Download 1st Quarter - Morgan Park High School

1st Quarter
Essential Questions
Unit 1 (Weeks 1-3/4)
How can we represent
real figures algebraically
and geometrically?
Unit 2 (Weeks 4/5-7)
How can we prove
geometric relationships
within and among
figures?
Major Content
Basic geometric figures:
points, lines, planes,
angles, and polygons
Logical basis and
structure of formal
proof.
Common Focus/Skills
1. Identify points, lines,
and planes by name and
relationship (e.g.
collinear, coplanar,
intersecting,
perpendicular, parallel).
1. Make conjectures and
find counterexamples.
2. Use distance and
midpoint formulas.
3. Measure and classify
angles and their parts.
4. Identify and use
special angle
relationships (e.g.
adjacent, vertical, linear
pair, supplementary, and
complementary)
2. Use logic to
determine the truth of
conjunctions,
disjunctions, and
conditional statements.
3. Use postulates and
theorems to write proofs
in paragraph and twocolumn form regarding
segment and angle
relationships.
IL Standards
/Performance
Descriptors
9C/H3 Represent,
solve, and explain
numerical and algebraic
relationships using
geometric concepts.
9A/I8 Calculate
2. Use slope of two
lines to determine
parallelism or
perpendicularity.
3. Write the equation of
a line in slope-intercept
and point-slope form.
4. Represent and find
the distance between a
point and a line and
between two parallel
lines.
5. Determine what can
and cannot be assumed
from a diagram.
6. Identify and name
polygons and find their
perimeters.
9A/H5 Solve pictorial
or word problems that
involve geometric
relationships within a
single shape or figure,
including the
Pythagorean Theorem.
Unit 3 (Weeks 8-10)
What special properties
arise from the
intersection or nonintersection of two
lines?
Parallel
lines/transversals,
slopes and equations of
lines, distance between
points, lines, and
planes.
1. Identify and use
properties of special
angle pairs created by
parallel lines and
transversals (e.g.
consecutive interior,
alternate interior,
alternate exterior, and
corresponding).
9C/I3 Provide a
counterexample to
disprove a conjecture.
9C/J2 Extend the ideas
of formal and informal
proof to non-geometric
situations.
9C/I2 Develop a formal
proof for a given
geometric situation on
the plane.
9A/I2 Classify angle
relationships for two or
more parallel lines
crossed by a
transversal.
9A/I3 Analyze
geometric situations
using Cartesian
coordinates.
distance, midpoint
coordinates, and slope
using coordinate
geometry.
Common Learning
Activities
9C/I2 Develop a formal
proof for a given
geometric situation on
the plane.
Algebra essentials
review
Discuss and model basic
interactions of points,
lines, and planes
Make a conjecture and
construct a simple proof,
or disprove by
counterexample
Springboard (optional):
“Riddle me This”
Measure segments and
angles using both
technology and formulas
Algebra pretest and
posttest
Discuss and model
special angle pairs
Discuss and model
coordinate linear
analysis
Springboard
(suggested): “Patios by
Madeline”
Springboard (required):
“What’s my Name?”
Products/Assessments
Review for MidSemester Exam
Daily bell-ringers
Mid-Semester Exam
Proof sets (in groups)
Daily bell ringers
Mid-chapter quizzes
Mid-chapter quizzes
Chapter test
Chapter test
Daily bell ringers
Mid-chapter quizzes
Chapter test
Notebooks/journals
Springboard embedded
assessment
2nd Quarter
Essential Questions
Major Content
Common Focus/Skills
Unit 4 (Weeks 11-13)
How can we identify
and prove relationships
between congruent
triangles?
Classification and
properties of triangles
by angles and sides;
triangle congruence
properties.
1. Classify triangles by
angles and sides.
2. Apply Angle Sum and
Exterior Angle
Theorems
3. Identify congruence
transformations
involving triangles.
4. Use SSS, SAS, ASA,
and AAS properties of
triangle congruence.
5. Use properties of
isosceles and equilateral
triangles.
IL Standards/
Performance Descriptors
6. Set up and write
coordinate proofs
involving triangles.
9A/H3 Identify possible
types of two- or threedimensional figures that
would match a set of
given conditions.
9A/I1 Describe and
apply properties of a
polygon or a circle in a
problem-solving
situation.
9A/I4 Represent
transformations of an
object in the plane using
sketches, coordinates,
and vectors.
Unit 5 (Weeks 14-16)
How can we indirectly
compare measurements?
Unit 6 (Weeks 17-19)
How can ratios and
proportions be used in
geometric analysis?
Special segments in a
triangle, inequality, and
indirect proof.
Proportional
relationships among
similar figures
1. Identify and use
perpendicular bisectors,
angle bisectors,
medians, and altitudes in
triangles.
