Download Geometry - USD 383

2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Geometry
Geometry
Welcome to math curriculum design maps for ManhattanOgden USD 383, striving to produce learners who are:
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Effective Communicators who clearly express ideas and effectively
communicate with diverse audiences,
Quality Producers who create intellectual, artistic and practical products
which reflect high standards
Complex Thinkers who identify, access, integrate, and use available
resources
Collaborative Workers who use effective leadership and group skills to
develop positive relationships within diverse settings.
Community Contributors who use time, energies and talents to improve
the welfare of others
Self-Directed Learners who create a positive vision for their future, set
priorities and assume responsibility for their actions. Click here for more.
Overview of Math Standards
Teams of teachers and administrators comprised the pK-12+ Vertical
Alignment Team to draft the maps below. The full set of Kansas College and
Career Standards (KCCRS) for Math, adopted in 2010, can be found here.
To reach these standards, teachers use Holt curriculum, resources,
assessments and supplemented instructional interventions.
1
Standards of Mathematical Practice
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. Click here for more.
Additionally, educators strive to provide math instruction centered on:
1: Focus - Teachers significantly narrow and deepen the scope of how time
and energy is spent in the math classroom. They do so in order to focus
deeply on only the concepts that are prioritized in the standards.
2: Coherence - Principals and teachers carefully connect the learning within
and across grades so that students can build new understanding onto
foundations.
3: Fluency - Students are expected to have speed and accuracy with simple
calculations; teachers structure class time and/or homework time for
students to memorize, through repetition, core functions.
4: Deep Understanding - Students deeply understand and can operate
easily within a math concept before moving on. They learn more than the
trick to get the answer right. They learn the math.
5: Application - Students are expected to use math concepts and choose the
appropriate strategy for application even when they are not prompted.
6: Dual Intensity - Students are practicing and understanding. There is
more than a balance between these two things in the classroom – both are
occurring with intensity. Click here for more.
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Geometry
Notes:
• Vocabulary terms are listed only in the unit they are first introduced.
Unit/Chapter
1. Basics of Geometry
1.1 Points, Lines and
Planes
1.2 Measuring and
Constructing
Angles
1.3 Using Midpoint and
Distance Formulas
1.4 Perimeter and Area
in the Coordinate
Plane???
1.5 Measuring and
Constructing
Angles
1.6 Describing Pairs of
Angles
1
KCCRS
Standards
G-CO.A.1
G-CO.D.12
G-GPE.B.7
G-MG.A.1
Vocabulary
Undefined terms
Point
Line
Plane
Collinear points
Coplanar points
Defined terms
Line segment
Endpoints
Ray
Opposite ray
Intersection
Postulate
Axiom
Coordinate
Distance
Construction
Congruent segments
Between
Midpoint
Segment bisector
Angle
Vertex
Sides of an angle
Interior of an angle
Exterior of an angle
Measure of an angle
Acute angle
Right angle
Essential Questions Resources
How can you solve real life
problems involving lines and
planes?
How can you measure and
construct a line segment
How can you find the
midpoint and length of a line
segment in a coordinate
plane?
How can you find the
perimeter and area of a
polygon in a coordinate
plane?
How can you measure and
classify an angle?
How can you describe angle
pair relationships and use
these descriptions to find
angle measures?
I Can…
…name points,
lines, planes,
segments, and
rays.
…find segment
lengths using
the Ruler
Postulate, the
Segment
Addition
Postulate,
midpoints,
segment
bisectors, and
Distance
Formula.
…classify
polygons and
angles.
…find
perimeters and
areas of
polygons in the
coordinate
plane.
Notes
Make sure
students have a
good grasp on
this chapter.
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Geometry
Unit/Chapter
2. Reasoning and
Proofs
2.1 Conditional
Statements?
2.2 Inductive and
Deductive
Reasoning??
2.3 Postulates and
Diagrams??
