Download RCHS Rev. 06/2011 Geometry A Unit 4 Expressing Geometric

RCHS Rev. 06/2011
Geometry
A
Unit 4 Expressing Geometric Properties With Equations
Length of
Unit
KY Common Core
Academic
Standards
___weeks
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).
Rowan County Senior High School 2010-2011
Vocabulary/Learning Targets
Vocabulary: side length, vertex, first quadrant, slope,
distance, midpoint, parallel, perpendicular, intersecting
Activities/Assessments/
Resources
Note:
Same with Unit 5
Unit Learning targets
Students will be able to:
I can recall previous understandings of coordinate
geometry (including, but not limited to: distance, midpoint
and slope formula, equation of a line, definitions of parallel
and perpendicular lines, etc.) (K)
From Appendix A: This unit has a close connection
with the next unit. For example, a curriculum might
merge G.GPE.1 and the unit 5 treatment of G.GPE.4
with the standards in this unit. Reasoning with
triangles in this unit is limited to right triangles;
I can represent the vertices of a figure in the coordinate
plane using variables. (R)
I can connect a property of a figure to the tool needed to
verify that property. (R)
I can use coordinates and the right tool to prove or
disprove a claim about a figure.
For example:
Use slope to determine if sides are parallel,
intersecting, or perpendicular;
Use the distance formula to determine if sides are
congruent or to decide if a point is inside a circle, outside a
circle, or on the circle;
Use the midpoint formula or the distance formula to
decide if a side has been bisected. (R)
Page 1
RCHS Rev. 06/2011
Geometry
A
Unit 4 Expressing Geometric Properties With Equations
Length of
Unit
KY Common Core
Academic
Standards
___weeks
G.GPE.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).
Rowan County Senior High School 2010-2011
Vocabulary/Learning Targets
Activities/Assessments/
Resources
Vocabulary: slope, parallel, perpendicular, product, line,
linear equation, slope-intercept form, point slope form
Unit Learning targets
Students will be able to:
I can recognize that slopes of parallel lines are equal. (K)
I can recognize that slopes of perpendicular lines are
opposite reciprocals (i.e, the slopes of perpendicular lines
have a product of -1). (K)
I can find the equation of a line parallel to a given line that
passes through a given point. (K)
I can find the equation of a line perpendicular to a given
line that passes through a given point. (K)
I can prove the slope criteria for parallel and perpendicular
lines and use them to solve geometric problems. (R)
From Appendix A: Relate work on parallel lines in
G.GPE.5 to work on A.REI.5 in High School Algebra 1
involving systems of equations having no solution or
infinitely many solutions.
Parallel Lines:
I can draw a line on a coordinate plane and translate that
line to produce its image. (K)
I can explain that these lines are parallel since translations
preserve angle. (K)
I can determine the slope of the original line and its image
after translation and show they have the same slope using
specific examples and general coordinates (x,y). (R)
I can state that parallel lines have the same slope. (K)
I can determine if lines are parallel using their slopes. (R)
Page 2
RCHS Rev. 06/2011
Geometry
A
I can write an equation for a line that is parallel to a given
line that passes through a given point. (R)
Perpendicular Lines:
I can draw a line on a coordinate plane and rotate that line
90° to produce a perpendicular image. (K)
I can determine the slope of the original line and its image
after a 90° rotation and show they have the opposite
reciprocal slopes using specific examples and general
coordinates (x,y). (R)
I can state that perpendicular lines have the opposite
reciprocal slopes. (K)
I can determine if lines are perpendicular using their
slopes. (R)
I can write an equation for a line that is perpendicular to a
given line that passes through a given point. (R)
Rowan County Senior High School 2010-2011
Page 3
RCHS Rev. 06/2011
Geometry
A
Unit 4 Expressing Geometric Properties With Equations
Length of
Unit
KY Common Core
Academic
Standards
___weeks
G.GPE.6 Find the
point on a directed
line segment
between two given
points that
partitions the
segment in a given
ratio.
Vocabulary/Learning Targets
Activities/Assessments/
Resources
Vocabulary: directed line segment, endpoint, ratio
Unit Learning targets
Students will be able to:
I can recall the definition of ratio. (K)
I can recall previous understandings of coordinate
geometry. (K)
Given a line segment (including those with positive and
negative slopes) and a ratio, I can find the point on the
segment that partitions the segment into the given ratio.
