Download Geometry - Trotwood-Madison City Schools

Trotwood-Madison City Schools Curriculum Map and Pacing Guide
Mathematics
Grading Period
Quarter 1
Grade/Course
.
Domain/Standard
August 2012
Time
10 Days
Mon.
Tues.
Wed.
Thur.
Fri.
1
2
3
6
7
8
9
10
13
14
15
16
17
Teacher PD
Teacher PD
23
24
20
First Day
21
22
G.CO.1. Know the 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.)
G.CO-12. Make formal geometric
constructions with a variety of tools
and methods (compass and
straightedge, string, reflective
devices, paper folding, dynamic
Mathematical Practices
geometric software, etc.). Copying a
1. Make sense of problems and persevere in segment; copying an angle; bisecting a
solving them.
segment; bisecting an angle;
2. Reason abstractly and quantitatively.
constructing perpendicular lines,
3. Construct viable arguments and critique including the perpendicular bisector
the reasoning of others.
of a line segment; and constructing a
4. Model with mathematics.
line parallel to a given line through a
5. Use appropriate tools strategically.
point not on the line.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in
repeated reasoning.
27
28
29
30
31
Instructional Strategies
(Including Interventions)
Geometry
Technology/
Resources
_
Assessments
(Formative,
Performance)
Review vocabulary associated with Geometer’s sketchpad, Bellwork, Chapter
geometry (e.g. point line and plane, computers, smart-board, Test, Quizzes,
angle, vertical angles and all
graphing calculators.
homework,
angles formed by parallel lines cut Discovering Geometry Classroom practice,
by transversal. Use graph paper, Textbook Chapter 1.1- Geometer’s
tracing paper or dynamic
1.3
Sketchpad
geometry software to obtain
investigations,
images of a given figure under
Textbook
specified rigid motions.
investigations
Have students identify examples
of points, lines and planes in
pictures and explain the meaning
of these terms in words.
Direct instruction about
geometric terms and definition of
geometric figures. Students will
keep terms in their notebooks.
They will make flash cards with
terms, definition and pictures.
TMCS—2012
Compass Learning
quizzes when used.
Trotwood-Madison City Schools Curriculum Map and Pacing Guide
Mathematics
Grading Period
Quarter 1
Grade/Course
.
Domain/
Standard
September 2012
G.CO-9. Prove theorems about
Mon.
Tues.
Wed.
Thur.
Fri.
3
4
5
6
7
10
11
12
13
14
17
18
19
20
21
24
25
26
27
28
Labor Day
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.
Time
18 days
Instructional Strategies
(Including Interventions)
Geometry
Technology/
Resources
_
Assessments
Use graph paper, tracing paper or Geometer’s sketchpad, Bellwork, Chapter
dynamic geometry software to
computers, smart-board, Test, Quizzes,
obtain images of a given figure
graphing calculators.
homework,
under specified rigid motions.
Discovering Geometry Classroom practice,
Textbook Finish Chapter Geometer’s
Use compass learning to front
1.4-1.6 Chapter 2.1-2.2, Sketchpad
load or intervene with students
and 2.5-2.6
investigations,
about angle relationships.
Textbook
Compass Learning
investigations
G.CO-12. Make formal geometric
Compass Learning
quizzes when used.
constructions with a variety of tools
and methods (compass and
straightedge, string, reflective
Mathematical Practices
devices, paper folding, dynamic
1. Make sense of problems and persevere in geometric software, etc.). Copying a
solving them.
segment; copying an angle; bisecting
2. Reason abstractly and quantitatively.
a segment; bisecting an angle;
3. Construct viable arguments and critique constructing perpendicular lines,
the reasoning of others.
including the perpendicular bisector
4. Model with mathematics.
of a line segment; and constructing a
5. Use appropriate tools strategically.
line parallel to a given line through a
6. Attend to precision.
point not on the line.
7. Look for and make use of structure.
8. Look for and express regularity in
.
repeated reasoning
TMCS—2012
Mathematics
Trotwood-Madison City Schools Curriculum Map and Pacing Guide
Grading Period
Quarter 1/2
Domain/Standard
October 2012
G.GPE.4. Use coordinates to
Mon.
