I can use the definition of
congruence in terms of rigid motions to decide if
they are congruent.
Unit 1 Geometric
Transformations
Week 3 – Congruence
15 Assessment Assessment Assessment
Unit 2 Pacing Chart
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Unit 2
Unit Week Day CCSS Standards Objective I Can Statements
Unit 2 Angles
and Lines
Week 4 – Algebraic
Definitions 16
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.
Know precise algebraic definitions of angle; complementary, supplementary
angles and angles on a straight line
I can give the precise algebraic definitions
complementary, supplementary angles and
angles on a straight line
Unit 2 Angles
and Lines
Week 4 – Algebraic
Definitions 17
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.
Know precise algebraic definitions of angle; angles at a point
I can give precise algebraic definitions of angle at a
point
Unit 2 Angles
and Lines
Week 4 – Algebraic
Definitions 18
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.
Know precise algebraic definitions of angle; Corresponding and alternate
angles
I can give algebraic definitions of
corresponding and alternate angles
Unit 2 Angles
and Lines
Week 4 – Algebraic
Definitions 19
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.
Know precise algebraic definitions of angle; vertical and interior angles
I can give the precise algebraic definitions of
vertical and interior angles
Unit 2 Pacing Chart
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Unit 2 Angles
and Lines
Week 4 – Algebraic
Definitions 20 Assessment Assessment Assessment
Unit 2 Angles
and Lines
Week 5 – Prove Geometric Theorems
21
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.
Prove that vertical angles are congruent
I can prove that vertical angles are congruent
Unit 2 Angles
and Lines
Week 5 – Prove Geometric Theorems
22
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.
Prove that alternate interior angles are congruent
I can prove that alternate interior angles are
congruent
Unit 2 Angles
and Lines
Week 5 – Prove Geometric Theorems
23
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.
Prove that corresponding angles are congruent
I can prove that corresponding angles are
congruent
Unit 2 Pacing Chart
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Unit 2 Angles
and Lines
Week 5 – Prove Geometric Theorems
24
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.
Prove that points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's
endpoints.
I can prove that points on a perpendicular bisector of a
line segment are exactly those equidistant from the
segment's endpoints.
Unit 2 Angles
and Lines
Week 5 – Prove Geometric Theorems
25 Assessment Assessment Assessment
Unit 2 Angles
and Lines
Week 6 – Prove Algebraically
26
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.
Given an angle, use the algebraic properties to show that alternate, vertical and corresponding angles
among others are equal
Given an angle, I can use the algebraic properties to
show that alternate, vertical and corresponding angles among others are
equal
Unit 2 Angles
and Lines
Week 6 – Prove Algebraically
27
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).
Prove the slope criteria for parallel and perpendicular lines
I can prove the slope criteria for parallel and
perpendicular lines
Unit 2 Pacing Chart
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Unit 2 Angles
and Lines
Week 6 – Prove Algebraically
28
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).
Use slope criteria 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).
I can use slope criteria to solve geometric problems (e.g., finding the equation
of a line parallel or perpendicular to a given
line that passes through a given point).
Unit 2 Angles
and Lines
Week 6 – Prove Algebraically
29
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.
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
I can find the point on a directed line segment
between two given points that partitions the segment
in a given ratio.
Unit 2 Angles
and Lines
Week 6 – Prove Algebraically
30 Assessment Assessment Assessment
Unit 3 Pacing Chart
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Unit 3
Unit Week Day CCSS Standards Objective I Can Statements
Unit 3 Triangles
Week 7 – Prove Theorems
about Triangles 31
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.
Prove that measures of interior angles of a triangle
sum to 180°
I can prove that measures of interior angles of a triangle sum
to 180°
Unit 3 Triangles
Week 7 – Prove Theorems
about Triangles 32
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.
Prove that base angles of isosceles triangles are
congruent
I can prove that base angles of isosceles triangles are congruent
Unit 3 Triangles
Week 7 – Prove Theorems
about Triangles 33
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.
Prove that the medians of a triangle meet at a point.
I can prove that the medians of a triangle meet at a point.
Unit 3 Triangles
Week 7 – Prove Theorems
about Triangles 34
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.
Summarize the week's topics
I can prove that measures of interior angles of a triangle sum
to 180° I can prove that base angles of
isosceles triangles are congruent I can prove that the medians of a
triangle meet at a point.
Unit 3 Pacing Chart
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Unit 3 Triangles
Week 7 – Prove Theorems
about Triangles 35 Assessment Assessment Assessment
Unit 3 Triangles
Week 8 – Geometric
Constructions 36
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.
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;
I can copy a segment; an angle; bisecting a segment and bisecting
an angle using variety of tools and methods (compass and
straightedge, string, reflective devices, paper folding, dynamic
geometric software, etc.)
Unit 3 Triangles
Week 8 – Geometric
Constructions 37
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.
Make formal geometric constructions with a variety
of tools and methods (compass and straightedge,
string, reflective devices, paper folding, dynamic
geometric software, etc.).constructing
perpendicular lines, including the perpendicular bisector of a line segment
I can construct perpendicular
lines, including the perpendicular bisector of a line segment using
variety of tools and methods (compass and straightedge,
string, reflective devices, paper folding, dynamic geometric
software, etc.)
