MONROVIA UNIFIED SCHOOL DISTRICT
INSTRUCTIONAL PACING GUIDE
Geometry
Department
Course Name
Math
Geometry
Grade Level
9-12
Instructional Reference CORE in CORE
Material(s)
Holt Geometry
*** This guide is intended to be a guide only. The timing is
recommended so that the material is learned by the indicated
benchmark assessment. Teachers will use their professional
judgement to modify the time given to ensure students have
adequate time to learn the material.
Math
“World Class Schools for World Class Students”
Standard
Resources Essential Questions/Vocabulary Timing
(Concepts to be Understood)
(Days)
Skills/Procedures
G.CO.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.
CORE 1-1 How do you use the
• Name geometric figures
undefined terms as the basic 2 days
elements of geometry.
Differentiation
Intervention
(SIOP, SDAIE, RTI)
Point, line, line segment
G.CO.1 - Know precise definitions of angle, circle, perpendicular line, CORE 1-2
parallel line, and line segment, based on the undefined notions of point,
line, distance along a line, and distance around a circular arc.
What tools and methods can 2 days • Copy, bisect and construct a
line segment.
you use to copy a segment,
bisect a segment, and
construct a circle?
Distance along a line, circle
G.CO.1 - Know precise definitions of angle, circle, perpendicular line, CORE 1-3
parallel line, and line segment, based on the undefined notions of point,
line, distance along a line, and distance around a circular arc.
What tools and methods can 2 days • Copy an angle
Construct the bisector of an
you use to copy an angle
angle
and bisect an angle?
Angle
Monrovia Unified School District
Instructional Pacing Guide
Geometry
Page 1 of 20
Last Revised: August 5, 2014
Standard
Resources Essential Questions/Vocabulary Timing
(Concepts to be Understood)
(Days)
Skills/Procedures
A.CED.1 - Create equations and inequalities in one variable and use
CORE 1-4
them to solve problems. Include equations arising from linear and
quadratic functions, and simple rational and exponential functions.
G.CO.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.Foundation
for G.CO.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.
How can you use angle pairs to
solve problems?
2 days • Measure angles
A.CED.4 - Rearrange formulas to highlight a quantity of interest, using CORE 1-5
the same reasoning as in solving equations. For example, rearrange
Ohm's law V = IR to highlight resistance R.
How can you express formulas in
different ways?
2 days • Solving formulas for specified
G.GPE.6 - Find the point on a directed line segment between two given CORE 1-6
points that partitions the segment in a given ratio.
G.GPE.4 - Find the point on a directed line segment between two given
points that partitions the segment in a given ratio.
How can you find midpoints 1 day
of segments and distances in
the coordinate plane.
•
G.CO.2 - Represent transformations in the plane using, e.g.,
CORE 1-7
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).
G.CO.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.
Prep for G.CO.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.
Performance Task and Test Review
Chapter 1 Cumulative Test - Target Date - 9/12/14
How do you identify
transformations that are rigid
motions?
• Classify transformations
• Identify rigid motions
Monrovia Unified School District
Instructional Pacing Guide
Differentiation
Intervention
(SIOP, SDAIE, RTI)
• Identify angles and angle pairs
• Find angle measures
•
1 day
•
•
variables
Rewriting formulas to solve
problems
Find the mid-point of line
segments
Use the midpoint formula
Find a distance in the
coordinate plane
1 day
1 day
Geometry
Page 2 of 20
Last Revised: August 5, 2014
Standard
Resources Essential Questions/Vocabulary Timing
(Concepts to be Understood)
(Days)
G.CO.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.
CORE 2-1
How can you use examples to
1 day
support or disprove a conjecture?
Skills/Procedures
• Make conjectures about
bisectors of obtuse angles
• Make conjectures about double
angles of acute angles
2 days • Use a Venn diagram to analyze
Mathematical Practice 3 - Construct viable arguments and critique the CORE 2-3
reasoning of others.
How can you effectively justify
arguments and critique the
arguments of others?
How can you connect statements
to visualize a chain of reasoning?
Mathematical Practice 3 - Construct viable arguments and critique the CORE 2-4
reasoning of others.
How can you analyze and critique
the reasoning of others?
2 days • Analyze bi-conditionals and
G.CO.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.
G.CO.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.
G.CO.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.
Performance Task and Test Review
Chapter 2 Cumulative Test - Target Date - 10/2/14
Prep for G.CO.9
CORE 2-5
What kinds of justifications can
you use in writing algebraic and
geometric proofs?
2 days
CORE 2-6
How can you organize the
deductive reasoning of a
geometric proof?