2.4 Algebraic
Reasoning
2.5 Proving Statements
about Segments
and Angles
2.6 Proving Geometric
Relationships
2
KCCRS
Standards
G-CO.C.9, 10, 11
G-SRT.B.4
Vocabulary
Obtuse angle
Straight angle
Congruent angles
Angel bisector
Complementary
angles
Supplementary angles
Adjacent angles
Linear pair
Vertical angles
Conditional statement
If-then form
Hypothesis
Conclusion
Negation
Converse
Inverse
Contrapositive
Equivalent statements
Perpendicular lines
Biconditional
statement
Truth value
Truth table
Conjecture
Inductive reasoning
Counterexample
Deductive reasoning
Line perpendicular to
a plane
Proof
Two-column proof
Theorem
Essential Questions Resources
I Can…
Notes
…construct
congruent
segments and
angles, and
bisect segments
and angles.
When is a conditional
statement true or false?
How can you use reasoning to
solve problems?
In a diagram, what can be
assumed and what needs to
be labeled?
How can algebraic properties
help you solve an equation?
How can you prove a
mathematical statement?
How can you use a flowchart
to prove a mathematical
statement?
…write
conditional and
biconditional
statements.
…use inductive
and deductive
reasoning.
…use properties
of equality to
justify the steps
in solving
equations and
to find segment
lengths and
angle measures.
…write twocolumn proofs,
flowchart
proofs, and
2.1-2.3 focus
on the basics
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Geometry
Unit/Chapter
KCCRS
Standards
3. Parallel and
G-CO.A.1
Perpendicular Lines
G-CO.C.9, D.12
3.1 Pairs of Lines and
G-GPE.B.5, 6
Angles
3.2 Parallel Lines and
Transversals
3.3 Proofs with Parallel
Lines
3.4 Proofs with
Perpendicular Lines
3.5 Equations of
Parallel and
Perpendicular Lines
Vocabulary
Flowchart proof
Paragraph proof
Parallel lines
Skew lines
Parallel lines
Transversal
Corresponding angles
Alternate interior
angles
Alternate exterior
angles
Consecutive interior
angles
Distance from a point
to a line
Perpendicular bisector
Directed line segment
Essential Questions Resources
What does it mean when two
lines are parallel, intersecting,
coincident, or skew?
When two parallel lines are
cut by a transversal which of
the resulting pairs of angles
are congruent?
For which of the theorems
involving parallel lines and
transversals is the converse
true?
What conjectures can you
make about perpendicular
lines?
How can you write an
equation of a line that is
parallel or perpendicular to a
given line and passes through
a given point?
I Can…
paragraph
proofs.
…identify
planes, pairs of
angles formed
by transversals,
parallel lines,
and
perpendicular
lines.
…use properties
and theorems of
parallel lines.
…prove
theorems about
parallel lines
and about
perpendicular
lines.
…write
equations of
parallel lines
and about
perpendicular
lines.
…find the
distance from a
point to a line.
3
Notes
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Geometry
Unit/Chapter
4. Transformations
4.1 Translations
4.2 Reflections
4.3 Rotations
4.4 Congruence and
Transformations
4.5 Dilations
4.6 Similarity and
Transformations
4
KCCRS
Standards
G-CO.A.2, 3, 4, 5
G-CO.B.6
G-MG.A.3
G-SRT.A.1a, 1b, 2
Vocabulary
Vector
Initial point
Terminal point
Horizontal component
Vertical component
Component form
Transformation
Image
Preimage
Translation
Rigid motion
Composition of
transformations
Reflection
Line of reflection
Glide reflection
Line symmetry
Line of symmetry
Rotation
Center of rotation
Angles of rotation
Rotational symmetry
Center of symmetry
Congruent figures
Congruence
transformation
Dilation
Center of dilation
Scale factor
Enlargement
Reduction
Similarity
transformation
Essential Questions Resources
How can you translate a figure
in a coordinate plane?