Unit 3 Pacing Chart
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Unit 3 Triangles
Week 8 – Geometric
Constructions 38
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.
Make formal geometric
constructions with a variety of tools and methods
(compass and straightedge, string, reflective devices, paper folding, dynamic
geometric software, etc.). Constructing a line parallel
to a given line through a point, not on the line.
I can construct a line parallel to a given line through a point, not on
the line using a variety of tools and methods (compass and
straightedge, string, reflective devices, paper folding, dynamic
geometric software, etc.)
Unit 3 Triangles
Week 8 – Geometric
Constructions 39
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.
Summarize- 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.
I can copy a line segment; an angle; bisecting a segment and
an angle I can construct perpendicular
lines, including the perpendicular bisector of a line segment
I can construct a line parallel to a given line through a point, not on
the line.
Unit 3 Triangles
Week 8 – Geometric
Constructions 40 Assessment Assessment Assessment
Unit 3 Pacing Chart
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Unit 3 Triangles
Week 9 – Inscribed and Circumscribed
Circles of a Triangle
41 CCSS.MATH.CONTENT.HSG.CO.D.13
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Construct an equilateral triangle inscribed in a
circle.
I can construct an equilateral triangle inscribed in a circle.
Unit 3 Triangles
Week 9 – Inscribed and Circumscribed
Circles of a Triangle
42 CCSS.MATH.CONTENT.HSG.CO.D.13
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Construct a square inscribed in a circle.
I can construct a square inscribed in a circle.
Unit 3 Triangles
Week 9 – Inscribed and Circumscribed
Circles of a Triangle
43 CCSS.MATH.CONTENT.HSG.CO.D.13
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Construct a regular hexagon inscribed in a
circle.
I can construct a regular hexagon inscribed in a circle.
Unit 3 Triangles
Week 9 – Inscribed and Circumscribed
Circles of a Triangle
44 CCSS.MATH.CONTENT.HSG.CO.D.13
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Sammarize - Construction of a equilateral triangle, a
square, and a regular hexagon inscribed in a
circle
I can construct an equilateral triangle inscribed in a circle.
I can construct an square inscribed in a circle.
I can construct a regular hexagon inscribed in a circle.
Unit 3 Triangles
Week 9 – Inscribed and Circumscribed
Circles of a Triangle
45 Assessment Assessment Assessment
Unit 4 Pacing Chart
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Unit 4
Unit Week Day CCSS Standards Objective I Can Statements
Unit 4 Triangle
Congruence
Week 10 – Transformat
ions to Theorems
46
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.
Come up with a result(conclusion) as a result:
Any rigid motion preserves angle measure.
Any rigid motion of the plane is a reflection, rotation, translation or a
glide reflection. Any rigid motion maps straight
segments to straight segments, lines to lines, and circles to circles.
A rigid motion maps any three non-collinear points into non-collinear
points.
I can explain how and why: Any rigid motion preserves angle
measure. Any rigid motion of the plane is a reflection, rotation, translation or
a glide reflection. Any rigid motion maps straight segments to straight segments,
lines to lines, and circles to circles.
A rigid motion maps any three non-collinear points into non-
collinear points.
Unit 4 Triangle
Congruence
Week 10 – Transformat
ions to Theorems
47
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.
Come up with a result(conclusion) as a result:
Any rigid plane motion is invertible. Any rigid motion with a fixed point is
either a reflection or a rotation
I can explain how and why: Any rigid plane motion is
invertible. Any rigid motion with a fixed
point is either a reflection or a rotation
Unit 4 Triangle
Congruence
Week 10 – Transformat
ions to Theorems
48
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.
Come up with a conclusion as a result:
The composition of two rigid motions is also a rigid motion
The composition of a half-turn and a reflection is a glide reflection.
I can explain how and why: The composition of two rigid motions is also a rigid motion The composition of a half-turn
and a reflection is a glide reflection.
Unit 4 Pacing Chart
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Unit 4 Triangle
Congruence
Week 10 – Transformat
ions to Theorems
49
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.
Come up with a conclusion as a result:
Successive reflection in two intersecting mirror lines produces a
rotation about the point of intersection through twice the angle
between the mirror lines. Successive reflection in parallel
mirror lines produces a translation in a direction perpendicular to the
mirrors through a distance equal to twice the distance between the
mirrors Any rigid motion of the Euclidean
plane can be written as a composition of no more than 3
reflections.
I can explain how and why; Successive reflection in two
intersecting mirror lines produces a rotation about the point of
intersection through twice the angle between the mirror lines. Successive reflection in parallel
mirror lines produces a translation in a direction
perpendicular to the mirrors through a distance equal to twice the distance between the mirrors
and
Any rigid motion of the Euclidean
plane can be written as a composition of no more than 3
reflections.
Unit 4 Triangle
Congruence
Week 10 – Transformat
ions to Theorems
50 Assessment Assessment Assessment
Unit 4 Triangle
Congruence
Week 11 – Proofs of
Congruent Triangles
51
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.
Identifying Congruent sides of a triangle
I can Identify congruent sides of a triangle
Unit 4 Pacing Chart
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Unit 4 Triangle
Congruence
Week 11 – Proofs of
Congruent Triangles
52
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.