2 days • Apply linear pair theorem
Mathematical Practice 3 - Construct viable arguments and critique the CORE 2-2
reasoning of others.
Monrovia Unified School District
Instructional Pacing Guide
CORE 2-7
CORE 3-1
conditional statements
2 days • Show logical reasoning
• Complete a chain of reasoning
definitions
Geometry
`
when writing proofs
What are some formats you can Skip
use to organize geometric proofs?
How many distinct angle
measures are formed when three
lines in a plane intersect in
different ways?
Differentiation
Intervention
(SIOP, SDAIE, RTI)
1 day
1 day
1 day
• Apply vertical angles and
common segments theorems
when writing proofs
• Sketch different triangle
possibilities
• Sketch different intersection
possibilities
Page 3 of 20
Last Revised: August 5, 2014
Standard
Resources Essential Questions/Vocabulary Timing
(Concepts to be Understood)
(Days)
G.CO.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.
CORE 3-2
How can you prove and use
1 day
theorems about angles formed by
transversals that intersect parallel
lines?
Skills/Procedures
• Know and apply the same-side
interior angles postulate
• Know and apply the alternate
interior angles theorem
• Know and apply the
corresponding angles theorem
• Know and apply the equalmeasure linear pair theorem
• Know the converse of the
same-side interior angles,
alternate interior angles and
corresponding angles theorems
G.CO.12 - Make formal geometric constructions with a variety of tools CORE 3-3
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.
G.CO.12 - Make formal geometric constructions with a variety of tools CORE 3-4
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.
How can you construct a line
parallel to another line that passes
through a given point?
2 days • Construct a parallel line
How can you construct
perpendicular lines and prove
theorems about perpendicular
bisectors?
1 day
G.GPE.6 - Find the point on a directed line segment between two given CORE 3-5
points that partitions the segment in a given ratio.
How do you find the point on a 1 day
directed line segment that
partitions the segment in a given
ratio?
Monrovia Unified School District
Instructional Pacing Guide
Geometry
Differentiation
Intervention
(SIOP, SDAIE, RTI)
• Construct a perpendicular
bisector
• Know and apply the
perpendicular bisector theorem
• Know and apply the converse
of the perpendicular bisector
theorem
• Construct a perpendicular to a
line
• Partition a segment
Page 4 of 20
Last Revised: August 5, 2014
Standard
Resources Essential Questions/Vocabulary Timing
(Concepts to be Understood)
(Days)
G.GPE. 5 - Prove the slope criteria for parallel and perpendicular lines CORE 3-6
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).
Chapter 3 Cumulative Test - Target Date - 10/17/14
Assessed Performance Task - Given with Interim 1
1st Interim Benchmark October 20th-October 24th
G.CO.6 - Use geometric descriptions of rigid motions to transform
CORE 4-1
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.
G.CO.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.
Skills/Procedures
Differentiation
Intervention
(SIOP, SDAIE, RTI)
Write equations of parallel 2 days
lines
Write equation perpendicular lines
1 day
1 day
5 days
How can you use transformations
to determine whether figures are
congruent?
2 days • Determine if figures are
G.GPE.4 - Use coordinates to prove simple geometric theorems
CORE 4-2
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).
G.GPE.7 - Use coordinates to compute perimeters of polygons and areas
of triangles and rectangles, e.g., using the distance formula.*
How can you classify triangles in
the coordinate plane?
2 days • Classify triangles by side
G.CO.10 - Prove theorems about triangles. Theorems include: measures CORE 4-3
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.
What are some theorems about
angle measure in triangles?
2 days
congruent
• Find a sequence of rigid
motions
lengths
• Classify triangles by angles
using side lengths
Prove the triangle sum theorem
Prove the exterior angle theorem
G.CO.7 - Use the definition of congruence in terms of rigid motions to CORE 4-4
show that two triangles are congruent if and only if corresponding pairs
of sides and corresponding pairs of angles are congruent.
Monrovia Unified School District
Instructional Pacing Guide
Prove the quadrilateral sum
theorem
How can you use properties of
1 day
rigid motions to draw conclusions
about corresponding sides and
corresponding angles in congruent
triangles?
Geometry
• Find an unknown dimension
• Use CPCTC (Corresponding
parts of congruent triangles are
congruent theorem)
Page 5 of 20
Last Revised: August 5, 2014
Standard
Resources Essential Questions/Vocabulary Timing
(Concepts to be Understood)
(Days)
G.CO.8 - Explain how the criteria for triangle congruence (ASA, SAS,
and SSS) follow from the definition of congruence in terms of rigid
motions.
G.CO.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.