1. Solve problems
involving ratios and
proportions.
2. Recognize and apply
properties of inequalities
in triangles.
3. Construct indirect
algebraic and geometric
proofs.
4. Apply the Triangle
Inequality Theorem. 5.
Apply the SAS
Inequality and SSS
Inequality Theorems.
9A/I10 Identify and
apply properties of
medians , altitudes,
perpendicular bisectors,
and midlines of
triangles.
9A/I1 Describe and
apply properties of a
polygon or a circle in a
problem-solving
situation.
9C/I6 Describe the
difference between an
inductive argument and
a deductive argument.
2. Solve problems
involving scale factor of
similar polygons.
3. Identify similar
triangles and solve
problems involving
proportionality of their
corresponding parts,
including sides, angle
bisectors, altitudes,
medians, and
perimeters.
4. Recognize and
describe characteristics
of fractals (optional)
6D/IH1 Develop, use,
analyze, and explain
methods for solving
number sentences or
word problems
involving proportions
with rational numbers.
9B/I1 Solve problems
using triangle
congruence and
similarity of figures.
9C/I1 Create and
critique arguments
concerning geometric
ideas and relationships
such as properties of
circles, triangles and
quadrilaterals.
Common Learning
Activities
9C/J1 Prove conjectures
about geometric figures
on the plane using
coordinate geometry.
Discuss and model
triangle classifications
and transformations
Model triangle
congruence proofs
Springboard (required):
“Truss Your Judgment”
9A/H4 Determine if a
triangle is possible using
side lengths and the
triangle inequality.
9C/I2 Develop a formal
proof for a given
geometric situation on
the plane.
Discuss and model use
of special segments in
triangles
Student examples of
real-life indirect proof
used to introduce
mathematical ones
Discuss and model
inequality theorems
Springboard (optional):
“What’s the Point”
Review for Semester 1
Exam
Review ratios and
proportions: model and
discuss their use in
geometric situations
Springboard
(suggested): “The
Sagging Gate”
3rd Quarter
Unit 7 (Weeks
20-22)
How can side
length affect
angle measure in
a triangle?
Unit 8 (Weeks
23-25)
How can we
classify and use
the properties of
specific
quadrilaterals?
Major Content
Special properties
of right triangles
and trigonometry.
Common
Focus/Skills
1. Use geometric
mean to solve
problems
involving the
altitude to the
hypotenuse of a
right triangle.
Interior and
exterior angle
sums; properties
of and coordinate
proofs involving
quadrilaterals.
1. Find the
interior and
exterior angle
sums of a
polygon.
Essential Questions
2. Use the
Pythagorean
Theorem.
3. Use properties
of 45-45-90 and
30-60-90
triangles.
4. Solve problems
involving basic
trigonometric
ratios, including
ones involving
angle of elevation
or depression.
IL Standards
/Performance
Descriptors
5. Use the Law of
Sines and Law of
Cosines to solve
triangles
(optional).
9A/H5 Solve
pictorial or word
problems that
involve geometric
relationships
within a single
geometric shape
or figure,
2. Recognize and
apply properties
of parallelograms
(including special
properties of
rectangles,
rhombi, and
squares) and
trapezoids.
3. Use
coordinates to
prove theorems
involving
quadrilaterals.
Unit 9 (Weeks 2627)
How can we view
geometric
relationships in
terms of
movement within
the plane?
Transformations,
tessellations,
dilations, vectors,
and matrices.
1. Use
transformational
analysis to identify
reflection, rotation,
translation, and
symmetry in
congruent figures.
2. Identify and
create specific
tessellations
3. Classify
dilations and
determine their
scale factors.
4. Find magnitude
and direction of,
and perform
translations with,
vectors (optional).
Unit 10 (Weeks
28-30)
What are the
relationships
among circles and
their parts?
Circumference and
equation of a
circle; angle, arc,
chord, secant, and
tangent
relationships.
1. Identify parts of
a circle and use to
find its
circumference.
2. Recognize and
use relationships
between angles,
arcs, chords,
tangents, and
secants.
3. Find measures
of intersecting
segments inside
and outside of a
circle.
4. Write the
equation of a circle
and graph in the
coordinate plane.
5. Use matrices to
determine
transformational
coordinates
(optional).
7C/I6 Calculate
by an appropriate
method the
length, width,
height, perimeter,
. . . angle
measures or sums
of angle measures
9A/I4 Represent
transformations of
an object in the
plane using
sketches,
coordinates, and
vectors.
9A/I1 Describe
and apply
properties of a
polygon or a circle
in a problemsolving situation.
9B/I3 Identify
including the
Pythagorean
Theorem.
9D/I2 Solve
problems
involving 45-4590 and 30-60-90
triangles.
9D/H3 Solve for
missing side
lengths using the
trigonometric
ratios in right
triangles.