Identifying Congruent angles of a triangle
I can Identify congruent angles of a triangle
Unit 4 Triangle
Congruence
Week 11 – Proofs of
Congruent Triangles
53
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.
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.
I can 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.
Unit 4 Triangle
Congruence
Week 11 – Proofs of
Congruent Triangles
54
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.
Show Congrence of image and object distance in dilation if the scale factor
is -1.
I can show congruence of image and object distance in dilation if
the scale factor is -1.
Unit 4 Triangle
Congruence
Week 11 – Proofs of
Congruent Triangles
55 Assessment Assessment Assessment
Unit 4 Triangle
Congruence
Week 12 – Congruent
Parts of Congruent Figures are Congruent
56
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.
Use the postulate SSS to show that triangles are congruent. Also, apply it so solve other geometric problems.
I can use the postulate SSS to show that triangles are
congruent. I can apply the postulate so solve
other geometric problems.
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Unit 4 Triangle
Congruence
Week 12 – Congruent
Parts of Congruent Figures are Congruent
57
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.
Use the postulate ASA to show that triangles are congruent. Also, apply it so solve other geometric problems.
Use the postulate ASA to show that triangles are congruent. Also, apply it so solve other
geometric problems.
Unit 4 Triangle
Congruence
Week 12 – Congruent
Parts of Congruent Figures are Congruent
58
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.
Use the postulate SAS to show that triangles are congruent. Also, apply it so solve other geometric problems.
I can use the postulate SAS to show that triangles are
congruent. I can apply the postulate to solve
other geometric problems.
Unit 4 Triangle
Congruence
Week 12 – Congruent
Parts of Congruent Figures are Congruent
59
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.
Use the postulates SSS, SAS, and ASA to show that triangles are congruent.
Also, apply them to solve other geometric problems.
I can use the postulates SSS, SAS, and ASA to show that triangles are congruent and also apply
them to solve other geometric problems.
Unit 4 Triangle
Congruence
Week 12 – Congruent
Parts of Congruent Figures are Congruent
60 Assessment Assessment Assessment
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Unit 5 Unit Week Day CCSS Standards Objective I Can Statements
Unit 5 Similarity
Transformations
Week 14 – Midpoint Theorem
66
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.
Show that when a line is bisected, the portions are
equal. Find the size of a line given a portion of the
bisecting line. Find the size of each portion of the line
is bisected etc
I can show that when a line is bisected, the portions are equal.
I can find the size of a line given a portion of the bisecting line.
I can find the size of each portion of the line is bisected
Unit 5 Similarity
Transformations
Week 14 – Midpoint Theorem
67
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.
Proving midpoint theorem I can prove midpoint theorem
Unit 5 Similarity
Transformations
Week 14 – Midpoint Theorem
68
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.
Explain how midpoint theorem leads to dilation
I can explain how midpoint theorem gives rise of a dilation
Unit 5 Similarity
Transformations
Week 14 – Midpoint Theorem
69
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.
Apply midpoint theorem to find the length of other
lines. Use dilation
I can apply midpoint theorem to find the length of other lines. Use
dilation
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Unit 5 Similarity
Transformations
Week 14 – Midpoint Theorem
70 Assessment Assessment Assessment
Unit 5 Similarity
Transformations
Week 15 – Dilations
and Similarity
71
CCSS.MATH.CONTENT.HSG.SRT.A.1 Verify experimentally the properties of dilations
given by a center and a scale factor: CCSS.MATH.CONTENT.HSG.SRT.A.1.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. CCSS.MATH.CONTENT.HSG.SRT.A.1.B
The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Verify experimentally the properties of dilations given by a center and a
scale factor:
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.
The dilation of a line segment is longer or
shorter in the ratio given by the scale factor.
I can verify experimentally the properties of dilations given by a
center and a scale factor:
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.
The dilation of a line segment is
longer or shorter in the ratio given by the scale factor.
Unit 5 Similarity
Transformations
Week 15 – Dilations
and Similarity
72
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 similarity for triangles as the equality of all corresponding pairs of angles and the
proportionality of all corresponding pairs of sides.
Given two figures, use the definition of similarity in
terms of similarity transformations to decide
if they are similar
Given two figures, I can use the definition of similarity in terms of
similarity transformations to decide if they are similar
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Unit 5 Similarity
Transformations
Week 15 – Dilations
and Similarity
73
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 similarity for triangles as the equality of all corresponding pairs of angles and the
proportionality of all corresponding pairs of sides.
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.
I can 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.
Unit 5 Similarity
Transformations
Week 15 – Dilations
and Similarity
74
CCSS.MATH.CONTENT.HSG.SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be
similar.
Use the properties of similarity transformations
to establish the AA criterion for two triangles
to be similar.
I can use the properties of similarity transformations to
establish the AA criterion for two triangles to be similar.
Unit 5 Similarity
Transformations
Week 15 – Dilations
and Similarity
75 Assessment Assessment Assessment
Unit 5 Similarity
Transformations
Week 16 – Prove
Theorems using
Similarity
76
CCSS.MATH.CONTENT.HSG.SRT.B.4 Prove theorems about triangles. Theorems include:
a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle
similarity.