G.SRT.5 - Use congruence and similarity criteria for triangles to solve
problems and to prove relationships in geometric figures.
CORE 4-5
G.CO.8 - Explain how the criteria for triangle congruence (ASA, SAS, CORE 4-6
and SSS) follow from the definition of congruence in terms of rigid
motions.
G.CO.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.
G.SRT.5 - Use congruence and similarity criteria for triangles to solve
problems and to prove relationships in geometric figures.
G.GPE. 5 - Prove the slope criteria for parallel and perpendicular lines CORE 4-7
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).
How can you establish the SSS
and SAS triangle?
1 day
How can you establish and use the 2
ASA and AAS triangle
congruence criteria?
How can CPCTC be used in
proving slope criteria for parallel
and perpendicular lines?
Skills/Procedures
Differentiation
Intervention
(SIOP, SDAIE, RTI)
• Know and apply SSS
congruence criterion
• Know and apply the angle
bisection theorem
• Know and apply the reflected
points on an angle theorem
• Know and apply the SAS
congruence criterion
• Know and apply the SSS
congruence criterion
days • Know and apply the ASA and
AAS congruence criterion
2 days
Prove that parallel lines have the
same slope
Prove that lines with the same
slope are parallel
G.GPE.4 - Use coordinates to prove simple geometric theorems
CORE 4-8
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).
Monrovia Unified School District
Instructional Pacing Guide
Prove that perpendicular lines
have slopes whose product is -1
How do you write a coordinate
proof?
Geometry
2 days • Prove or disprove a statement
• Write a coordinate proof
Page 6 of 20
Last Revised: August 5, 2014
Standard
Resources Essential Questions/Vocabulary Timing
(Concepts to be Understood)
(Days)
G.CO.10 - Prove theorems about triangles. Theorems include: measures CORE 4-9
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.
What special relationships exist
among the sides and angles of
isosceles triangles?
Skills/Procedures
Differentiation
Intervention
(SIOP, SDAIE, RTI)
1 day
Prove the isosceles triangle
theorem
Prove the converse of the
isosceles triangle theorem
Performance Task and Test Review
Chapter 4 Cumulative Test - Target Date - 11/21/14
G.GPE.2 - Derive the equation of a parabola given a focus and directrix. CORE 5-1
G.C.3 - Construct the inscribed and circumscribed circles of a triangle,
and prove properties of angles for a quadrilateral inscribed in a circle.
CORE 5-2
G.CO.10 - Prove theorems about triangles. Theorems include: measures CORE 5-3
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.
G.GPE.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).
G.GO.10 - Prove theorems about triangles. Theorems include: measures CORE 5-4
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.
G.GPE.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
Monrovia Unified School District
Instructional Pacing Guide
1 day
1 day
How do you write the equation of
a parabola given its focus and
directrix?
2 days • Create a parabola
How do you construct the
circle that circumscribes a
triangle?
1 day
• Derive the equation of a
parabola
• Write the equation of a
parabola
• Construct a circumscribed
circle
• Construct an inscribed circle
How do you inscribe a circle in a
triangle?
What can you conclude about the 1 day
medians of a triangle?
Prove the concurrency of medians
theorem.
What must be true about the
segment that connects the
midpoints of two sides of a
triangle?
1 day
Prove the mid-segment theorem
Geometry
Page 7 of 20
Last Revised: August 5, 2014
Standard
Resources Essential Questions/Vocabulary Timing
(Concepts to be Understood)
(Days)
Skills/Procedures
Differentiation
Intervention
(SIOP, SDAIE, RTI)
containing the point (0, 2).
G.GO.10 - Prove theorems about triangles. Theorems include: measures CORE 5-5
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.
How can you use
inequalities related to
triangle side lengths and
angle measures in proofs?
1 day
G.GO.10 - Prove theorems about triangles. Theorems include: measures CORE 5-6
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.
When two sides of a triangle 1 day
have fixed lengths and the
angle included by them
changes, how does the third
side change?
Review for Test
Cumulative Test ( We are not yet at the end of chapter 5, but may
want to administer cumulative test to help review for finals.
Assessed Performance Task - Given with Interim 2
1 day
1 day
2nd Interim (Benchmark) December 15th- December 19th (Finals)
G.SRT.8 - Use trigonometric ratios and the Pythagorean Theorem to
solve right triangles in applied problems.
5 days
———-
CORE 5-7
G.SRT.6 - Understand that by similarity, side ratios in right triangles are CORE 5-8
properties of the angles in the triangle, leading to definitions of
trigonometric ratios for acute angles.