Tues.
Wed.
Thur.
Fri.
1
2
3rd Grade
3
OAA
4
5
8
9
10
11
12
15
16
17
18 End 1st
19
Quarter
arter
Records Day
24
25
26
Begin OGT
thru 11/2
31
ferences
thru 11/2
22 2
nd
23
Quarter
29
30
Con
Grade/Course
.
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.GPE.5. Prove the slope
criteria for parallel and
perpendicular lines and uses them to
solve geometric problems (e.g., find
the equation of a line parallel or
perpendicular to a given line that
Mathematical Practices
passes through a given
1. Make sense of problems and persevere in
point).
solving them.
2. Reason abstractly and quantitatively.
G.GPE.6. Find the point on a
3. Construct viable arguments and critique
directed line segment between two
the reasoning of others.
given points that partitions the
4. Model with mathematics.
segment in a given ratio
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
G.CO.7. Use the definition of
8. Look for and express regularity in
congruence in terms of rigid motions
repeated reasoning.
to show that two triangles are
congruent if and only if
corresponding pairs of sides and
corresponding pairs of angles are
congruent.
G.CO.8. Explain how the criteria
for triangle congruence (ASA, SAS,
and SSS) follow from the definition
of congruence in terms of rigid
Time
20 days
Instructional Strategies
(Including Interventions)
Geometry
Technology/
Resources
Students will do the investigation
for triangle sums. Have students
cut out a triangle size of their
own choosing. Students will tare
the thee angles off the triangle
and rearrange them on a straight
angle to show that the sum of the
three angle is 180 degrees
Should also include
slopes of parallel lines in
a coordinate plane and
use this knowledge to
proving properties of
geometric figures in a
coordinate plane. This
has a small section in
Use graph paper, tracing paper or the text: “Using Your
Algebra Skills 3: Slopes
dynamic geometry software to
of parallel and
obtain images of a given figure
perpendicular lines”
under specified rigid motions.
p165. May also need to
Investigations in geometer’s
look outside the text
sketchpad will be used to help
students see that the ASA, SSS, for engaging activities.
and SAS definitions prove that
Geometer’s sketchpad,
triangles are congruent. And to
graphing calculators and
show that base angles of any
isosceles triangles are congruent. Discovering Geometry
Textbook
Chapter 4 (4.1-4.8,
Use compass learning to front
except 4.7) and other
load or intervene with students
resources.
about triangle relationships
including congruence, angle sum,
and specific types of triangles.
Compass learning
_
Assessments
(Formative,
Performance)
Bellwork, Chapter
Test, Quizzes,
homework,
Classroom practice,
Geometer’s
Sketchpad
investigations,
Textbook
investigations
Compass Learning
quizzes when used.
Trotwood-Madison City Schools Curriculum Map and Pacing Guide
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
TMCS—2012
Trotwood-Madison City Schools Curriculum Map and Pacing Guide
Mathematics
Grading Period
Quarter 2
Grade/Course
.
Domain/Standard
November 2012
G.CO.11. Prove theorems about
Mon.
Tues.
Wed.
Thur.
Fri.
1
2 Conf.
Comp
Day
5
6
7
8
9
12
13
14
15
16
19
20
21
22
23
parallelograms. Theorems include:
opposite sides are congruent, opposite
angles are congruent, the diagonals of
a parallelogram bisect each other, and
conversely, rectangles are
parallelograms with congruent
diagonals.
G.CO.12. Make formal geometric
constructions with a variety of tools
and methods (compass and
26
27
28
29
30
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
Mathematical Practices
1. Make sense of problems and persevere in line parallel to a given line through a
point not on the line.
solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique G.SRT.4. Prove theorems about
the reasoning of others.
triangles. Theorems inclulde: a line
4. Model with mathematics.
parallel to one side of a triangle
5. Use appropriate tools strategically.
divides the other two proportionally,
6. Attend to precision.
and conversely; the Pythagorean
7. Look for and make use of structure.
theorem proved using triangle
8. Look for and express regularity in
similarity.
repeated reasoning.
