Download Geometry Q3

ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
Grade Level
Expectation
Evidence Outcome
2. Concepts of similarity
are foundational to
geometry and its
applications
a.Understand similarity in terms of
similarity transformations. (CCSS: GSRT)
i.
ii.
iii.
2. Concepts of similarity
are foundational to
geometry and its
applications
Student-Friendly
Learning Objective
We will identify similar
polygons and apply
properties similar polygons
in problem solving
Level of
Thinking
Resource Correlation
Comp
Apply
7.2 Ratios in Similar
Polygons
Verify experimentally the
properties of dilations given
by a center and a scale
factor. (CCSS: G-SRT.1)
b. Prove theorems involving
similarity. (CCSS: G-SRT)
Academic
Vocabulary
Similar
Similar Polygons
Similarity Ratio
7.2 Tech Lab- Explore
the Golden Ratio pg 460
V
Given two figures, use the
definition of similarity in
terms of similarity
transformations to decide if
they are similar. (CCSS: GSRT.2)
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.
(CCSS: G-SRT.2)
a. Understand similarity in terms of
similarity transformations. (CCSS: GSRT)
i.
TIMELINE: 3rd Quarter
GRADE: High School
(NOTE in CC Edition this
is section 7.1 pg 466)
(Note: 7.1 Ratios and
Proportions in original
edition is not aligned
with new state
standards. It may need
to be presented as a
review at the beginning
of this lesson.)
We will draw and describe
similarity transformations in
a coordinate plane.
We will apply properties of
similarity transformations to
determine whether
polygons are similar and to
prove that all circles are
similar.
Apply
Evaluate
Synthesis
7.2 Similarity and
transformations
Similarity
Transformation
IN CC Edition Only pg
472
ii. Prove that all circles are similar.
(CCSS: G-C.1)
© Learning Keys, 800.927.0478, www.learningkeys.org
Page 1
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
Grade Level
Expectation
Evidence Outcome
2. Concepts of similarity
are foundational to
geometry and its
applications
a.Understand similarity in terms of
similarity transformations. (CCSS: GSRT).
ii. Given two figures, use the
definition of similarity in terms of
similarity transformations to decide if
they are similar. (CCSS: G-SRT.2)
TIMELINE: 3rd Quarter
GRADE: High School
Student-Friendly
Learning Objective
We will prove triangles are
similar by applying AA, SSS
and SAS and apply in
problem solving
Level of
Thinking
Apply
Analysis
Evaluate
Resource Correlation
Academic
Vocabulary
7.3 Triangle Similarity
AA, SSS and SAS pg
470
(pg 482 in CC Edition)
7.3 Tech Lab- Predict
Triangle Similarity
Relationships pg 468
iii. 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. (CCSS:
G-SRT.2)
iv. Use the properties of similarity
transformations to establish the AA
criterion for two triangles to be
similar. (CCSS: G-SRT.3)
a. Prove theorems involving
similarity. (CCSS: G-SRT)
iii. Use congruence and similarity
criteria for triangles to solve
problems and to prove relationships
in geometric figures. (CCSS: GSRT.5)
© Learning Keys, 800.927.0478, www.learningkeys.org
Page 2
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
Grade Level
Expectation
Evidence Outcome
2. Concepts of similarity
are foundational to
geometry and its
applications
a.Understand similarity in terms of
similarity transformations. (CCSS: GSRT)
ii.Given two figures, use the
definition of similarity in terms of
similarity transformations to decide if
they are similar. (CCSS: G-SRT.2)
iii. 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. (CCSS:
G-SRT.2)
TIMELINE: 3rd Quarter
GRADE: High School
Student-Friendly
Learning Objective
We will apply properties of
similar triangles to find
segment lengths and apply
proportionality and triangle
angle bisector theorems in
problem solving.
Level of
Thinking
Apply
Resource Correlation
Academic
Vocabulary
7.4- Applying Properties
of Similar Triangles pg
481
(CC edition pg 495)
7.4 Technology Lab –
Investigate Angle
Bisectors of a triangle
pg 480
(CC Edition pg 494)
b. Prove theorems involving
similarity. (CCSS: G-SRT)
i. Prove theorems about
triangles.9 (CCSS: G-SRT.4)
iii. Use congruence and similarity
criteria for triangles to solve
problems and to prove relationships
in geometric figures. (CCSS: GSRT.5)
© Learning Keys, 800.927.0478, www.learningkeys.org
Page 3
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
Grade Level
Expectation
Evidence Outcome
2. Concepts of similarity
are foundational to
geometry and its
applications
b. Prove theorems involving
similarity. (CCSS: G-SRT)
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)
iii. Use congruence and
similarity criteria for triangles to
solve problems and to prove
relationships in geometric
figures. (CCSS: G-SRT.5)
i.
ii.
iii.
iv.