G.SRT.8 - Use trigonometric ratios and the Pythagorean Theorem to
solve right triangles in applied problems.
Review for Test
Chapter 5 Cumulative Test - Target Date - 01/13/14
Monrovia Unified School District
Instructional Pacing Guide
• Prove side relationships.
• Prove angle relationships.
How can you apply the
Pythagorean Theorem?
1 day • Use Pythagorean Theorem
What can you say about the side
lengths associated with special
right triangles?
2 days • Solve special triangles.
with lengths.
• Use Pythagorean Theorem
with velocities.
1 day
Geometry
Page 8 of 20
Last Revised: August 5, 2014
Standard
Resources Essential Questions/Vocabulary Timing
(Concepts to be Understood)
(Days)
G.CO.13 - Construct an equilateral triangle, a square, and a regular
hexagon inscribed in a circle.
CORE 6-1
How do you inscribe a regular
polygon in a circle?
1 day
Skills/Procedures
• Inscribe a regular polygon.
• Inscribe a square.
G.CO.11 - Prove theorems about parallelograms. Theorems include:
CORE 6-2
opposite sides are congruent, opposite angles are congruent, the
diagonals of a parallelogram bisect each other, and conversely, rectangles
are parallelograms with congruent diagonals.
G.SRT.5 - Use congruence and similarity criteria for triangles to solve
problems and to prove relationships in geometric figures.
G.SRT.5 - Use congruence and similarity criteria for triangles to solve CORE 6-3
problems and to prove relationships in geometric figures.
What can you conclude about the 2 days
sides, angles, and diagonals of a
parallelogram?
• Prove opposite sides of a
parallelogram are congruent.
• Prove diagonals of a
parallelogram bisect each
other.
What criteria can you use to prove 2 days
that a quadrilateral is a
parallelogram?
• Prove opposites criterion for a
parallelogram.
• Prove opposite angles criterion
for a parallelogram.
G.CO.11 - Prove theorems about parallelograms. Theorems include:
CORE 6-4
opposite sides are congruent, opposite angles are congruent, the
diagonals of a parallelogram bisect each other, and conversely, rectangles
are parallelograms with congruent diagonals.
G.SRT.5 - Use congruence and similarity criteria for triangles to solve
problems and to prove relationships in geometric figures.
G.GPE.4 - Use coordinates to prove simple geometric theorems
CORE 6-5
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).
G.CO.9 - Prove theorems about lines and angles. Theorems include:
CORE 6-6
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.
Performance Task and Review
Chapter 6 Cumulative Test - Target Date - 1/30/14
Prep for G.SRT.2 - Given two figures, use the definition of similarity in CORE 7-1
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.
Prep for G.SRT.1b - The dilation of a line segment is longer or shorter
in the ratio given by the scale factor.
What are the properties of a
rectangles and rhombuses?
1 day
• Prove the rectangle theorem.
• Prove diagonals of a rhombus
are perpendicular.
How can you use slope in
coordinate proofs?
2 days
• Prove a quadrilateral is a
parallelogram.
• Prove a quadrilateral is a
rectangle.
How can auxiliary segments be
used in proofs?
2 days
• Prove using reasoning between
congruent angles and
congruent sides.
Monrovia Unified School District
Instructional Pacing Guide
How can you use ratios of
corresponding side lengths to
solve problems involving similar
polygons?
Geometry
1 day
1 day
1 day
Differentiation
Intervention
(SIOP, SDAIE, RTI)
• Determine polygon similarity.
• Find unknown lengths in
similar polygons.
Page 9 of 20
Last Revised: August 5, 2014
Standard
Resources Essential Questions/Vocabulary Timing
(Concepts to be Understood)
(Days)
Skills/Procedures
G.CO.2 - Represent transformations in the plane using, e.g.,
CORE 7-2
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).
G.SRT.1 - Verify experimentally the properties of dilations given by a
center and a scale factor.
G.SRT.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.
G.C.1 - Prove that all circles are similar.
G.SRT.2 - Given two figures, use the definition of similarity in terms of CORE 7-3
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.
G.SRT.3 - Use the properties of similarity transformations to establish
the AA criterion for two triangles to be similar.
What are the key properties of
2 days
dilations, and how can dilations be
used to show figures are similar?
• Determine if figures are
similar.
• Prove all circles are similar.
What can you conclude about
2 days
similar triangles and how can you
prove triangles are similar?
• Apply similarity to triangles.
• Identify congruent angles and
proportional sides.
• Prove AA Similarity criterion.
G.SRT.4 - Prove theorems about triangles. Theorems include: a line
CORE 7-4
parallel to one side of a triangle divides the other two proportionally, and
conversely; the Pythagorean Theorem proved using triangle similarity.