Prove that a line parallel to one side of a triangle divides the other two
proportionally
I can prove that a line parallel to one side of a triangle divides the
other two proportionally
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Unit 5 Similarity
Transformations
Week 16 – Prove
Theorems using
Similarity
77
CCSS.MATH.CONTENT.HSG.SRT.B.4 Prove theorems about triangles. Theorems include:
a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle
similarity.
Pythagorean Theorem proved using triangle
similarity.
I can prove Pythagorean Theorem using triangle similarity.
Unit 5 Similarity
Transformations
Week 16 – Prove
Theorems using
Similarity
78
CCSS.MATH.CONTENT.HSG.SRT.B.5 Use congruence and similarity criteria for triangles
to solve problems and to prove relationships in geometric figures.
Use congruence and similarity criteria for
triangles to solve problems
I can use congruence and similarity criteria for triangles to
solve problems
Unit 5 Similarity
Transformations
Week 16 – Prove
Theorems using
Similarity
79
CCSS.MATH.CONTENT.HSG.SRT.B.5 Use congruence and similarity criteria for triangles
to solve problems and to prove relationships in geometric figures.
Use congruence and similarity criteria for
triangles prove relationships in geometric
figures.
I can use congruence and similarity criteria for triangles
prove relationships in geometric figures.
Unit 5 Similarity
Transformations
Week 16 – Prove
Theorems using
Similarity
80 Assessment Assessment Assessment
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Unit 6
Unit Week Day CCSS Standards Objective I Can Statements
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 18 – Indirect
Measurements 86
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.
Identify opposite, adjacent and hypotenuse of right
triangles. Define trigonometric ratios.
I can Identify opposite, adjacent and hypotenuse of
right triangles I can define trigonometric
ratios.
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 18 – Indirect
Measurements 87
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.
Find trigonometric ratios of angles
I can find trigonometric ratios of angles
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 18 – Indirect
Measurements 88
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.
Define trigonometric ratios of compliments.
I can define trigonometric ratios of compliments.
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 18 – Indirect
Measurements 89
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.
Use similarity to find the trigonometric ratios of triangles with common
angles.
I can use similarity to find the trigonometric ratios of
triangles with common angles.
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Unit 6 Right
Triangle Relationships
and Trigonometry
Week 18 – Indirect
Measurements 90 Assessment Assessment Assessment
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 19 – Trigonometric
Ratios 91
CCSS.MATH.CONTENT.HSG.SRT.C.7 Explain and use the relationship between the sine
and cosine of complementary angles.
Explain the relationship between sine and cosine of
complementary angles
I can explain the relationship between sine
and cosine of complementary angles
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 19 – Trigonometric
Ratios 92
CCSS.MATH.CONTENT.HSG.SRT.C.7 Explain and use the relationship between the sine
and cosine of complementary angles.
Use the relationship between the sine and cosine of complementary angles to solve geometric problems
I can use the relationship between the sine and cosine of complementary angles to solve geometric problems
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 19 – Trigonometric
Ratios 93
CCSS.MATH.CONTENT.HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean
Theorem to solve right triangles in applied problems.*
Use trigonometric ratios to solve a triangle
I can use trigonometric ratios to solve a triangle
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 19 – Trigonometric
Ratios 94
CCSS.MATH.CONTENT.HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean
Theorem to solve right triangles in applied problems.*
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in
word problems
I can use trigonometric ratios and the Pythagorean
Theorem to solve right triangles in word problems
Unit 6 Pacing Chart
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Unit 6 Right
Triangle Relationships
and Trigonometry
Week 19 – Trigonometric
Ratios 95 Assessment Assessment Assessment
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 20 – Special Right
Triangles 96
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.
Find the trigonometric ratios of 30-60-90 right triangle
I can find the trigonometric ratios of 30-60-90 right
triangle
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 20 – Special Right
Triangles 97
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.
Solve 30-60-90 right triangle I can solve 30-60-90 right
triangle
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 20 – Special Right
Triangles 98
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.
Find the trigonometric ratios of 45-45-90 right triangle
I can find the trigonometric ratios of 45-45-90 right
triangle
Unit 6 Right
Triangle Relationships
and Trigonometry
Week 20 – Special Right
Triangles 99
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.
Solve 45-45-90 right triangle I can solve 45-45-90 right
triangle
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Unit 6 Right
Triangle Relationships
and Trigonometry
Week 20 – Special Right
Triangles 100 Assessment Assessment Assessment
Unit 7 Pacing Chart
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Unit 7
Unit Week Day CCSS Standards Objective I Can Statements
Unit 7 Quadrilaterals
Week 22 – Defining
Quadrilaterals with
Coordinates
106
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).
Define and identify quadrilaterals
I can define and identify quadrilaterals
Unit 7 Quadrilaterals
Week 22 – Defining
Quadrilaterals with
Coordinates
107
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).
Determine the properties that can be
used to identify a square and a rectangle on an xy
plane. Determine the coordinate of the
missing vertex that makes up a rectangle or
a square.