TIMELINE: 3rd Quarter
GRADE: High School
S
Represent transformations in
the plane using1 appropriate
tools. (CCSS: G-CO.2)
Describe transformations as
functions that take points in
the plane as inputs and give
other points as outputs.
(CCSS: G-CO.2)
Compare transformations
that preserve distance and
angle to those that do
not.2 (CCSS: G-CO.2)
© Learning Keys, 800.927.0478, www.learningkeys.org
Student-Friendly
Learning Objective
Level of
Thinking
We will apply ratios to make
indirect measurements and
apply scale drawing in
problem solving
Apply
We will apply Similarity
properties in the coordinate
plane (dilations) and write
coordinate proofs to prove
figures similar
Apply
Synthesis
Resource Correlation
7.5 Using Proportional
Relationships pg 488
Academic
Vocabulary
Indirect Measurement
Scale Drawing
Scale
(CC Edition pg 502)
7.6 Dilations and
Similarity in the
coordinate Plane pg 495
Dilation
Scale Factor
(CC edition pg 509)
Connecting Geometry to
Algebra- Direct Variation
pg 501
(CC edition pg 517)
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ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
Grade Level
Expectation
Evidence Outcome
2. Concepts of similarity
are foundational to
geometry and its
applications
c. Define trigonometric ratios and
solve problems involving right
triangles. (CCSS: G-SRT)
i.
2. Concepts of similarity
are foundational to
geometry and its
applications
2. Concepts of similarity
are foundational to
geometry and its
applications
TIMELINE: 3rd Quarter
GRADE: High School
Explain that by similarity,
side ratios in right triangles
are properties of the angles
in the triangle, leading to
definitions of trigonometric
ratios for acute angles.
(CCSS: G-SRT.6)
c. Define trigonometric ratios and
solve problems involving right
triangles. (CCSS: G-SRT)
i. Explain that by similarity, side
ratios in right triangles are properties
of the angles in the triangle, leading
to definitions of trigonometric ratios
for acute angles. (CCSS: G-SRT.6)
c. Define trigonometric ratios and
solve problems involving right
triangles. (CCSS: G-SRT)
ii. Explain and use
Student-Friendly
Learning Objective
Level of
Thinking
Resource Correlation
We will apply geometric
means to find segment
lengths in right triangles
and apply similarity
relationships in right
triangles to solve problems
Apply
8.1 Similarity in Right
Triangles pg 518
We will find sine, cosine
and tangent of acute
angles. We will apply
trigonometric ratios to find
side lengths in right
triangles and apply in
problem solving
Apply
We will apply the
relationship between the
sine and cosine of
complementary angles
Apply
Academic
Vocabulary
Geometric Mean
(CC edition pg 534)
8.2 Trigonometric Ratios
pg 525
(CC Edition pg 540)
Trigonometric Ratios
Sine
Cosine
Tangent
8.2 Technology LabExplore Trigonometric
Ratios pg 524
Trigonometric Ratios
and Complementary
Angles
CC Edition ONLY pg 549
the relationship
between the sine
and cosine of
complementary
angles. (CCSS: GSRT.7)
© Learning Keys, 800.927.0478, www.learningkeys.org
Page 5
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
Grade Level
Expectation
2. Concepts of similarity
are foundational to
geometry and its
applications
TIMELINE: 3rd Quarter
GRADE: High School
Evidence Outcome
a. Define trigonometric ratios
and solve problems involving
right triangles. (CCSS: GSRT)
Student-Friendly
Learning Objective
Level of
Thinking
We will apply inverse
trigonometric ratios to find
angle measures in right
triangles and apply in
problem solving
Apply
a. Define trigonometric ratios
and solve problems involving
right triangles. (CCSS: GSRT)
We will solve problems
involving angles of
elevation and angles of
depression
Apply
b. Use the rules of probability to
compute probabilities of
compound events in a uniform
probability model. (CCSS: S-CP)
iv.Use permutations and
combinations to compute
probabilities and solve problems
(CCSS: S-CP.9)
© Learning Keys, 800.927.0478, www.learningkeys.org
8.3- Solving Right
Triangles pg 534
8.4 Angles of Elevation
and Depression pg 544
Angle of Elevation
Angle of Depression
(CC edition pg 562)
8.4 Geometry LabIndirect Measurement
Using Trigonometry pg
550
iii. Use trigonometric ratios
and the Pythagorean
Theorem to solve right
triangles in applied
problems.* (CCSS: GSRT.8)
3. Probability models
outcomes for situations
in which there is
inherent randomness
Academic
Vocabulary
(CC Edition pg 552)
Connecting Geometry to
Algebra – Inverse
Functions pg 533
iii. Use trigonometric ratios
and the Pythagorean
Theorem to solve right
triangles in applied
problems.* (CCSS: GSRT.8)