G.SRT.5 - Use congruence and similarity criteria for triangles to solve
problems and to prove relationships in geometric figures.
How does a line that is parallel to 1 day
one side of a triangle divide the
two sides that it intersects?
• Prove triangle proportionality
theorem.
• Prove the converse of the
triangle proportionality
theorem.
G.SRT.5 - Use congruence and similarity criteria for triangles to solve CORE 7-5
problems and to prove relationships in geometric figures.
G.MG.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).*
How can you use similar triangles 2 days
and similar rectangles to solve
problems?
• Find an unknown distance.
• Find an unknown height.
• Solve a problem about similar
triangles.
G.CO.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).
Performance Task
Chapter 7 Cumulative Test - Target Date - 2/19/14
How can you represent dilations
in the coordinate plane?
• Draw a dilation in a coordinate
plane.
Monrovia Unified School District
Instructional Pacing Guide
CORE 7-6
1 day
Differentiation
Intervention
(SIOP, SDAIE, RTI)
1 day
1 day
Geometry
Page 10 of 20
Last Revised: August 5, 2014
Standard
Resources Essential Questions/Vocabulary Timing
(Concepts to be Understood)
(Days)
Skills/Procedures
G.SRT.4 - Prove theorems about triangles. Theorems include: a line
CORE 8-1
parallel to one side of a triangle divides the other two proportionally, and
conversely; the Pythagorean Theorem proved using triangle similarity.
G.SRT.5 - Use congruence and similarity criteria for triangles to solve
problems and to prove relationships in geometric figures.
How can you use right triangle
similarity to prove the
Pythagorean Theorem?
G.SRT.6 - Understand that by similarity, side ratios in right triangles are CORE 8-2
properties of the angles in the triangle, leading to definitions of
trigonometric ratios for acute angles.
G. SRT.7 - Explain and use the relationship between the sine and cosine
of complementary angles.
G.SRT.8 - Use trigonometric ratios and the Pythagorean Theorem to
solve right triangles in applied problems.
G.SRT.8 - Use trigonometric ratios and the Pythagorean Theorem to
CORE 8-3
solve right triangles in applied problems.
G.SRT.8 - Use trigonometric ratios and the Pythagorean Theorem to
CORE 8-4
solve right triangles in applied problems.
How do you find the tangent, sine, 2 day
cosine ratios for acute angles in a
right triangle?
• Find the tangent of an angle.
• Solve a real-world problem.
• Find the sine and cosine of an
angle.
How do you find an unknown
1 day
angle measure in a right triangle?
How can you use trigonometric 1 day
ratios to solve problems involving
angles of elevation and
depression?
How can you find the side lengths 1 day
and angle measures of non-right
triangles?
• Use an inverse trigonometric
ratio.
• Solve a problem with an angle
of depression.
• Solve a problem with an angle
of elevation.
How can you apply trigonometry 1 day
to solve vector problems?
• Solve a vector problem.
Mathematical Practice 4 - Model with mathematics.
G.SRT.10 - Prove the Laws of Sines and Cosines and use them to
solve problems.
CORE 8-5
Mathematical Practice 8 - Look for and express regularity in repeated
reasoning.
G.SRT.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).
CORE 8-6
Chapter 8 Cumulative Test - Target Date - 3/6/14
S.CP.9 - Use permutations and combinations to compute
probabilities of compound events and solve problems.
2 day
Prove the Pythagorean Theorem
1 day
2 days
Mathematical Practice 7 - Look for and make use of structure.
CORE 13-1 What are permutations and
combinations and how can you
use them to calculate
probabilities?
S.MD.6 - Use probabilities to make fair decisions (e.g., drawing by
lots, using a random number generator).
CORE 13-2 How can you use probabilities to 2 days
help you make fair decisions?
Monrovia Unified School District
Instructional Pacing Guide
Differentiation
Intervention
(SIOP, SDAIE, RTI)
Geometry
• Find permutations.
• Use permutations to calculate a
probability.
• Find combinations.
• Use combinations to calculate
a probability.
• Use a random sample.
• Use a convenience sample.
Page 11 of 20
Last Revised: August 5, 2014
Standard
Resources Essential Questions/Vocabulary Timing
(Concepts to be Understood)
(Days)
Skills/Procedures
S.CP.2 - Understand that two events A and B are independent if the
CORE 13-3 How do you find the probability
probability of A and B occurring together is the product of their
of independent and dependent
probabilities, and use this characterization to determine if they are
events?
independent.