Fall Break
Time
16 days
Instructional Strategies
(Including Interventions)
Geometry
Technology/
Resources
_
Assessments
(Formative,
Performance)
Have students make a chart with
Geometer’s sketchpad, Bellwork, Chapter
headings, (number of sides, number of graphing calculators Test, Quizzes,
triangles drawn, sum of the angles of and Discovering
homework,
the polygon. The teachers should put Geometry Textbook
Classroom
the same chart on board/smartboard. Chapter 5 and other practice,
While in groups, students are then
resources.
Geometer’s
asked to draw a triangle and draw a
Sketchpad
diagonal from one and only one vertex Note: 5.1 and 5.2 can investigations,
to each of the other non-consecutive be done in one class
Textbook
vertices. This will form x number of session. Two class
investigations
triangles. Next the students will
sessions on 5.3-5.6.
multiply the number of triangles by
Compass Learning
180 degrees to get their polygon’s
Compass learning
quizzes when used.
angle sum. Each group will then
record their data into the class chart.
As a whole group the formula can then
be discovered.
Use graph paper, tracing paper or
dynamic geometry software to obtain
images of a given figure under
specified rigid motions.
Use compass learning to front load or
intervene with students about
segment, line and polygon
relationships.
TMCS—2012
Trotwood-Madison City Schools Curriculum Map and Pacing Guide
Mathematics
Grading Period
Quarter 2
Grade/Course
.
Domain/Standard
December 2012
G.CO.11. Prove theorems about
Mon.
Tues.
Wed.
Thur.
3
4
5
6
7
10
11
12
13
14
17
18
19
20
21
24
Winter 25
Break Begins
26
27
28
Fri. parallelograms. Theorems include:
opposite sides are congruent, opposite
angles are congruent, the diagonals of a
parallelogram bisect each other, and
conversely, rectangles are
parallelograms with congruent diagonals.
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
Mathematical Practices
the tangent where the radius intersects
1. Make sense of problems and persevere in
the circle.
solving them.
2. Reason abstractly and quantitatively.
G.C.3. Construct the inscribed and
3. Construct viable arguments and critique
circumscribed circles of a triangle, and
the reasoning of others.
prove properties of angles for a
4. Model with mathematics.
quadrilateral inscribed in a circle.
5. Use appropriate tools strategically.
6. Attend to precision.
G.C.4. (+) Construct a tangent line
7. Look for and make use of structure.
from a point outside a given circle to
8. Look for and express regularity in
the circle.
repeated reasoning
31
Instructional Strategies
(Including Interventions)
Time
15 days
Technology/
Resources
_
Assessments
(Formative,
Performance)
Use graph paper, tracing paper or
Computer’s,
Bellwork, Chapter
dynamic geometry software to obtain Geometer’s sketchpad, Test, Quizzes,
images of a given figure under
graphing calculators homework,
specified rigid motions. Students will and Discovering
Classroom
construct polygons on geometers and Geometry Textbook
practice,
note the different properties to draw Chapter 5.7 and
Geometer’s
conclusions about its properties.
Chapter 6.1-6.4 and
Sketchpad
other resources.
investigations,
Students will use Geometer’s
Textbook
Sketchpad to complete investigation 1 Compass learning
investigations
and 2 in section 6.2.
Use compass learning to front load or
intervene with students about circle
relationships.
G. CO. 13 Construct an equilateral
triangle, a square, and regular hexagon
inscribed in a circle.
G.CO.12. Make formal geometric
constructions with a variety of tools and
methods (compass and straightedge,
string, reflective devices, paper folding,
dynamic geometric software, etc.).
(+) for Honors Geometry only
Geometry
TMCS—2012
Compass Learning
quizzes when used.
Trotwood-Madison City Schools Curriculum Map and Pacing Guide
Mathematics
Grading Period
Quarter 2/3
Domain/Standard
January 2013
G.CO.2. Represent transformations
Mon.
Tues.
Wed.
Thur.
Fri.
1
2
3
4
Winter
Break Ends
7
8
9
10
11
14
15
16
17 2nd
Quarter
ends
21 MLK
Day
28
22 3rd
23
24
30
31
Quarter
Begins
29
18
Records
Day
25
Grade/Course
.
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).