(R)
I can calculate the point(s) on a directed line segment
whose endpoints are (x1 ,y1) and (x2,y2) that partitions the
line segment into a given ratio, r1 to r2 using the formula
x = r2x1 +r1x2 and y = r2y1 + r1y2
r1 + r2
r 1 + r2
(e.g., For the directed line segment whose endpoints are
(0,0) and (4,3), the point that partitions the segment into a
ratio of 3 to 2 can be found:
x = (2•0 + 3• 4) = 12 and y = (2•0 + 3• 3) = 9
(3+2)
5
(3 + 2)
5
So the point is (12/5, 9/5).) (R)
Rowan County Senior High School 2010-2011
Page 4
RCHS Rev. 06/2011
Geometry
A
Unit 4 Expressing Geometric Properties With Equations
Length of
Unit
KY Common Core
Academic
Standards
___weeks
G.GPE.7 Use
coordinates to
compute perimeters
of polygons and
area of triangles and
rectangles, e.g.,
using the distance
formula.*(*Modeling
Standard)
Vocabulary/Learning Targets
Activities/Assessments/
Resources
Vocabulary: coordinate plane, coordinates, distance
formula, perimeter, polygon, area, triangle, rectangle
Unit Learning targets
Students will be able to:
I can use the coordinates of the vertices of a polygon to
find the necessary dimensions for finding the perimeter
(i.e., the distance between vertices). (K)
I can use the coordinates of the vertices of a triangle to
find the necessary dimensions (base, height) for finding
the area (i.e., the distance between vertices by counting,
distance formula, Pythagorean Theorem, etc.). (K)
I can use the coordinates of the vertices of a rectangle to
find the necessary dimensions (base, height) for finding
the area (i.e., the distance between vertices by counting,
distance formula). (K)
Formulate a model of figures in contextual problems to
compute area and/or perimeter. (R)
From Appendix A: G.GPE.7 provides practice with the
distance formula and its connection with the
Pythagorean theorem.
I can use coordinates of the vertices of a polygon graphed
in the coordinate plane and use the distance formula to
compute the perimeter. (S)
I can use the coordinates of the vertices of triangles and
rectangles graphed in the coordinate plane to compute
area. (S)
Rowan County Senior High School 2010-2011
Page 5
RCHS Rev. 06/2011
Geometry
A
Unit 4 Expressing Geometric Properties With Equations
Length of
Unit
KY Common Core
Academic
Standards
___weeks
G.GPE.2 Derive the
equation of a
parabola given a
focus and directrix.
Vocabulary/Learning Targets
Activities/Assessments/
Resources
Vocabulary: parabola, focus, directrix, distance formula,
factor, perfect square trinomial
Unit Learning targets
Students will be able to:
I can define a parabola including the relationship of the
focus and the equation of the directrix to the parabolic
shape.
From Appendix A: The directrix should be parallel to a
coordinate axis. (K)
Derive the equation of parabola given the focus and
directrix. (K)
I can define a parabola. (K)
I can find the distance from a point on the parabola (x,y) to
the directrix. (S)
I can find the distance from a point on the parabola (x,y) to
the focus using the distance formula (Phytagorean
Theorem). (S)
I can equate the two distance expressions for a parabola
to write its equation. (S)
I can identify the focus and directrix of a parabola when
given its equation. (R)
Rowan County Senior High School 2010-2011
Page 6
RCHS Rev. 06/2011
Geometry
A
Unit 5 Circles
Length of
Unit
KY Common Core
Academic
Standards
___weeks
G.C.1 Prove that all
circles are similar.