S.CP.3 - Understand the conditional probability of A given B as P(A and
B)/P(B), and interpret independence of A and B as saying that the
conditional probability of A given B is the same as the probability of A,
and the conditional probability of B given A is the same as the
probability of B.
S.CP.4 - Construct and interpret two-way frequency tables of data when
two categories are associated with each object being classified. Use the
two-way table as a sample space to decide if events are independent and
to approximate conditional probabilities. For example, collect data from a
random sample of students in your school on their favorite subject among
math, science, and English. Estimate the probability that a randomly
selected student from your school will favor science given that the
student is in tenth grade. Do the same for other subjects and compare the
results.
S.CP.8 - Apply the general Multiplication Rule in a uniform
probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and
interpret the answer in terms of the model.
Mathematical Practice 1 - Make sense of problems and persevere in
solving them.
2 days
• Determine if events are
independent.
• Use the probability of
independent events formula.
• Show that events are
independent.
• Find the probability of
dependent events.
• Use the multiplication rule.
S.CP.3 - Understand the conditional probability of A given B as P(A and CORE 13-4
B)/P(B), and interpret independence of A and B as saying that the
conditional probability of A given B is the same as the probability of A,
and the conditional probability of B given A is the same as the
probability of B.
S.CP.6 - Find the conditional probability of A given B as the fraction of
B's outcomes that also belong to A, and interpret the answer in terms of
the model.
CORE 13-5
S.CP.7 - Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and
B), and interpret the answer in terms of the model.
2 days
• Find conditional probabilities.
• Use the formula for conditional
probability.
How do you calculate a
conditional probability?
How do you find the probability 1 day
of mutually exclusive events and
overlapping events?
• Find the probability of
mutually exclusive events.
• Find the probability of
overlapping events.
• Use the addition rule.
1 day
1 day
Performance Task and Review
Chapter 13 Cumulative Test - Target Date - 4/21/14
Monrovia Unified School District
Instructional Pacing Guide
Differentiation
Intervention
(SIOP, SDAIE, RTI)
Geometry
Page 12 of 20
Last Revised: August 5, 2014
Standard
Resources Essential Questions/Vocabulary Timing
(Concepts to be Understood)
(Days)
Skills/Procedures
G.CO.2 - Represent transformations in the plane using, e.g.,
CORE 9-1
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).
G.CO.4 - Develop definitions of rotations, reflections, and translations in
terms of angles, circles, perpendicular lines, parallel lines, and line
segments.
G.CO.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.
Mathematical Practice 3 - Construct viable arguments and critique the
reasoning of others.
How do you draw the image of a
figure under a reflection?
2 days • Draw a reflection image.
G.CO.2 - Represent transformations in the plane using, e.g.,
CORE 9-2
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).
G.CO.4 - Develop definitions of rotations, reflections, and translations in
terms of angles, circles, perpendicular lines, parallel lines, and line
segments.
G.CO.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.
How do you draw the image of a
figure under a translation?
2 days • Name a vector.
G.CO.2 - Represent transformations in the plane using, e.g.,
CORE 9-3
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).
G.CO.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.
How do you draw the image 1 day
of a figure under a rotation?
CAHSEE REVIEW (10th Grade CAHSEE - 3/17-3/18)
G.CO.5 - Given a geometric figure and a rotation, reflection, or
CORE 9-4
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.
Monrovia Unified School District
Instructional Pacing Guide
How can you use more than one
transformation to map one figure
onto another?
Geometry
Differentiation
Intervention
(SIOP, SDAIE, RTI)
• Construct a reflection image.
• Draw a reflection in the
coordinate plane.
• Construct a translation image.
• Draw a translation in the
coordinate plane.
• Draw a rotation image.
2 days
1 day
Page 13 of 20
Last Revised: August 5, 2014
Standard
Resources Essential Questions/Vocabulary Timing
(Concepts to be Understood)
(Days)
G.CO.3 - Given a rectangle, parallelogram, trapezoid, or regular
polygon, describe the rotations and reflections that carry it onto itself.
CORE 9-5
G.CO.5 - Given a geometric figure and a rotation, reflection, or
CORE 9-6
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.
G.CO.2 - Represent transformations in the plane using, e.g.,
CORE 9-7
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).
How do you determine whether a 1 day
figure has line symmetry or
rotational symmetry?
How can you use transformations 1 day
to describe tessellations?
• Identify line symmetry.
• Identify rotational symmetry.
How do you draw the image of a 1 day
figure under a dilation.
• Construct a dilation image.