Common Learning
Activities
9D/J1 Solve
problems using
the Laws of
Sines/Cosines.
Discuss and
model use of right
triangle properties
Introduce use of
SOHCAHTOA
9A/I1 Describe
and apply
properties of a
polygon or a
circle.
9B/I5 Analyze
and describe the
transformations
that lead to
successful
tessellations of one
or more figures.
6B/J9 Solve
problems using
matrices.
relationships
among circles,
arcs, chords,
tangents, and
secants.
9A/I3 Analyze
geometric
situations using
Cartesian
coordinates.
9A/I3 Analyze
geometric
situations using
Cartesian
coordinates.
Discuss and
model use of
angle sum
properties
Model
transformational
and algebraic
comparison of
figures
Confirm special
quadrilateral
properties through
measurement
Display studentcreated
tessellations
Daily bell ringers
Springboard
(optional):
“Miror, Mirror on
the Floor”
Daily bell ringers
Springboard
(required):
“Community
Quilting Project”
Daily bell ringers
Mid-chapter
quizzes
Mid-chapter
quizzes
Mid-chapter
quizzes
Chapter test
Chapter test
Chapter test
Springboard
(suggested):
“Picture This”
Products/Assessments
of common
geometric figures,
or combinations
of common
geometric figures.
Springboard
embedded
assessment
Review for MidSemester Exam
Confirm circle
properties by
measurement using
ruler and protractor
Mid-Semester
Exam
Daily bell ringers
Mid-chapter
quizzes
Chapter test
Notebooks/journals
4th Quarter
Essential Questions
Unit 11 (Weeks 31-33)
How are the areas of
two-dimensional figures
determined?
Major Content
Perimeter/circumference
and area of polygons
and circles; geometric
probability; segments
and sectors of circles.
Common Focus/Skills
1. Use formulas and
measurements to find
perimeter/circumference
and area of
parallelograms,
triangles, trapezoids,
rhombi, regular
polygons, irregular
figures, and circles.
2. Solve problems
involving geometric
probability.
Unit 12 (Weeks 34-36)
How are the surface
areas of threedimensional figures
determined?
Nets and surface area of
prisms, cylinders,
pyramids, cones, and
spheres.
1. Use nets to find
surface area of a threedimensional figure.
2. Use formulas and
measurements to find
lateral and total surface
areas of prisms,
cylinders, pyramids, and
cones.
3. Use formulas and
measurements to find
surface area of a sphere.
3. Solve problems
involving segments and
sectors of circles.
IL Standards
/Performance
Descriptors
7C/I6 Calculate by an
appropriate method the
length, width, height,
perimeter, area, volume,
surface area, angle
measures or sums of
angle measures of
common geometric
figures, or combinations
of common geometric
figures.
10C/I1 Determine
geometric probability
based on area.
9A/I5 Design a net that
will create a given
figure when folded.
7C/I6 Calculate by an
appropriate method the
length, width, height,
perimeter, area, volume,
surface area, angle
measures or sums of
angle measures of
common geometric
figures, or combinations
of common geometric
figures.
Unit 13 (Weeks 37-38)
How are the volumes of
three-dimensional
figures determined?
Volume of prisms,
cylinders, pyramids,
cones, and spheres;
congruence and
similarity of solids;
coordinates in space.
1. Use formulas and
measurements to find
volume of prisms,
cylinders, pyramids, and
cones.
2. Use formulas and
measurements to find
volume of a sphere.
3. Identify and use the
properties of congruent
or similar solids.
4. Graph and determine
measurements of solids
in space (optional).
7C/I6 Calculate by an
appropriate method the
length, width, height,
perimeter, area, volume,
surface area, angle
measures or sums of
angle measures of
common geometric
figures, or combinations
of common geometric
figures.
7C/H8 Determine the
volume of a sphere.
7C/I5 Determine the
ratio of similar figure
perimeters, areas, and
volumes using the ratio
of similitude.
9A/I3 Analyze
Common Learning
Activities
Products/Assessments
Measure polygons and
circles and use results in
length and area formulas
Build Sierpinski’s
Pyramid
geometric situations
using Cartesian
coordinates.
Review for Final Exam
Use polyhedral models
to illustrate
determination and
comparison of volume
Use classroom to set up
and solve probability
problems involving area
Measure nets and fold
into polyhedra: use
results to determine
surface area
Springboard (required):
“Coming Full Circle”
Daily bell ringers
Springboard (optional):
“Plenty of Polygons”
Daily bell ringers
Springboard
(suggested): “Crystal
Globe”
Final Exam
Mid-chapter quizzes
Mid-chapter quizzes
Daily bell ringers
Chapter test
Chapter test
Mid-chapter quizzes
Springboard embedded
assessment
Chapter test
Notebooks/journals