Vocabulary/Learning Targets
Activities/Assessments/
Resources
Vocabulary: circle, similar figures, rigid motion, dilation,
angle measure, preimage, image, central angle
Unit Learning targets
Students will be able to:
I can recognize when figures are similar. (Two figures are
similar if one is the image of the other under a
transformation from the plane into itself that multiplies all
distances by the same positive scale factor, k. That is to
say, one figure is a dilation of the other. ) (K)
I can compare the ratio of the circumference of a circle to
the diameter of the circle. (R)
I can discuss, develop and justify this ratio for several
circles. (R)
Determine that this ratio is constant for all circles. (R)
I can prove that all circles are similar by showing that for a
dilation centered at the center of a circle, the preimage
and the image have equal central measure. (R)
Rowan County Senior High School 2010-2011
Page 7
RCHS Rev. 06/2011
Geometry
A
Unit 5 Circles
Length of
Unit
___weeks
KY Common Core
Academic
Standards
G.C.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.
Rowan County Senior High School 2010-2011
Vocabulary/Learning Targets
Activities/Assessments/
Resources
Vocabulary: central angle, inscribed angle,
circumscribed angle, diameter, radius, chord, tangent,
circle, intersect, endpoints, right angle, perpendicular
Unit Learning targets
Students will be able to:
I can identify inscribed angles, radii, chords, central
angles, circumscribed angles, diameter, and tangent. (K)
I can recognize that inscribed angles on a diameter are
right angles. (K)
I can recognize that radius of a circle is perpendicular to
the radius at the point of tangency. (K)
I can examine the relationship between central, inscribed
and circumscribed angles by applying theorems about
their measures. (R)
I can describe the relationship between a central angle
and the arc it intercepts. (R)
I can describe the relationship between an inscribed angle
and the arc it intercepts. (R)
I can describe the relationship between a circumscribed
angle and the arcs it intercepts. (R)
I can recognize that an inscribed angle whose sides
intersect the endpoints of the diameter of a circle is a right
angle. (K)
I can recognize that the radius of a circle is perpendicular
to the tangent where the radius intersects the circle. (K)
Page 8
RCHS Rev. 06/2011
Geometry
A
Unit 5 Circles
Length of
Unit
___weeks
KY Common Core
Academic
Standards
Vocabulary/Learning Targets
G.C.3 Construct the
inscribed and
circumscribed
circles of a triangle,
and prove
properties of angles
for a quadrilateral
inscribed in a circle.
Vocabulary: inscribed, circumscribed, angle bisector,
perpendicular bisector, construction, compass,
straightedge, intersection, incenter, circle, circumcenter,
quadrilateral, arc, inscribed angle, ARC Addition Postulate,
equation, opposite angles, supplementary
Activities/Assessments/
Resources
Unit Learning targets
Students will be able to:
I can define inscribed and circumscribed circles of a
triangle. (K)
I can recall midpoint and bisector definitions. (K)
I can define a point of concurrency (K)
I can define the terms inscribed, circumscribed, angle
bisector, and perpendicular bisector (K)
I can construct the inscribed circle whose center is the
point of intersection of the angle bisectors (the incenter).
(P)
I can construct the circumscribed circle whose center is
the point of intersection of the perpendicular bisectors of
each side of the triangle (the circumcenter). (P)
I can apply the Arc Addition Postulate to solve for missing
arc measures. (S)
I can prove that opposite angles in an inscribed
quadrilateral are supplementary. (R)
Rowan County Senior High School 2010-2011
Page 9
RCHS Rev. 06/2011
Geometry
A
Unit 5 Circles
Length of
Unit
___weeks
KY Common Core
Academic
Standards
G.C. 4 (+) Construct
a tangent line from a
point outside a
given circle to the
circle.
Vocabulary/Learning Targets
Activities/Assessments/
Resources
Vocabulary: tangent line, circle, perpendicular, radius,
endpoint, midpoint, line segment, point
Unit Learning targets
Students will be able to:
I can recall vocabulary: tangent, radius, perpendicular
bisector, and midpoint (K)
I can identify the center of the circle. (K)
I can define and identify a tangent line. (K)
I can synthesize theorems that apply to circles and
tangents, such as:
Tangents drawn from a common external point are
congruent.
A radius is perpendicular to a tangent at the point of
tangency. (R)
I can construct the perpendicular bisector of the line
segment between the center C to the outside point P. (P)
I can construct arcs on circle C from the midpoint Q,
having length of CQ. (P)
I can construct a tangent line from a point outside the
circle to the circle using construction tools or computer
software. (P)
Rowan County Senior High School 2010-2011
Page 10
RCHS Rev. 06/2011
Geometry
A
Unit 5 Circles
Length of
Unit
___weeks
KY Common Core
Academic
Standards
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.