Assessed Performance Task - Given with Interim 3
———-
3rd Interim - SUMMATIVE (Benchmark) March 23rd - 26th
CORE 10-1 What formula can you use to find
G.SRT.9 - Derive the formula A = 1/2 ab sin(C) for the area of a
the area of a triangle if you know
triangle by drawing an auxiliary line from a vertex perpendicular to
the length of two sides and the
the opposite side.
measure of an included angle.
G.GMD.1 - Give an informal argument for the formulas for the
CORE 10-2 How do you justify and use
circumference of a circle, area of a circle, volume of a cylinder, pyramid,
the formula for the
and cone. Use dissection arguments, Cavalieri's principle, and informal
circumference of a circle?
limit arguments.
G.MG.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).*
Mathematical Practice 8 - Look for and express regularity in repeated
reasoning.
G.MG.1 - Use geometric shapes, their measures, and their properties to CORE 10-3 How can you find areas of
describe objects (e.g., modeling a tree trunk or a human torso as a
irregular shapes?
cylinder).*
G.MG.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).*
3 days
2 days
G.GPE.7 - Use coordinates to compute perimeters of polygons and areas CORE 10-4 How do you find the perimeter
of triangles and rectangles, e.g., using the distance formula.*
and area of polygons in the
G.MG.2 - Apply concepts of density based on area and volume in
coordinate plane?
modeling situations (e.g., persons per square mile, BTUs per cubic
foot).*
Monrovia Unified School District
Instructional Pacing Guide
Skills/Procedures
Geometry
Differentiation
Intervention
(SIOP, SDAIE, RTI)
• Describe tessellations.
• Use an area formula.
1day
• Justify the circumference
formula.
2 days
• Find area using addition.
• Find area using subtraction.
2 days
• Find perimeters.
• Approximating a population
density.
Page 14 of 20
Last Revised: August 5, 2014
Standard
Resources Essential Questions/Vocabulary Timing
(Concepts to be Understood)
(Days)
G.CO.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).
CORE 10-5 What happens when you change
the dimensions of a figure using
different scale factors along two
dimensions?
1 day
Performance Task and Review
Chapter 10 Cumulative Test - Target Date - 5/9/14
G.GMD.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.
1 day
1 day
2 days
G.GMD.1 - Give an informal argument for the formulas for the
CORE 11-2 How do you calculate the
circumference of a circle, area of a circle, volume of a cylinder, pyramid,
volume of a prism or
and cone. Use dissection arguments, Cavalieri's principle, and informal
cylinder and use volume
limit arguments.
formulas to solve design
G.GMD.2 - Give an informal argument using Cavalieri's principle
problems?
for the formulas for the volume of a sphere and other solid figures.
G.MG.2 - Apply concepts of density based on area and volume in
modeling situations (e.g., persons per square mile, BTUs per cubic foot).
Design a box with maximum
G.MG.3 - Apply geometric methods to solve design problems (e.g.,
volume.
designing an object or structure to satisfy physical constraints or
minimize cost; working with typographic grid systems based on ratios).
G.GMD.1 - Give an informal argument for the formulas for the
CORE 11-3 How do you calculate the volume
circumference of a circle, area of a circle, volume of a cylinder, pyramid,
of a pyramid or cone and use
and cone. Use dissection arguments, Cavalieri's principle, and informal
volume to solve problems?
limit arguments.
G.GMD.3 - Use volume formulas for cylinders, pyramids, cones, and
spheres to solve problems.*
G.GMD.2 - Give an informal argument using Cavalieri's principle CORE 11-4 How do you calculate the volume
of a sphere and use the volume
for the formulas for the volume of a sphere and other solid figures.
G.GMD.3 - Use volume formulas for cylinders, pyramids, cones, and
formula to solve problems?
spheres to solve problems.
Performance Task
Chapter 11 Cumulative Test - Target Date - 5/23/14
Monrovia Unified School District
Instructional Pacing Guide
Geometry
Differentiation
Intervention
(SIOP, SDAIE, RTI)
2 days
S.CP.1 - Describe events as subsets of a sample space (the set of
CORE 10-6 How can you use set theory to
outcomes) using characteristics (or categories) of the outcomes, or as
help you calculate theoretical
unions, intersections, or complements of other events ("or," "and," "not").
probabilities?
CORE 11-1 How do you identify cross
sections of three-dimensional
figures and how do you use
rotations to generate threedimensional figures?
Skills/Procedures
• Calculate theoretical
probability.
• Identify cross sections of a
cylinder.
• Generate three dimensional
figures.
2 days
• Compare densities.
• Find the volume of an oblique
cylinder.
2 days
• Solve a volume problem.
2 days
• Solve a volume problem.