G.CO.3. Given a rectangle,
parallelogram, trapezoid, or regular
describe the rotations and reflections
that carry it onto itself.
G.CO.4. Develop definitions of
rotations, reflections, and translations
in terms of angles, circles,
perpendicular lines, parallel lines, and
Mathematical Practices
1. Make sense of problems and persevere in line segments.
solving them.
2. Reason abstractly and quantitatively.
G.CO.5. Given a geometric figure and
3. Construct viable arguments and critique a rotation, reflection, or translation,
the reasoning of others.
draw the transformed figure using, e.g.,
4. Model with mathematics.
graph paper, tracing paper, or geometry
5. Use appropriate tools strategically.
software. Specify a sequence of
6. Attend to precision.
transformations that will carry a given
7. Look for and make use of structure.
figure onto another.
8. Look for and express regularity in
repeated reasoning.
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.
Time
12
days
Geometry
_
Instructional Strategies
(Including Interventions)
Technology/
Resources
Use graph paper, tracing paper or
dynamic geometry software to
obtain images of a given figure
under specified rigid motions.
Students will construct polygons on
geometers and perform
transformations such as rotations,
translations, reflections, and
dilation. using these investigations
students will develop coordinate
rules for transformations and
composite transformations
Computer’s, Geometer’s
sketchpad, graphing
calculators and
Discovering Geometry
Textbook Chapter 6.5
and 6.7 and Chapter 7.17.3 must include
dilations from a
different source and
other resources.
Bellwork, Chapter
Test, Quizzes,
homework,
Classroom
practice,
Geometer’s
Sketchpad
investigations,
Textbook
investigations
Compass Learning
Compass Learning
quizzes when used.
Use compass learning to front load
or intervene with students about
transformations.
Assessments
(Formative,
Performance)
Trotwood-Madison City Schools Curriculum Map and Pacing Guide
G.CO.12. Make formal geometric
constructions with a variety of tools and
methods (compass and straightedge,
string, reflective devices, paper folding,
dynamic geometric software, etc.).
G.SRT.1. Verify experimentally the
properties of dilations given by a center
and a scale factor.
a. A dilation takes a line not passing
through the center of the dilation to a
parallel line, and leaves a line passing
through the center
unchanged.
b. The dilation of a line segment is
longer or shorter in the ratio given by
the scale factor.
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.
TMCS—2012
Trotwood-Madison City Schools Curriculum Map and Pacing Guide
Mathematics
Grading Period
Quarter 3
Grade/Course
.
Domain/Standard
February 2013
G.SRT.8. Use trigonometric ratios
Mon.
Tues.
Wed.
1
and the Pythagorean Theorem to solve
right triangles in applied problems.
G.SRT.4. Prove theorems about
Thur.
Fri.
4
5
6
7
8
11
12
13
14
15
18 President
19
20
21
22
27
28
29
Day
25
26
Con
ferences
triangles. Theorems include: a line
parallel to one side of a triangle
divides the other two proportionally,
and conversely; the Pythagorean
theorem proved using triangle
similarity.
G.SRT.6 Understand that by
similarity, side ratios in right triangles
are properties of the angles in the
triangle, leading to definitions of
Mathematical Practices
1. Make sense of problems and persevere in trigonometric ratios for acute angles.
solving them.
G.SRT.9 (+) Derive the formula A
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique = 1/2 ab sin(C) for the area of a
triangle by drawing an auxiliary line
the reasoning of others.
from a vertex perpendicular to the
4. Model with mathematics.
opposite side.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in
repeated reasoning.
G.SRT.10 (+) Prove the Laws of
Sines and Cosines and use them to
solve problems.
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).
Time
20 days
Instructional Strategies
(Including Interventions)
Use graph paper, tracing paper or
dynamic geometry software to
obtain images of a given figure
under specified rigid motions.
Students test indirect
measurement using Geometer’s
Sketchpad to explore indirect
measurement using trigonometric
ratios with right triangles.
Geometry
Technology/
Resources
Computer’s, Geometer’s
sketchpad, graphing
calculators and
Discovering Geometry
Textbook Chapter 9.19.4 and Chapter 12.112.2 and other
resources.