I can determine the properties that can be used to identify a square and a rectangle on an
xy plane. I can determine the
coordinate of the missing vertex that makes up a rectangle or a square.
Unit 7 Quadrilaterals
Week 22 – Defining
Quadrilaterals with
Coordinates
108
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).
Determine the properties that can be
used to identify a rhombus and a
parallelogram on an xy plane. Determine the
coordinate of the missing vertex that
makes up a rectangle or a square.
I can determine the properties that can be used to identify a rhombus and a parallelogram
on an xy plane. I can determine the
coordinate of the missing vertex that makes up a rectangle or a square.
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Unit 7 Quadrilaterals
Week 22 – Defining
Quadrilaterals with
Coordinates
109
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).
Determine the properties that can be
used to identify a trapezoid on an xy
plane. Determine the coordinate of the
missing vertex that makes up a rectangle or
a square.
I can determine the properties that can be used to identify a
trapezoid on an xy plane I can Determine the
coordinate of the missing vertex that makes up a rectangle or a square.
Unit 7 Quadrilaterals
Week 22 – Defining
Quadrilaterals with
Coordinates
110 Assessment Assessment Assessment
Unit 7 Quadrilaterals
Week 23 – Parallelogram
Proofs 111
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.
Prove that Opposite sides of a parallelogram
are equal
I can prove that Opposite sides of a parallelogram are
equal
Unit 7 Quadrilaterals
Week 23 – Parallelogram
Proofs 112
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.
Prove that Opposite angles of a
parallelogram are equal
I can prove that Opposite angles of a parallelogram are
equal
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Unit 7 Quadrilaterals
Week 23 – Parallelogram
Proofs 113
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.
Prove that diagonals of a parallelogram are not
equal. Show that at their intersection,
opposite angles are equal and adjacent
angles are supplementary angles.
I can prove that diagonals of a parallelogram are not equal.
I can show that at their intersection, opposite angles are equal and adjacent angles
are supplementary angles.
Unit 7 Quadrilaterals
Week 23 – Parallelogram
Proofs 114
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.
Prove that diagonals of a rectangle are equal.
Show that at their intersection, opposite angles are equal and adjacent angles are
supplementary angles.
Prove that diagonals of a rectangle are equal. Show that at their intersection, opposite angles are equal and adjacent
angles are supplementary angles.
Unit 7 Quadrilaterals
Week 23 – Parallelogram
Proofs 115 Assessment Assessment Assessment
Unit 7 Quadrilaterals
Week 24 – Coordinate
Proofs 116
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.*
Find perimeter and area of the triangle on xy
plane
I can find perimeter and area of the triangle on xy plane
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Unit 7 Quadrilaterals
Week 24 – Coordinate
Proofs 117
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.*
Find perimeter and area of square and rectangle
on xy plane
I can find perimeter and area of square and rectangle on xy
plane
Unit 7 Quadrilaterals
Week 24 – Coordinate
Proofs 118
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.*
Find perimeter and area of rhombus and
parallelogram on xy plane
I can find perimeter and area of rhombus and parallelogram
on xy plane
Unit 7 Quadrilaterals
Week 24 – Coordinate
Proofs 119
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.*
Find perimeter and area of the trapezoid on xy
plane
I can find perimeter and area of the trapezoid on xy plane
Unit 7 Quadrilaterals
Week 24 – Coordinate
Proofs 120 Assessment Assessment Assessment
Unit 8 Pacing Chart
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Unit 8
Unit Week Day CCSS Standards Objective I Can Statements
Unit 8 Circles
Week 25 – Inscribed in a
Circle 121
CCSS.MATH.CONTENT.HSG.C.A.1 Prove that all circles are similar.
Prove that all circles are similar.
I can prove that all circles are similar.
Unit 8 Circles
Week 25 – Inscribed in a
Circle 122
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.
Identify and describe relationships among
inscribed angles, radii, and chords.
I can Identify and describe relationships among inscribed
angles, radii, and chords.
Unit 8 Circles
Week 25 – Inscribed in a
Circle 123
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.
Include the relationship between central,
inscribed, and circumscribed angles
I can Include the relationship between central, inscribed, and circumscribed angles
Unit 8 Circles
Week 25 – Inscribed in a
Circle 124
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.
Inscribed angles on a diameter are right
angles; The radius of a circle is perpendicular to the
tangent where the radius intersects the circle.
I know that Inscribed angles on a diameter are right angles;
I know that the radius of a circle is perpendicular to the
tangent where the radius intersects the circle.
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Unit 8 Circles
Week 25 – Inscribed in a
Circle 125 Assessment Assessment Assessment
Unit 8 Circles
Week 26 – Circle
Relationships 126
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.
Construct the inscribed and circumscribed circles
of a triangle
I can construct the inscribed and circumscribed circles of a
triangle
Unit 8 Circles
Week 26 – Circle
Relationships 127
CCSS.MATH.CONTENT.HSG.C.A.4 (+) Construct a tangent line from a point outside a given circle
to the circle.
Construct a tangent line from a point outside a
given circle to the circle.
I can construct a tangent line from a point outside a given
circle to the circle.
Unit 8 Circles
Week 26 – Circle
Relationships 128
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.