Rowan County Senior High School 2010-2011
Vocabulary/Learning Targets
Activities/Assessments/
Resources
Vocabulary: similarity, rigid motion, dilation, angle
measure, length, proportional, arc, constant of
proportionality, radian, angle, area, circle, sector, formula,
intercepted arc
Unit Learning targets
Students will be able to:
I can recall how to find the area and circumference of a
circle.(K)
I can explain that 1° = Π/180 radians (K)
I can recall (from G.C.1) that all circles are similar. (K)
I can determine the constant of proportionality (scale
factor). (K)
I can justify the radii of any two circles (r1 and r2) and the
arc lengths (s1 and s2) determined by congruent central
angles are proportional, such that r1 /s1 = r2/s2 (R)
I can verify that the constant of a proportion is the same as
the radian measure, Θ, of the given central angle.
Conclude s = r Θ (R)
From Appendix A: Emphasize the similarity of all circles.
Note that by similarity of sectors with the same central
angle, arc lengths are proportional to the radius. Use this
as a basis for introducing radian as a unit of measure. It is
not intended that it be applied to the development of
circular trigonometry in this course.
I can define similarity as rigid motions with dilations, which
preserves angle measures and make lengths proportional
(K)
I can use similarity to calculate the length of an arc. (S)
I can define the radian measure of an angle as the ratio of
an arc length to its radius and calculate a radian measure
Page 11
RCHS Rev. 06/2011
Geometry
A
when given an arc length and its radius. (R)
I can convert degrees to radians using the constant of
proportionality (2π x angle measure / 360° ). (K)
I can calculate the area of a circle.(S)
I can define a sector of a circle. (K)
I can calculate the area of a sector using the ratio of the
intercepted arc measure and 360° multiplied by the area of
the circle. (R)
Unit 5 Expressing Geometric Properties with Equations
Length of
Unit
___weeks
KY Common Core
Academic
Standards
G.GPE.1 Derive the
equation of a circle
of given center and
radius using the
Rowan County Senior High School 2010-2011
Vocabulary/Learning Targets
Activities/Assessments/
Resources
Vocabulary: distance formula, Pythagorean Theorem,
difference, coordinates, radius, circle, hypotenuse,
equation, center, complete the square, quadratic equation,
conic equation, standard form, general form
Page 12
RCHS Rev. 06/2011
Pythagorean
Theorem; complete
the square to find
the center and
radius of a circle
given by an
equation.
Rowan County Senior High School 2010-2011
Geometry
A
Unit Learning targets
Students will be able to:
I can define a circle. (K)
I can use Pythagorean Theorem. (K)
I can complete the square of a quadratic equation. (K)
I can derive equation of a circle using the Pythagorean
Theorem – given coordinates of the center and length of
the radius. (R)
I can determine the center and radius by completing the
square. (R)
From Appendix A: Emphasize the similarity of all circles.
Note that by similarity of sectors with the same central
angle, arc lengths are proportional to the radius. Use this
as a basis for introducing radian as a unit of measure. It is
not intended that it be applied to the development of
circular trigonometry in this course.
I can identify the center and radius of a circle given its
equation. (K)
I can draw a right triangle with a horizontal leg, a vertical
leg, and the radius of a circle as its hypotenuse. (K)
I can use the distance formula (Pythagorean Theorem),
the coordinates of a circle’s center, and the circle’s radius
to write the equation of the circle. (R)
I can convert an equation of a circle in general (quadratic)
form to standard form by completing the square. (S)
I can identify the center and radius of a circle given its
equation. (R)
Page 13
RCHS Rev. 06/2011
Geometry
A
Unit 5 Expressing Geometric Properties with Equations
Length of
Unit
___weeks
KY Common Core
Academic
Standards
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).