_
Assessments
(Formative,
Performance)
Bellwork, Chapter
Test, Quizzes,
homework,
Classroom
practice,
Geometer’s
Sketchpad
investigations,
Textbook
investigations
Note: 12.3-12.4 are to
Use compass learning to front load be done in Honors
Geometry. Also
Compass Learning
or intervene with students about
remember
that
we
have
quizzes when used.
Pythagorean Theorem.
skipped chapter 8 and 11
Students will do the Investigation so any exercises in
chapters 9 and 12 that
“The Three Sides of a Right
involve finding the area
Triangle” to help them see the
proof of the Pythagorean Theorem. of geometric figure or
similar figures may need
They will also use Geometer’s
to be omitted for now.
Sketchpad to find Pythagorean
After these concepts
Triples.
are addressed then
those exercises can be
used for practice or
assessment.
TMCS—2012
Trotwood-Madison City Schools Curriculum Map and Pacing Guide
Mathematics
Grading Period
Quarter 3
Domain/Standard
March 2013
G.GMD.1. Give an informal
Mon.
Tues.
Wed.
Thur.
Fri.
1 Conf.
Comp Day
4
5
6
7
8
11
12
13
OGT
14
15
18
19
20
OGT
21
22
25
26
27 3rd
28
Quarter
Ends
Records
Day
29
Good
Friday
Grade/Course
.
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.GPE.7. Use coordinates to
compute perimeters of polygons and
areas of triangles and rectangles,
e.g., using the distance formula.★
G.C.5. Derive using similarity the
fact that the length of the arc
intercepted by an angle is
Mathematical Practices
proportional to the radius, and
1. Make sense of problems and persevere in define the radian measure of the
solving them.
angle as the constant of
2. Reason abstractly and quantitatively.
proportionality; derive the formula
3. Construct viable arguments and critique for the area of a sector.
the reasoning of others.
G.SRT.9 (+) Derive the formula
4. Model with mathematics.
A = 1/2 ab sin(C) for the area of a
5. Use appropriate tools strategically.
triangle by drawing an auxiliary line
6. Attend to precision.
from a vertex perpendicular to the
7. Look for and make use of structure.
opposite side.
8. Look for and express regularity in
repeated reasoning.
Time
11 days
Instructional Strategies
(Including Interventions)
Geometry
Technology/
Resources
_
Assessments
(Formative,
Performance)
Use graph paper, tracing
Computer’s, Geometer’s
Bellwork, Chapter
paper or dynamic geometry
sketchpad, graphing calculators. Test, Quizzes,
software to obtain images of a
homework,
given figure under specified The Text Discovering Geometry Classroom
rigid motions. Students will
chapter 8 is a review of grade practice,
construct various geometric 7th and 8th grade standards.
Geometer’s
figures e.g. polygons, circles, Our standards encourage
Sketchpad
sectors, and regular polygons students to approach areas and investigations,
and use these figures to help perimeters through problem
Textbook
them derive formulas for
solving and modeling. Students investigations
their areas.
will need to be able to apply
their knowledge of area to solve Compass Learning
Use compass learning to front
real world problems. (We are all quizzes when
load or intervene with
aware that students are coming used.
students about area of
to us deficient but we need to
geometric figures.
push our students to be more
independent learners.)
Students will do the
Investigation “The Three
Note: You may now want to
Sides of a Right Triangle” to
revisit those exercises that
help them see the proof of
involved area now. They can be
the Pythagorean Theorem.
used as practice or assessment
They will also use Geometer’s
from chapters 9 or 12. These
Sketchpad to find
exercises may provide the
Pythagorean Triples.
opportunity for students to
apply area.
In Honors Geometry you can
revisit Standard G.SRT.9 (+)
TMCS—2012
Trotwood-Madison City Schools Curriculum Map and Pacing Guide
Mathematics
Grading Period
Quarter 4
Grade/Course
.
Domain/Standard
April 2013
19 days
G.GMD.3. Use volume formulas for
2
Spring
3
Break
4
5
cylinders, pyramids, cones, and
spheres to solve problems.★
9
10
11
12
G.SRT.2. Given two figures, use the
Mon.
