Download Geometry Q1 - Rocky Ford School District

ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
Grade Level
Expectation
Evidence Outcome
Student-Friendly
Learning Objective
1. Objects in the plane
can be transformed, and
those transformations
can be described and
analyzed mathematically
a. Experiment with transformations
in the plane. (CCSS: G-CO)
We will identify, name and
draw points, lines, segments
rays and planes and apply
basic facts about points
lines and planes.
i.
State 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. (CCSS: GCO.1)
1. Objects in the plane
can be transformed, and
those transformations
can be described and
analyzed mathematically
d. Make geometric constructions.
(CCSS: G-CO)
1. Objects in the plane
can be transformed, and
those transformations
can be described and
analyzed mathematically
d. Make geometric constructions.
(CCSS: G-CO)
i.
ii.
TIMELINE: 1st Quarter
GRADE: High School
Make formal geometric
constructions7 with a variety
of tools and
methods.8 (CCSS: GCO.12)
Make formal geometric
constructions7 with a variety
of tools and
methods.8 (CCSS: GCO.12)
© Learning Keys, 800.927.0478, www.learningkeys.org
Level of
Thinking
Know
Apply
Resource Correlation
Holt McDougal GeometryCommon Core Edition
Teachers Editionpg 6
1.1 Understanding Points,
Lines and Planes
Academic
Vocabulary
Point
Line
Plane
Collinear
Coplanar
Segment
Endpoint
Ray
Opposite rays
postulate
We will apply length and
midpoint of a segment and
construct midpoints and
congruent segments
Apply
Synthesis
1.2 Measuring and
constructing segements
Pg 13
Coordinate
Distance
Length
Congruent
segments
Construction
Between
Midpoint
Bisect
Segment bisector
We will name and classify
angles. We will also
measure and construct
angles and angle bisectors.
Know
Apply
Synthesis
1.3 Measuring and
Constructing Angles
Pg 20
Angle
Vertex
Interior of an angle
Exterior of an angle
Measure
Degree
Acute angle
Right angle
Obtuse angle
Straight angle
Congruent angles
Angle bisector
Page 1
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
Grade Level
Expectation
1. Objects in the plane
can be transformed, and
those transformations
can be described and
analyzed mathematically
3. Expressions can be
represented in multiple,
equivalent forms
4. Solutions to
equations, inequalities
and systems of
equations are found
using a variety of tools
Evidence Outcome
a. Experiment with
transformations in the plane.
(CCSS: G-CO)
i.
State 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. (CCSS: GCO.1)
a.Interpret the structure of
expressions.(CCSS: A-SSE)
i.
TIMELINE: 1st Quarter
GRADE: High School
Interpret expressions that
represent a quantity in
terms of its context.*
(CCSS: A-SSE.1)
Student-Friendly
Learning Objective
Level of
Thinking
Resource Correlation
Academic
Vocabulary
We will identify adjacent,
vertical, complementary and
supplementary angles. We
will solve to find measures
of pairs of angles and apply
in problem solving.
Know
Apply
1.4 Pairs of Angles pg 28
Adjacent Angles
Linear Pair
Complementary
Angles
Supplementary
Angles
Vertical Angles
We will apply formulas for
perimeter, area and
circumference, rearrange
formulas to isolate particular
terms and apply in problem
solving
Apply
1.5 Using Formulas in
Geometry pg 36
Perimeter
Area
Base
Height
Diameter
Radius
Circumference
pi
a.Create equations that describe
numbers or relationships. (CCSS: ACED)
iv. Rearrange formulas to
highlight a quantity of
interest, using the same
reasoning as in solving
equations.22 (CCSS: ACED.4)
© Learning Keys, 800.927.0478, www.learningkeys.org
Page 2
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
TIMELINE: 1st Quarter
GRADE: High School
Grade Level
Expectation
Evidence Outcome
Student-Friendly
Learning Objective
3. Objects in the plane
can be described and
analyzed algebraically
a. Express Geometric Properties
with Equations. (CCSS: G-GPE)
We will develop and apply
the formula for midpoint on
the coordinate plane. We
will apply the Pythagorean
theorem to develop the
distance formula to find the
distance between two points
on a coordinate plane.
ii. Use coordinates to prove
simple geometric theorems
algebraically. (CCSS: G-GPE)
4. Use coordinates and the
distance formula to compute
perimeters of polygons and
areas of triangles and
rectangles.* (CCSS: GGPE.7)
© Learning Keys, 800.927.0478, www.learningkeys.org
Level of
Thinking
Apply
Analysis
synthesis
Resource Correlation
1.6 Midpoint and
distance in the coordinate
plane. Pg 43
Academic
Vocabulary
Coordinate plane
Leg
hypotenuse
Page 3
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
Grade Level
Expectation
Evidence Outcome
Student-Friendly
Learning Objective
1. Objects in the plane
can be transformed, and
those transformations
can be described and
analyzed mathematically
a. Experiment with transformations
in the plane. (CCSS: G-CO)
We will identify reflections,
rotations and translations.,
represent transformations
with functions and graph
transformations in the
coordinate plane.
ii.Represent transformations in the
plane using1 appropriate tools.