Rowan County Senior High School 2010-2011
Vocabulary/Learning Targets
Activities/Assessments/
Resources
Vocabulary: side length, vertex, first quadrant, slope,
distance, midpoint, parallel, perpendicular, intersecting
Unit Learning targets
Students will be able to:
I can recall previous understandings of coordinate
geometry (including, but not limited to: distance, midpoint
and slope formula, equation of a line, definitions of parallel
and perpendicular lines, etc.) (K)
I can use coordinates to prove simple geometric theorems
algebraically. (R)
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).
From Appendix A: Include simple proofs involving circles.
I can represent the vertices of a figure in the coordinate
plane using variables. (R)
I can connect a property of a figure to the tool needed to
verify that property. (R)
I can use coordinates and the right tool to prove or
disprove a claim about a figure.
For example:
Use slope to determine if sides are parallel,
intersecting, or perpendicular;
Use the distance formula to determine if sides are
congruent or to decide if a point is inside a circle, outside a
circle, or on the circle;
Use the midpoint formula or the distance formula to
decide if a side has been bisected. (R)
Page 14
RCHS Rev. 06/2011
Geometry
A
Unit 5 Modeling with Geometry
Length of
Unit
___weeks
KY Common Core
Academic
Standards
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).*(*Modelin
g Standard)
Vocabulary/Learning Targets
Activities/Assessments/
Resources
Vocabulary: circumference, area, perimeter, volume
Unit Learning targets
Students will be able to:
I can use measures and properties of geometric shapes to
describe real world objects. (K)
Given a real world object, I can classify the object as a
known geometric shape - use this to solve problems in
context. (R)
From Appendix A: Focus on situations in which the
analysis of circles is required.
I can represent real-world objects as geometric figures. (R)
I can estimate measure (circumference, area, perimeter,
volume) of real-world objects using comparable geometric
shapes or three-dimensional figures. (R)
I can apply the properties of geometric figures to
comparable real-world objects (e.g., The spokes of a
wheel of a bicycle are equal lengths because they
represent the radii of a circle.). (R)
Rowan County Senior High School 2010-2011
Page 15
RCHS Rev. 06/2011
Geometry
A
Unit 6 Conditional Probability and the Rules of Probability
Length of
Unit
KY Common Core
Academic
Standards
___weeks
S.CP.1 Describe
events as subsets of
a sample space (the
set of outcomes)
using characteristics
(or categories) of the
outcomes, or as
unions, intersections,
or complements of
other events (“or”,
“and”, “not”).
___weeks
S. CP 2 Understand
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.
Statistics and
Rowan County Senior High School 2010-2011
Vocabulary/Learning Targets
Activities/Assessments/
Resources
Vocabulary: event, sample space, subset union,
intersection, complement
Unit Learning targets
Students will be able to:
I can define event and sample space. (K)
I can establish events as subsets of a sample space. (S)
I can define union, intersection, and complement. (K)
I can establish events as subsets of a sample space (the
set of outcomes) using characteristics of the outcomes,
based on the union, intersection, or complement of other
events (‘or’, “and”, “not’). (S)
Vocabulary: independent events, probability, product,
event
Unit Learning targets
Students will be able to:
I can define and identify independent events. (K)
I can explain and provide an example to illustrate that for
two dependent events, the probability of the events
occurring together is the product of the probability of each
event. (R)
I can calculate the probability of an event.
I can predict if two events are independent, explain my
reasoning, and check my statement by calculating P(A and
B) and P(A) x P(B). (R)
Page 16
RCHS Rev. 06/2011
Geometry
A
Unit 6 Conditional Probability and the Rules of Probability
Length of
Unit
___weeks
KY Common Core
Academic
Standards
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.
Statistics and
Probability is a
Modeling
Conceptual
Category.
Vocabulary/Learning Targets
Activities/Assessments/
Resources
Vocabulary: probability, dependent events, conditional
probability, independent events
Unit Learning targets
Students will be able to:
I can define dependent events and conditional probability.
(K)
I can explain that conditional probability is the probability
of an event occurring given the occurrence of some other
event and give examples that illustrate conditional
probability. (R)
I can explain that for two events A and B, the probability of
event A occurring given the occurrence of event B is
P(A│B) = P(A and B) and give examples to show how
P(B)
to use the formula (R)
I can explain that A and B are independent events if the
occurrence of A does not impact the probability of B
occurring and vice versa (i.e., A and B are independent
events if P(B│A) = P(B) and P(A│B) = P(A)). (R)
I can determine if two events are independent and justify
my conclusion. (R)
Rowan County Senior High School 2010-2011
Page 17
RCHS Rev. 06/2011
Geometry
A
Unit 6 Conditional Probability and the Rules of Probability
Length of
Unit
___weeks
KY Common Core
Academic
Standards
S.CP. 4 Construct
and interpret twoway 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 10th grade.