1
8
4th
Quarter
Begins
Tues.
Wed.
Thur.
Fri.
15
16
17
18
19
22
23
24
25
26
Begin OAA
thru 5/10
OAA Test
thru 5/10
29
30
Mathematical Practices
1. Make sense of problems and persevere in
solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique
the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in
repeated reasoning
Instructional Strategies
(Including Interventions)
Time
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.SRT.3. Use the properties of similarity
transformations to establish the AA criterion
for two triangles to be similar.
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).*
Geometry
Technology/
Resources
Use graph paper, tracing
Computer’s, Geometer’s
paper or dynamic geometry sketchpad, graphing
software to obtain images of calculators and
a given figure under specified Discovering Geometry
rigid motions. Students test Textbook Chapter 1.8,
indirect measurement using 10.1, 10.4, 10.5 and other
Geometer’s Sketchpad to
resources.
explore volumes, and similar
figures.
The text does a pretty
good job with real world
problem involving volume,
Use compass learning to
front load or intervene with displacement and density.
students about the concept
of volume and similar
geometric 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).*
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).*
TMCS—2012
_
Assessments
(Formative,
Performance)
Bellwork, Chapter
Test, Quizzes,
homework,
Classroom
practice,
Geometer’s
Sketchpad
investigations,
Textbook
investigations
Compass Learning
quizzes when
used.
Trotwood-Madison City Schools Curriculum Map and Pacing Guide
Mathematics
Grading Period
Quarter 4
Grade/Course
.
Domain/Standard
May 2013
Time
S.CP.1. Describe events as subsets of a sample
Mon.
Tues.
Wed.
1
13
7
14
Fri.
2
thru 5/10
3
9
thru 5/10
10
OAA Test
15
16
17
OAA Test
6
Thur.
8
20
21
22
23
24
27
28
29
30
31
Memorial Day
22 days
space (the set of
outcomes) using characteristics (or categories) of the
outcomes, or as unions, intersections, or complements
of other events (“or,” “and,”
“not”).
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.
S.CP.3. Understand the conditional probability of
Mathematical Practices
1. Make sense of problems and persevere in
solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique
the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in
repeated reasoning.
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.
TMCS—2012
Instructional Strategies
(Including Interventions)
Use compass learning to
front load or intervene
with students on
applications of probability.
There is not much in the
text about probability so
we will need to seek
activities outside of the
text for these standards.
Students could explore
geometric probability using
2 Explorations:
1. Geometric Probability I
p86
2. Geometric probability
II p442-444.
Geometry
Technology/
Resources
Explorations:
1. Geometric
Probability I p86
2. Geometric
probability II p442444.
_
Assessments
(Formative,
Performance)
Bellwork,
Chapter Test,
Quizzes,
homework,
Classroom
practice,
Geometer’s
Sketchpad
investigations,
Textbook
investigations
Compass
Learning
quizzes when
used.
Trotwood-Madison City Schools Curriculum Map and Pacing Guide
Mathematics
Grading Period
Quarter 4
Grade/Course
.
Domain/Standard
June 2013
Time
Continue with the probability unit from May.
Mon.
3
Tues.
4
Wed.
Thur.
5 Last Day
6 Last Day
for
Students
Fri.
7
for
Teachers
10
11
12
13
14
17
18
19
20
21
24
25
26
27
28
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.
S.CP.6. Find the conditional probability of A given B as
Mathematical Practices
1. Make sense of problems and persevere in
solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique
the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in
repeated reasoning.
the fraction of B’s outcomes that also belong to A, and
interpret the answer in terms of the model.
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.
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.
S.CP.9 (+) Use permutations and combinations to
compute probabilities of compound events and solve
problems.
S.MD.6 (+) Use probabilities to make fair decisions
(e.g., drawing by lots, using a random number generator).
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).
TMCS—2012
Instructional Strategies
(Including Interventions)
Geometry
Technology/
Resources
_
Assessments
(Formative,
Performance)
Bellwork,
Chapter Test,
Quizzes,
homework,
Classroom
practice,
Geometer’s
Sketchpad
investigations,
Textbook
investigations
Compass
Learning quizzes
when used.