(CCSS: G-CO.2)
iii.Describe transformations as
functions that take points in the
plane as inputs and give other
points as outputs. (CCSS: G-CO.2)
TIMELINE: 1st Quarter
GRADE: High School
Level of
Thinking
Know
Comp
Apply
Sythesis
Resource Correlation
1.7 Transformation in the
coordinate plane pg 50
1.7 Tech Lab Explore
transformations Tech
lab. (Geometry Software
required.)
(Could also use NCTM
online manipulativesgeometry,
transformations)
Academic
Vocabulary
Transformation
Preimage
Image
Reflection
Rotation
translation
iv. Compare transformations that
preserve distance and angle to
those that do not.2 (CCSS: G-CO.2)
vi.Develop definitions of rotations,
reflections, and translations in terms
of angles, circles, perpendicular
lines, parallel lines, and line
segments. (CCSS: G-CO.4)
vii.Given a geometric figure and a
rotation, reflection, or translation,
draw the transformed figure using
appropriate tools.3 (CCSS: G-CO.5)
© Learning Keys, 800.927.0478, www.learningkeys.org
Page 4
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
TIMELINE: 1st Quarter
GRADE: High School
Grade Level
Expectation
Evidence Outcome
Student-Friendly
Learning Objective
1. Objects in the plane
can be transformed, and
those transformations
can be described and
analyzed mathematically
PREP for
We will apply inductive
reasoning to identify
patterns and make
conjectures. We will write
counterexamples to
disprove conjectures.
c. Prove geometric theorems.
(CCSS: G-CO)
i.
ii.
iii.
Prove theorems
about lines and
angles.4 (CCSS: GCO.9)
Prove theorems
about
triangles.5 (CCSS:
G-CO.10)
Prove theorems
about
parallelograms.6 (C
CSS: G-CO.11)
© Learning Keys, 800.927.0478, www.learningkeys.org
Level of
Thinking
Apply
Analysis
Synthesis
Evaluation
Resource Correlation
2.1 Using inductive
reasoning to make
conjectures. Pg 74
Academic
Vocabulary
Inductive
Reasoning
Conjecture
Counter Example
Page 5
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
TIMELINE: 1st Quarter
GRADE: High School
Grade Level
Expectation
Evidence Outcome
Student-Friendly
Learning Objective
1. Objects in the plane
can be transformed, and
those transformations
can be described and
analyzed mathematically
PREP for
We will identify, write and
analyze the truth value of
conditional statements. We
will write inverse, converse,
and contrapositive of a
conditional statement.
c. Prove geometric theorems.
(CCSS: G-CO)
i.
ii.
iii.
Prove theorems
about lines and
angles.4 (CCSS: GCO.9)
Prove theorems
about
triangles.5 (CCSS:
G-CO.10)
Prove theorems
about
parallelograms.6 (C
CSS: G-CO.11)
© Learning Keys, 800.927.0478, www.learningkeys.org
Level of
Thinking
Know
Apply
Analysis
Synthesis
Evaluation
Resource Correlation
2.2 Conditional
Statements pg 81
(2.3 Geometry Lab,
Solving Logic Puzzles pg
94. After Conditional
Statements)
Academic
Vocabulary
Conditional
statement
Hypothesis
Conclusion’
Truth value
Negation
Converse
Inverse
Contrapositive
Logically equivalent
statements
Page 6
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
TIMELINE: 1st Quarter
GRADE: High School
Grade Level
Expectation
Evidence Outcome
Student-Friendly
Learning Objective
1. Objects in the plane
can be transformed, and
those transformations
can be described and
analyzed mathematically
PREP for
We will evaluate if a
statement is applying
inductive or deductive
reasoning and apply the law
of detachment and the Law
of Syllogism in logical
reasoning to make
c. Prove geometric theorems.
(CCSS: G-CO)
i.
ii.
iii.