1 day
1 day
Page 15 of 20
Last Revised: August 5, 2014
Standard
Resources Essential Questions/Vocabulary Timing
(Concepts to be Understood)
(Days)
G.C.2 - Identify and describe relationships among inscribed angles, radii, CORE 12-1
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.
Skills/Procedures
Differentiation
Intervention
(SIOP, SDAIE, RTI)
If time
What is the relationship
between a tangent line to a permits
circle and the radius drawn
from the center too the point
of tangency?
Prove the tangent-radious
theorem.
G.C.2 - Identify and describe relationships among inscribed angles, radii, CORE 12-2 How are arcs and chords of circles If time
and chords. Include the relationship between central, inscribed, and
associated with central angles?
permits
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.
G.CO.1 - Know precise definitions of angle, circle, perpendicular line, CORE 12-3 How do you find the area of a
If time • Find the area of a sector. Find
parallel line, and line segment, based on the undefined notions of point,
sector of a circle, and how do you permits arc length.
line, distance along a line, and distance around a circular arc.
calculate arc length in a circle?
• Convert to radian measure.
G.C.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.
G.GMD.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.
G.C.2 - Identify and describe relationships among inscribed angles, radii, CORE 12-4 What is the relationship between If time • Find arc and angle measures.
and chords. Include the relationship between central, inscribed, and
central angles and inscribed
permits
circumscribed angles; inscribed angles on a diameter are right angles; the
angles in a circle?
radius of a circle is perpendicular to the tangent where the radius
intersects the circle.
G.C.3 - Construct the inscribed and circumscribed circles of a triangle,
and prove properties of angles for a quadrilateral inscribed in a circle.
G.CO.9 - Prove theorems about lines and angles. Theorems include:
CORE 12-5 When two tangents are
If time
vertical angles are congruent; when a transversal crosses parallel lines,
drawn to a circle, how do permits
alternate interior angles are congruent and corresponding angles are
you find the measure of the
congruent; points on a perpendicular bisector of a line segment are
angle formed at their
exactly those equidistant from the segment's endpoints.
intersections?
G.C.4 - Construct a tangent line from a point outside a given circle to
the circle.
Prove circumscribed angle
theorem.
Monrovia Unified School District
Instructional Pacing Guide
Geometry
Page 16 of 20
Last Revised: August 5, 2014
Standard
Resources Essential Questions/Vocabulary Timing
(Concepts to be Understood)
(Days)
Skills/Procedures
G.C.2 - Identify and describe relationships among inscribed angles, radii, CORE 12-6
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.
G.MG.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).*
How can you estimate the If time • Approximate distance to the
distance to the horizon using permits horizon.
results about segments
related to circles?
A.REI.7 - Solve a simple system consisting of a linear equation and a
CORE 12-7
quadratic equation in two variables algebraically and graphically. For
example, find the points of intersection between the line y = -3x and the
circle x2 + y2 = 3.
G.GPE.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.
G.GPE.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).
Chapter 12 Cumulative Test - Target Date - 5/23/14
Assessed Performance Task to be given with the Summative
Assessment
SUMMATIVE ASSESSMENT (Benchmark) June 4th- June 6th
How can you write and use If time • Find the center and radius of a
equations of circles in the permits circle.
• Write a coordinate proof.
coordinate plane?
Monrovia Unified School District
Instructional Pacing Guide
Differentiation
Intervention
(SIOP, SDAIE, RTI)
Secant-tangent product
theorem
• Solve a system by graphing.
Derive the equation of a
circle.
1 day
3 days
Geometry
Page 17 of 20
Last Revised: August 5, 2014
Department Policies
Grading Scale:
97% - 100%
93% - 96%
90% - 92%
87% - 89%
83% - 86%
80% - 82%
77% - 79%
73% - 76%
70% - 72%
67% - 69%
66% - 60%
0% - 50%
A+
A
AB+
B
BC+
C
CD+
D
F
Grade Weights:
Assignment Type
Percent of Grade
Assessments/Projects
35%
Assignments
30%
Interim #1/#3
10%
Interim #2/#4
25%
Makeup Work: Makeup work is accepted for full credit if the student have an excused absence. The student will have an amount of time equal to the number of days absent to complete
any missed assignments.
Late Work Policy: Late work may be accepted at the discretion of the teacher.
Testing Policy: Students will be allowed to make-up a test if they have an excused absence. They will have the amount of days equal to the days they were absent to prepare for the test.
Teacher Policies: [please insert relevant policy]
Monrovia Unified School District
Instructional Pacing Guide
Geometry
Page 18 of 20
Last Revised: August 5, 2014