Do the same for other
subjects and compare
the results.
Rowan County Senior High School 2010-2011
Vocabulary/Learning Targets
Vocabulary: two-way frequency table, display, data,
variable, category, random sample, probability, event,
independent events, formula, conditional probability
Unit Learning targets
Students will be able to:
I can determine when a two-way frequency table is an
appropriate display for a set of data. (R)
I can collect data from a random sample. (S)
I can construct a two-way frequency table for the data
using the appropriate categories for each variable. (S)
I can decide if events are independent of each other by
comparing P(B│A) and P(B) or P(A│B) and P(A). (R)
I can calculate the conditional probability of A given B
using the formula P(A│B) = P(A and B) . (S)
P(B)
I can pose a question for which a two-way frequency is
appropriate, use statistical technique to sample the
population, and design an appropriate product to
summarize the process and report the results. (P)
Activities/Assessments/
Resources
Use the two-way table as a
sample space to decide if events
are independent and to
approximate conditional
probabilities.
From Appendix A: Build on work
with two-way tables from
Algebra 1 Unit 3 (S.ID.5) to
develop understanding of
conditional probability and
independence.
Interpret two-way frequency
tables of data when two
categories are associated with
each object being classified.
(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 10th grade.
Do the same for other subjects
and compare the results.)
Page 18
RCHS Rev. 06/2011
Geometry
A
Unit 6 Conditional Probability and the Rules of Probability
Length of
Unit
___weeks
KY Common Core
Academic
Standards
S.CP.5 Recognize
and explain the
concepts of
conditional
probability and
independence in
everyday language
and everyday
situations. For
example, compare
the chance of
having lung cancer
if you are a smoker
with the chance of
being a smoker if
you have lung
cancer. Statistics
and Probability is a
Modeling
Conceptual
Category.
Rowan County Senior High School 2010-2011
Vocabulary/Learning Targets
Activities/Assessments/
Resources
Vocabulary: conditional probability, dependent events,
independence, independent events
Unit Learning targets
Students will be able to:
I can illustrate the concept of conditional probability using
everyday examples of dependent events. (R)
I can illustrate the concept of independence using
everyday examples of independent events.
Page 19
RCHS Rev. 06/2011
Geometry
A
Unit 6 Conditional Probability and the Rules of Probability
Length of
Unit
KY Common Core
Academic
Standards
___weeks
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.
Statistics and
Probability is a
Modeling
Conceptual
Category.
Rowan County Senior High School 2010-2011
Vocabulary/Learning Targets
Activities/Assessments/
Resources
Vocabulary: probability, event, dependent event,
conditional probability, intersection, set
Unit Learning targets
Students will be able to:
I can find the conditional probability of A given B as the
fraction of B’s outcomes that also belong to A.
I can interpret the answer in terms of the model.
I can calculate the probability of the intersection of two
events. (S)
I can calculate the conditional probability of A given B
using the model P(A│B) = P(A and B) . (S)
P(B)
I can interpret probability based on the context of the given
problem. (R)
Page 20
RCHS Rev. 06/2011
Geometry
A
Unit 6 Conditional Probability and the Rules of Probability
Length of
Unit
___weeks
___weeks
KY Common Core
Academic
Standards
Vocabulary/Learning Targets
S.CP.7 Apply the
Additional Rule, P(A
or B) = P(A) + P(B) –
P(A and B) and
interpret the answer
in terms of the
model.
Statistics and
Probability is a
Modeling
Conceptual
Category.
Vocabulary: probability, event, intersection, union,
Addition Rule
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.
Statistics and
Probability is a
Modeling
Conceptual
Category.