Prove theorems
about lines and
angles.4 (CCSS: GCO.9)
Prove theorems
about
triangles.5 (CCSS:
G-CO.10)
Prove theorems
about
parallelograms.6 (C
CSS: G-CO.11)
© Learning Keys, 800.927.0478, www.learningkeys.org
Level of
Thinking
Apply
Evaluate
Resource Correlation
Academic
Vocabulary
2.3 Using deductive
reasoning to Verify
Conjectures
Deductive
Reasoning
Page 7
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
TIMELINE: 1st Quarter
GRADE: High School
Grade Level
Expectation
Evidence Outcome
Student-Friendly
Learning Objective
1. Objects in the plane
can be transformed, and
those transformations
can be described and
analyzed mathematically
PREP for
We will write and analyze
biconditional statements
and apply in writing
definitions of geometry
terms.
c. Prove geometric theorems.
(CCSS: G-CO)
i.
ii.
iii.
Prove theorems
about lines and
angles.4 (CCSS: GCO.9)
Prove theorems
about
triangles.5 (CCSS:
G-CO.10)
Prove theorems
about
parallelograms.6 (C
CSS: G-CO.11)
© Learning Keys, 800.927.0478, www.learningkeys.org
Level of
Thinking
Apply
Sythesis
Evaluate
Analysis
Resource Correlation
2.4 Biconditional
Statements and
definitions pg 96
Academic
Vocabulary
Biconditional
statements
Definition
Polygon
Triangle
quadrilateral
Page 8
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
TIMELINE: 1st Quarter
GRADE: High School
Grade Level
Expectation
Evidence Outcome
Student-Friendly
Learning Objective
1. Objects in the plane
can be transformed, and
those transformations
can be described and
analyzed mathematically
PREP for
We will identify properties of
equality and congruence
and apply the properties to
write algebraic proofs.
Know
Apply
Synthesis
2.5 Algebraic Proof pg
104
proof
We will prove geometric
theorems about lines and
angles by applying
deductive reasoning and
write proofs in two-column
form
Anal
Synthesis
Evaluation
2.6 Geometric Proof pg
110
(Geometry Lab 2.6 Design
Plans for proofs pg 117)
Theorem
Two-column proof
c. Prove geometric theorems.
(CCSS: G-CO)
i.
ii.
iii.
1. Objects in the plane
can be transformed, and
those transformations
can be described and
analyzed mathematically
Resource Correlation
Academic
Vocabulary
Prove theorems
about lines and
angles.4 (CCSS: GCO.9)
Prove theorems
about
triangles.5 (CCSS:
G-CO.10)
Prove theorems
about
parallelograms.6 (C
CSS: G-CO.11)
c. Prove geometric theorems.
(CCSS: G-CO)
i.
Level of
Thinking
Prove theorems
about lines and
angles.4 (CCSS: GCO.9)
© Learning Keys, 800.927.0478, www.learningkeys.org
Page 9
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
TIMELINE: 1st Quarter
GRADE: High School
Grade Level
Expectation
Evidence Outcome
Student-Friendly
Learning Objective
1. Objects in the plane
can be transformed, and
those transformations
can be described and
analyzed mathematically
c. Prove geometric theorems.
(CCSS: G-CO)
We will prove geometric
theorems about triangles by
applying deductive
reasoning and write proofs
in flowchart and paragraph
forms.
Anal
Synthesis
Evaluation
2.7 Flow Chart and
Paragraph Proofs pg 118
Flowchart proof
Paragraph Proof
1. Objects in the plane
can be transformed, and
those transformations
can be described and
analyzed mathematically
a. Experiment with transformations
in the plane. (CCSS: G-CO)
We will identify parallel,
perpendicular and skew
lines and apply in problem
solving. We will identify the
angles formed by two lines
and a transversal and apply
in problem solving.
Know
Comp
Apply
3.1 Lines and angles pg
146
Parallel lines
Perpendicular lines
Skew lines
Parallel planes
Transversal
Corresponding
angles
Alternate interior
angles
Alternate exterior
angles
Same-side interior
angles
. Objects in the plane
can be transformed, and
those transformations
can be described and
analyzed mathematically
c. Prove geometric theorems
(CCSS: G-CO)
We will prove and apply
theorems about angles
formed by parallel lines and
a transversal and apply in
problem solving
Apply
Analysis
Synthesis
ii.
i.
Prove theorems
about
triangles.5 (CCSS:
G-CO.10)
State 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. (CCSS: GCO.1)
i.
Prove theorems
about lines and
angles.4 (CCSS: GCO.9)
Level of
Thinking
Resource Correlation
(Connecting to Algebra,
Systems of equations pg
152)
Academic
Vocabulary
3.2 Angles formed by
parallel lines and
transversals pg 155
(3.2 Tech lab Explore
Parallel lines and
transversals. Pg 154
Requires geometry
software)
.