Derive the equation of a circle of given center and
radius using the Pythagorean Theorem
I can derive the equation of a circle of given center and
radius using the Pythagorean Theorem
Unit 8 Circles
Week 26 – Circle
Relationships 129
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.
Complete the square to find the center and
radius of a circle given by an equation.
I can complete the square to find the center and radius of a
circle given by an equation.
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Unit 8 Circles
Week 26 – Circle
Relationships 130 Assessment Assessment Assessment
Unit 8 Circles
Week 27 – Proofs with
Circles 131
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.
Prove properties of angles for a quadrilateral
inscribed in a circle.
I can prove properties of angles for a quadrilateral
inscribed in a circle.
Unit 8 Circles
Week 27 – Proofs with
Circles 132
CCSS.MATH.CONTENT.HSG.C.B.5 Derive using similarity the fact that the length of the arc
intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of
proportionality; derive the formula for the area of a sector.
Derive using similarity the fact that the length
of the arc intercepted by an angle is proportional
to the radius, and
I can derive using similarity the fact that the length of the arc intercepted by an angle is
proportional to the radius, and
Unit 8 Circles
Week 27 – Proofs with
Circles 133
CCSS.MATH.CONTENT.HSG.C.B.5 Derive using similarity the fact that the length of the arc
intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of
proportionality; derive the formula for the area of a sector.
Define the radian measure of the angle as
the constant of proportionality
I can define the radian measure of the angle as the constant of proportionality
Unit 8 Circles
Week 27 – Proofs with
Circles 134
CCSS.MATH.CONTENT.HSG.C.B.5 Derive using similarity the fact that the length of the arc
intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of
proportionality; derive the formula for the area of a sector.
Derive the formula for the area of a sector.
I can derive the formula for the area of a sector.
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Unit 8 Circles
Week 27 – Proofs with
Circles 135 Assessment Assessment Assessment
Unit 8 Circles
Week 28 – Conics
136 CCSS.MATH.CONTENT.HSG.GPE.A.2
Derive the equation of a parabola given a focus and directrix. Find the directrix and the
focus of a parabola I can find the directrix and the
focus of a parabola
Unit 8 Circles
Week 28 – Conics
137 CCSS.MATH.CONTENT.HSG.GPE.A.2
Derive the equation of a parabola given a focus and directrix.
Find the equation of the parabola given the
directrix and the focus
I can find the equation of the parabola given the directrix
and the focus
Unit 8 Circles
Week 28 – Conics
138
CCSS.MATH.CONTENT.HSG.GPE.A.3 (+) Derive the equations of ellipses and hyperbolas given the
foci, using the fact that the sum or difference of distances from the foci is constant.
Derive the equations of ellipses given the foci, using the fact that the sum or difference of
distances from the foci is constant.
I can derive the equations of ellipses given the foci, using
the fact that the sum or difference of distances from
the foci is constant.
Unit 8 Circles
Week 28 – Conics
139
CCSS.MATH.CONTENT.HSG.GPE.A.3 (+) Derive the equations of ellipses and hyperbolas given the
foci, using the fact that the sum or difference of distances from the foci is constant.
Derive the equations of hyperbolas given the foci,
using the fact that the sum or difference of
distances from the foci is constant.
I can derive the equations of hyperbolas given the foci,
using the fact that the sum or difference of distances from
the foci is constant.
Unit 8 Pacing Chart
HighSchoolMathTeachers.com @2018
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Unit 8 Circles
Week 28 – Conics
140 Assessment Assessment Assessment
Unit 9 Pacing Chart
HighSchoolMathTeachers.com @2018
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Unit 9
Unit Week Day CCSS Standards Objective I Can Statements
Unit 9 Geometric
Modeling in Two
Dimensions
Week 28 – 2D
Applications 141
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.
Give an informal argument for the formulas for the circumference
I can give an informal argument for the formulas for
the circumference
Unit 9 Geometric
Modeling in Two
Dimensions
Week 28 – 2D
Applications 142
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.
Applications of circumference
I can discuss the applications of circumference
Unit 9 Geometric
Modeling in Two
Dimensions
Week 28 – 2D
Applications 143
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.
Give an informal argument for the
formulas for area of a circle
I can give an informal argument for the formulas for
area of a circle
Unit 9 Geometric
Modeling in Two
Dimensions
Week 28 – 2D
Applications 144
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.
Applications of area of a circle
I can discuss the applications of area of a circle
Unit 9 Pacing Chart
HighSchoolMathTeachers.com @2018
Page 37
Unit 9 Geometric
Modeling in Two
Dimensions
Week 28 – 2D
Applications 145 Assessment Assessment Assessment
Unit 9 Geometric
Modeling in Two
Dimensions
Week 29 – Solve Design
Problem 146
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).*
Use triangular, square and rectangular designs
in modeling without interchanging between
any two or more designs
I can use triangular, square and rectangular designs in
modeling without interchanging between any
two or more designs
Unit 9 Geometric
Modeling in Two
Dimensions
Week 29 – Solve Design
Problem 147
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).*
Use triangular, square and rectangular designs
in modeling by interchanging between
any two or more designs
I can use triangular, square and rectangular designs in modeling by interchanging between any two or more
designs
Unit 9 Geometric
Modeling in Two
Dimensions
Week 29 – Solve Design
Problem 148
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).*
Use circular and quadrilateral designs in
modeling
I can use circular and quadrilateral designs in
modeling
Unit 9 Geometric
Modeling in Two
Dimensions
Week 29 – Solve Design
Problem 149
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).*
Use 2D designs in modeling
I can use 2D designs in modeling
Unit 9 Pacing Chart
HighSchoolMathTeachers.com @2018
Page 38
Unit 9 Geometric
Modeling in Two
Dimensions
Week 29 – Solve Design
Problem 150 Assessment Assessment Assessment
Unit 9 Geometric
Modeling in Two
Dimensions
Week 28 – 2D
Applications 141
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.