Vocabulary: probability, event, conditional probability,
General Multiplication Rule, intersection
Rowan County Senior High School 2010-2011
Activities/Assessments/
Resources
Unit Learning targets
Students will be able to:
I can apply the Addition rule to determine the probability of
the union of two events using the formula P(A or B) = P(A)
+ P(B) – P(A and B). (S)
I can interpret the probability of unions and intersections
based on the context of the given problem. (R)
Unit Learning targets
Students will be able to:
I can use the multiplication rule with correct notation.
I can apply the general Multiplication Rule to calculate the
probability of the intersection of two events using the
formula P(A and B) = P(A)P(B|A) = P(B)P(A|B).
I can Interpret conditional probability based on the context
of the given problem.
Page 21
RCHS Rev. 06/2011
Geometry
A
Unit 6 Conditional Probability and the Rules of Probability
Length of
Unit
___weeks
KY Common Core
Academic
Standards
S.CP.9 (+) Use
permutations and
combinations to
compute
probabilities of
compound events
and solve problems.
Statistics and
Probability is a
Modeling
Conceptual
Category.
Vocabulary/Learning Targets
Activities/Assessments/
Resources
Vocabulary: fundamental counting principle, outcomes,
sample space, factorial, permutation, combination,
compound event, probability
Unit Learning targets
Students will be able to:
I can apply the fundamental counting principle to find the
total number possible outcomes in a sample space. (S)
I can define factorial, permutation, combination and
compound event. (K)
I can distinguish between situations that require
permutations and those that require combinations. (R)
I can apply the permutation formula to determine the
number of outcomes in an event
nPr =n!/(n-r)! (S)
I can apply the combination formula to determine the
number of outcomes in an event.
nCr =n!/(n-r)!r! (S)
I can compute probabilities of compound events. (S)
I can solve problems involving permutations and
combinatations. (S)
I can write and solve original problems involving
compound events, permutations, and/or combinations (P)
Rowan County Senior High School 2010-2011
Page 22
RCHS Rev. 06/2011
Geometry
A
Unit 6 Using Probability to Make Decisions
Length of
Unit
KY Common Core
Academic
Standards
Vocabulary/Learning Targets
Activities/Assessments/
Resources
Vocabulary: probability, event, theoretical probability,
___weeks
S.MD.6 (+) Use
probabilities to
make fair decisions
(e.g. drawing by
lots, using a
random number
generator.)
This unit sets the
stage for work in
Algebra II, where the
ideas of statistical
inference are
introduced. Evaluating
the risks associated
with conclusions
drawn from sample
data (i.e. incomplete
information) requires
an understanding of
probability concepts.
experimental probability,
Unit Learning targets
Students will be able to:
I can compute Theoretical and Experimental Probabilities.
(K)
I can use probabilities to make fair decisions (e.g. drawing
by lots, using a random number generator.) (R)
I can analyze decisions and strategies using probability
concepts (e.g., product testing, medical testing, pulling a
hockey goalie at the end of a game.)
From Appendix A: This unit sets the stage for work in
Algebra II, where the ideas of statistical inference are
introduced. Evaluating the risks associated with
conclusions drawn from sample data (i.e. incomplete
information) requires an understanding of probability
concepts.
Rowan County Senior High School 2010-2011
Page 23
RCHS Rev. 06/2011
Geometry
A
Unit 6 Using Probability to Make Decisions
Length of
Unit
___weeks
KY Common Core
Academic
Standards
S.MD.7 (+) Analyze
decisions and
strategies using
probability concepts
(e.g., product
testing, medical
testing, pulling a
hockey goalie at the
end of a game.)
Statistics and
Probability is a
Modeling
Conceptual
Category.
Vocabulary/Learning Targets
Activities/Assessments/
Resources
Vocabulary: probability, event, product testing, medical
testing
Unit Learning targets
Students will be able to:
I can recall prior understandings of probability.
I can analyze decisions and strategies using probability
concepts (e.g., product testing, medical testing, pulling a
hockey goalie at the end of a game.)
From Appendix A: This unit sets the stage for work in
Algebra II, where the ideas of statistical inference are
introduced. Evaluating the risks associated with
conclusions drawn from sample data (i.e. incomplete
information) requires an understanding of probability
concepts.
Rowan County Senior High School 2010-2011
Page 24