© Learning Keys, 800.927.0478, www.learningkeys.org
10
Page
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
TIMELINE: 1st Quarter
GRADE: High School
Grade Level
Expectation
Evidence Outcome
Student-Friendly
Learning Objective
. Objects in the plane
can be transformed, and
those transformations
can be described and
analyzed mathematically
c. Prove geometric theorems
(CCSS: G-CO)
We will apply the angles
formed by a transversal to
prove two lines are parallel.
i.
Prove theorems
about lines and
angles.4 (CCSS: GCO.9)
We will apply the properties
of a transversal to construct
parallel lines
Level of
Thinking
Apply
Evaluate
Synthesis
Resource Correlation
Academic
Vocabulary
3.3 Proving lines parallel
pg 162
(3.3 Geometry Lab,
Construct Parallel Lines
pg 170)
d. Make geometric constructions.
(CCSS: G-CO)
i.
Make formal geometric
constructions7 with a variety
of tools and
methods.8 (CCSS: GCO.12)
© Learning Keys, 800.927.0478, www.learningkeys.org
11
Page
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
Grade Level
Expectation
Evidence Outcome
Student-Friendly
Learning Objective
Objects in the plane can
be transformed, and
those transformations
can be described and
analyzed mathematically
c. Prove geometric theorems
(CCSS: G-CO)
We will prove and apply
theorems about
perpendicular lines.
i.
Prove theorems
about lines and
angles.4 (CCSS: GCO.9)
d. Make geometric constructions.
(CCSS: G-CO)
ii.
3. Objects in the plane
can be described and
analyzed algebraically
TIMELINE: 1st Quarter
GRADE: High School
Level of
Thinking
Apply
Evaluate
Synthesis
Resource Correlation
3.4 Perpendicular Lines
pg 172
(3.4 Geometry Lab
Construct Perpendicular
Lines pg 179)
We will apply properties of
perpendicular lines to
construct perpendicular
bisectors and perpendicular
lines.
Academic
Vocabulary
Perpendicular
bisector
Distance from a
point to a line
Make formal geometric
constructions7 with a variety
of tools and
methods.8 (CCSS: GCO.12)
a. Express Geometric Properties
with Equations. (CCSS: G-GPE)
ii. Use coordinates to prove
simple geometric theorems
algebraically. (CCSS: GGPE)
We will find the slope of a
line and apply slope
evaluate if lines are parallel
or perpendicular.
Apply
Evaluate
3.5 Slope of lines pg 182
Rise
Run
slope
2. Prove the slope
criteria for parallel and
perpendicular lines and
use them to solve
geometric
problems.12(CCSS: GGPE.5)
© Learning Keys, 800.927.0478, www.learningkeys.org
12
Page
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
TIMELINE: 1st Quarter
GRADE: High School
Grade Level
Expectation
Evidence Outcome
Student-Friendly
Learning Objective
3. Objects in the plane
can be described and
analyzed algebraically
a. Express Geometric Properties
with Equations. (CCSS: G-GPE)
We will graph lines and
write their equations in
slope-intercept and pointslope form. We will evaluate
lines to classify them as
parallel, intersecting or
coinciding)
ii. Use coordinates to prove
simple geometric theorems
algebraically. (CCSS: GGPE)
Level of
Thinking
Apply
Analysis
Synthesis
Resource Correlation
3.6 Lines in the
Coordinate Plane pg 190
Academic
Vocabulary
Point Slope Form
Slope-Intercept
Form
(3.6 Technology Lab pg
188 Explore parallel and
perpendicular lines )
2. Prove the slope
criteria for parallel and
perpendicular lines and
use them to solve
geometric
problems.12(CCSS: GGPE.5)
© Learning Keys, 800.927.0478, www.learningkeys.org
13
Page
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
GRADE: High School
Grade Level
Expectation
Evidence Outcome
Student-Friendly
Learning Objective
1. Visual displays and
summary statistics
condense the
information in data sets
into usable knowledge
b. Summarize, represent, and
interpret data on two categorical and
quantitative variables. (CCSS: S-ID)
We will review scatterplots
and apply linear equation
skills learned in 3.6 to
graphing and writing
equations for lines
associated with data sets.
ii. Represent data on two
quantitative variables on a scatter
plot, and describe how the variables
are related. (CCSS: S-ID.6)
Level of
Thinking
TIMELINE: 1st Quarter
Resource Correlation
Scatter Plots and Lines of
Best Fit – Connecting
Geometry to Data
Analysis pg 198
Academic
Vocabulary
Scatterplot
Lines of Best Fit
2.Informally assess the fit of a
function by plotting and analyzing
residuals. (CCSS: S-ID.6b)
3. Fit a linear function for a scatter
plot that suggests a linear
association. (CCSS: S-ID.6c)
© Learning Keys, 800.927.0478, www.learningkeys.org
14
Page