Give an informal argument for the formulas for the circumference
I can give an informal argument for the formulas for
the circumference
Unit 9 Geometric
Modeling in Two
Dimensions
Week 28 – 2D
Applications 142
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.
Applications of circumference
I can discuss the applications of circumference
Unit 9 Geometric
Modeling in Two
Dimensions
Week 28 – 2D
Applications 143
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.
Give an informal argument for the
formulas for area of a circle
I can give an informal argument for the formulas for
area of a circle
Unit 9 Geometric
Modeling in Two
Dimensions
Week 28 – 2D
Applications 144
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.
Applications of area of a circle
I can discuss the applications of area of a circle
Unit 9 Pacing Chart
HighSchoolMathTeachers.com @2018
Page 39
Unit 9 Geometric
Modeling in Two
Dimensions
Week 28 – 2D
Applications 145 Assessment Assessment Assessment
Unit 9 Geometric
Modeling in Two
Dimensions
Week 29 – Solve Design
Problem 146
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).*
Use triangular, square and rectangular designs
in modeling without interchanging between
any two or more designs
I can use triangular, square and rectangular designs in
modeling without interchanging between any
two or more designs
Unit 9 Geometric
Modeling in Two
Dimensions
Week 29 – Solve Design
Problem 147
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).*
Use triangular, square and rectangular designs
in modeling by interchanging between
any two or more designs
I can use triangular, square and rectangular designs in modeling by interchanging between any two or more
designs
Unit 9 Geometric
Modeling in Two
Dimensions
Week 29 – Solve Design
Problem 148
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).*
Use circular and quadrilateral designs in
modeling
I can use circular and quadrilateral designs in
modeling
Unit 9 Geometric
Modeling in Two
Dimensions
Week 29 – Solve Design
Problem 149
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).*
Use 2D designs in modeling
I can use 2D designs in modeling
Unit 9 Pacing Chart
HighSchoolMathTeachers.com @2018
Page 40
Unit 9 Geometric
Modeling in Two
Dimensions
Week 29 – Solve Design
Problem 150 Assessment Assessment Assessment
Unit 10 Pacing Chart
HighSchoolMathTeachers.com @2018
Page 41
Unit 10
Unit Week Day CCSS Standards Objective I Can Statements
Unit 10 Understanding and Modeling
Three-Dimensional
Figures
Week 30 – Volume
151
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.
CCSS.MATH.CONTENT.HSG.GMD.A.2 (+) Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other
solid figures.
Give an informal argument using
Cavalieri's principle for the formulas for the
volume of a sphere and other solid figures.
I can give an informal argument using Cavalieri's
principle for the formulas for the volume of a sphere and
other solid figures.
Unit 10 Understanding and Modeling
Three-Dimensional
Figures
Week 30 – Volume
152
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.
CCSS.MATH.CONTENT.HSG.GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and
spheres to solve problems.*
Discuss the application of volume of a sphere
I can discuss the application of volume of a sphere
Unit 10 Understanding and Modeling
Three-Dimensional
Figures
Week 30 – Volume
153
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.
CCSS.MATH.CONTENT.HSG.GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and
spheres to solve problems.*
Discuss the application of volume of a cylinder
I can discuss the application of volume of a cylinder
Unit 10 Pacing Chart
HighSchoolMathTeachers.com @2018
Page 42
Unit 10 Understanding and Modeling
Three-Dimensional
Figures
Week 30 – Volume
154
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.
CCSS.MATH.CONTENT.HSG.GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and
spheres to solve problems.*
Discuss the application of volume of pyramids
and cones
I can discuss the application of volume of pyramids and
cones
Unit 10 Understanding and Modeling
Three-Dimensional
Figures
Week 30 – Volume
155 Assessment Assessment Assessment
Unit 10 Understanding and Modeling
Three-Dimensional
Figures
Week 31 – Cross
Sections 156
CCSS.MATH.CONTENT.HSG.GMD.B.4 Identify the shapes of two-dimensional cross-sections of
three-dimensional objects, and identify three-dimensional objects generated by rotations of two-
dimensional objects.
Identify the shapes of two-dimensional cross-
sections(polygon sections) of three-
dimensional objects
I can Identify the shapes of two-dimensional cross-
sections(polygon sections) of three-dimensional objects
Unit 10 Understanding and Modeling
Three-Dimensional
Figures
Week 31 – Cross
Sections 157
CCSS.MATH.CONTENT.HSG.GMD.B.4 Identify the shapes of two-dimensional cross-sections of
three-dimensional objects, and identify three-dimensional objects generated by rotations of two-
dimensional objects.