2. Concepts of similarity
are foundational to
geometry and its
applications
Resource Correlation
NOTE 8.5 and 8.6 not in
Colorado Standards
We will solve problems
involving the Fundamental
Counting Principal,
permutations and
combinations
Apply
13.1 Permutations and
Combinations pg 870
CC edition
(NOTE this whole
chapter is in CC Edition
only)
Fundamental
Counting Principal
Permutation
Factorial
Combination
Page 6
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
Grade Level
Expectation
3. Probability models
outcomes for situations
in which there is
inherent randomness
3. Probability models
outcomes for situations
in which there is
inherent randomness
Evidence Outcome
b. Use the rules of probability to
compute probabilities of
compound events in a uniform
probability model. (CCSS: S-CP)
iv.Use permutations and
combinations to compute
probabilities and solve problems
(CCSS: S-CP.9)
a.Understand independence and
conditional probability and use them
to interpret data. (CCSS: S-CP)
i. Describe events as subsets of a
sample space5 using characteristics
(or categories) of the outcomes, or
as unions, intersections, or
complements of other
events.6(CCSS: S-CP.1)
TIMELINE: 3rd Quarter
GRADE: High School
Student-Friendly
Learning Objective
Level of
Thinking
We will compare theoretical
and experimental
probability, find the
probability of theoretical
and experimental
probability and apply in
geometric probability
problems
Apply
Analysis
We will determine whether
events are independent or
dependant. We find the
probability of independent
and dependant events.
Apply
Analysis
Evaluate
Resource Correlation
13.2 Theoretical and
Experimental Probability
pg 878 CC edition
13.2 Technology Lab
Explore Simulations pg
886 CC Edition
13.3 Independent and
Dependant Events pg
887 CC Edition
Academic
Vocabulary
Probability
Outcome
Sample Space
Event
Equally likely
outcomes
Favorable outcomes
Theoretical
probability
Complement
Geometric Probability
Experiment
Trial
Experimental
probability
Independent Events
Dependant Events
Conditional
probability
ii. Explain that two events A and B
are independent if the probability of
A and B occurring together is the
product of their probabilities, and use
this characterization to determine if
they are independent. (CCSS: SCP.2)
iii. Using the conditional probability of
A given B as P(A and B)/P(B),
© Learning Keys, 800.927.0478, www.learningkeys.org
Page 7
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
Grade Level
Expectation
Evidence Outcome
TIMELINE: 3rd Quarter
GRADE: High School
Student-Friendly
Learning Objective
Level of
Thinking
Resource Correlation
Academic
Vocabulary
interpret the 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.
(CCSS: S-CP.3)
v. Recognize and explain the
concepts of conditional probability
and independence in everyday
language and everyday
situations.8 (CCSS: S-CP.5)
3. Probability models
outcomes for situations
in which there is
inherent randomness
a. Understand independence and
conditional probability and use them
to interpret data. (CCSS: S-CP)
Iv .Construct and interpret two-way
frequency tables of data when two
categories are associated with each
object being classified. Use the twoway table as a sample space to
decide if events are independent and
to approximate conditional
probabilities.7 (CCSS: S-CP.4)
© Learning Keys, 800.927.0478, www.learningkeys.org
We will construct and
interpret two-way frequency
tables of data when two
categories are associated
with each object being
classified.
Apply
Evaluate
Synthesis
13.4 Two way tables pg
899 CC Edition
Joint Relative
Frequency
Marginal relative
frequency
Conditional relative
frequency
Page 8
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Geometry
TIMELINE: 3rd Quarter
GRADE: High School
Grade Level
Expectation
Evidence Outcome
3. Probability models
outcomes for situations
in which there is
inherent randomness
b. Use the rules of probability to
compute probabilities of compound
events in a uniform probability
model. (CCSS: S-CP)
i.
ii.
Student-Friendly
Learning Objective
We will find the probability
of mutually exclusive events
and inclusive events and
apply in problem solving
Level of
Thinking
Apply
Resource Correlation
13.5 Compound Events
pg 907 CC Edition
Academic
Vocabulary
Simple Event
Compound Event
Mutually Exclusive
Events
Inclusive Events
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. (CCSS:
S-CP.6)
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.
(CCSS: S-CP.7)
© Learning Keys, 800.927.0478, www.learningkeys.org
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