Identify the shapes of two-dimensional cross-
sections(circular sections) of three-dimensional
objects
I can Identify the shapes of two-dimensional cross-
sections(circular sections) of three-dimensional objects
Unit 10 Pacing Chart
HighSchoolMathTeachers.com @2018
Page 43
Unit 10 Understanding and Modeling
Three-Dimensional
Figures
Week 31 – Cross
Sections 158
CCSS.MATH.CONTENT.HSG.GMD.B.4 Identify the shapes of two-dimensional cross-sections of
three-dimensional objects, and identify three-dimensional objects generated by rotations of two-
dimensional objects.
identify three-dimensional objects
generated by rotations of polygon and circular
faces
I can identify three-dimensional objects generated
by rotations of polygon and circular faces
Unit 10 Understanding and Modeling
Three-Dimensional
Figures
Week 31 – Cross
Sections 159
CCSS.MATH.CONTENT.HSG.GMD.B.4 Identify the shapes of two-dimensional cross-sections of
three-dimensional objects, and identify three-dimensional objects generated by rotations of two-
dimensional objects.
identify three-dimensional objects
generated by rotations of 2D fused faces
I can identify three-dimensional objects generated by rotations of 2D fused faces
Unit 10 Understanding and Modeling
Three-Dimensional
Figures
Week 31 – Cross
Sections 160 Assessment Assessment Assessment
Unit 10 Understanding and Modeling
Three-Dimensional
Figures
Week 32 – 3D
Applications
161
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).*
Model a tree trunk. Identify all the objects
used in modeling. Suggest any other objects that may be used instead
of the one(s) used.
I can model a tree trunk. I can Identify all the objects
used in modeling. I can suggest any other objects that
may be used instead of the one(s) used.
Unit 10 Understanding and Modeling
Three-Dimensional
Figures
Week 32 – 3D
Applications
162
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).*
Model a human torso. Identify all the objects
used in modeling. Suggest any other objects that may be used instead
of the one(s) used.
I can Model a human torso. I can Identify all the objects
used in modeling. I can suggest any other objects
that may be used instead of the one(s) used.
Unit 10 Pacing Chart
HighSchoolMathTeachers.com @2018
Page 44
Unit 10 Understanding and Modeling
Three-Dimensional
Figures
Week 32 – 3D
Applications
163
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).*
Come up with different models of a house.
Identify all the objects used in modeling.
Suggest any other objects that may be used instead
of the one(s) used.
I can come up with different models of a house.
I can Identify all the objects used in modeling.
I can suggest any other objects that may be used instead of
the one(s) used.
Unit 10 Understanding and Modeling
Three-Dimensional
Figures
Week 32 – 3D
Applications
164
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).
Apply concepts of density based on area and
volume in modeling situations (e.g., persons
per square mile, BTUs per cubic foot).
I can apply concepts of density based on area and volume in
modeling situations (e.g., persons per square mile, BTUs
per cubic foot).
Unit 10 Understanding and Modeling
Three-Dimensional
Figures
Week 32 – 3D
Applications
165 Assessment Assessment Assessment
Unit 10 Understanding and Modeling
Three-Dimensional
Figures
Week 33 – 3D Design Problems
166
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).*
Apply geometric methods to solve design problems of the Conical structures
or object to satisfy physical constraints or minimize cost; working with typographic grid
systems based on ratios
I can apply geometric methods to solve design problems of
the Conical structures or object to satisfy physical
constraints or minimize cost; working with typographic grid
systems based on ratios
Unit 10 Pacing Chart
HighSchoolMathTeachers.com @2018
Page 45
Unit 10 Understanding and Modeling
Three-Dimensional
Figures
Week 33 – 3D Design Problems
167
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).*
Apply geometric methods to solve design problems
of the Cylindrical structures or object to
satisfy physical constraints or minimize
cost; working with typographic grid systems
based on ratios
I can apply geometric methods to solve design problems of the Cylindrical structures or
object to satisfy physical constraints or minimize cost; working with typographic grid
systems based on ratios
Unit 10 Understanding and Modeling
Three-Dimensional
Figures
Week 33 – 3D Design Problems
168
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).*
Apply geometric methods to solve design problems
of the cubical and cuboidal structures or
object to satisfy physical constraints or minimize
cost; working with typographic grid systems
based on ratios
I can apply geometric methods to solve design problems of
the cubical and cuboidal structures or object to satisfy
physical constraints or minimize cost; working with typographic gridd systems
based on ratios
Unit 10 Understanding and Modeling
Three-Dimensional
Figures
Week 33 – 3D Design Problems
169
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).*
Apply geometric methods to solve design problems of the pyramid structure
or object to satisfy physical constraints or minimize cost; working with typographic grid
systems based on ratios
I can apply geometric methods to solve design problems of
the pyramid structure or object to satisfy physical
constraints or minimize cost; working with typographic grid
systems based on ratios
Unit 10 Understanding and Modeling
Three-Dimensional
Figures
Week 33 – 3D Design Problems
170 Assessment Assessment Assessment