How can you reflect a figure in
a coordinate plane?
How can you rotate a figure in
a coordinate plane?
What conjectures can you
make about a figure reflected
in two lines?
What does it mean to dilate a
figure?
When a figure is translated,
reflected, rotated, or dilated
in the plane, is the image
always similar to the original
figure?
I Can…
…perform
translations,
reflections,
rotations,
dilations, and
compositions of
transformations
.
…solve real-life
problems
involving
transformations
.
…identify lines
of symmetry
and rotational
symmetry.
…describe and
perform
congruence
transformations
and similarity
transformations
.
Notes
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Geometry
Unit/Chapter
KCCRS
Standards
Vocabulary
Essential Questions Resources
I Can…
Similar figures
5. Congruent Triangles
5.1 Angles of Triangles
5.2 Congruent
Polygons
5.3 Proving Triangle
Congruence by SAS
5.4 Equilateral and
Isosceles Triangles
5.5 Proving Triangle
Congruence by SSS
5.6 Proving Triangle
Congruence by ASA
and AAS
5.7 Using Congruent
Triangles
5.8 Coordinate
Proofs???
G-CO.C.10
G-MG.A.1, 3
G-CO.B.7, 8
G-CO.D.13
G-SRT.B.5
G-GPE.B.4
Interior angles
Exterior angles
Corollary to a theorem
Corresponding parts
Legs
Vertex angle
Base
Base angles
Hypotenuse
Coordinate proof
How are the angle measures
of a triangle related?
Given two congruent
triangles, how can you use
rigid motions to map one
triangle to the other triangle?
What can you conclude about
two triangles when you know
that two pairs of
corresponding sides and the
corresponding included angles
are congruent?
What conjectures can you
make about the side lengths
and angles measures of an
isosceles triangle?
What can you conclude about
two triangles when you know
the corresponding sides are
congruent?
5
…identify and
use
corresponding
parts.
…use theorems
about the
angles of a
triangle.
…Use SAS, SSS,
HL, ASA, and
AAS to prove
two triangles
congruent.
…prove
constructions.
…write
coordinate
proofs.
Notes
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Geometry
Unit/Chapter
KCCRS
Standards
Vocabulary
Essential Questions Resources
I Can…
What information is sufficient
to determine whether two
triangles are congruent?
How can you use congruent
triangles to make an indirect
measurement?
6. Relationships
Within Triangles
6.1 Perpendicular and
Angle Bisectors
6.2 Bisectors of
Triangles
6.3 Medians and
Altitudes of
Triangles
6.4 Triangle and
Midsegment
Theorem
6.5 Indirect Proof??
And Inequalities in
One Triangle
6.6 Inequalities in Two
Triangles
6
G-CO.C.9, 10
G-MG.A.1, 3
G-CO.D.12
G-C.A.3
Equidistant
Concurrent
Point of concurrency
Circumcenter
Incenter
Median of a triangle
Centroid
Altitude of a triangle
Orthocenter
Midsegment of a
triangle
Indirect proof
How can you use a coordinate
plane to write a proof?
What conjectures can you
make about a point on the
perpendicular bisector of a
segment and a point on the
bisector of an angle?
What conjectures can you
make about the perpendicular
bisectors and the angle
bisectors of a triangle?
What conjectures can you
make about the medians and
altitudes of a triangle?
How are the midsegments of a
triangle related to the sides of
the triangle?
How are the sides related to
the angles of a triangle? How
…understand
and us angle
bisectors and
perpendicular
bisectors to find
measures.
…find and use
the
circumference,
incenter,
centroid, and
orthocenter of a
triangle.
…use the
Triangle
Midsegment
Theorem and
the Triangle
Notes
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Geometry
Unit/Chapter
7. Quadrilaterals and
Other Polygons
7.1 Angles of Polygons
7.2 Properties of
Parallelograms
7.3 Proving that a
Quadrilateral is a
parallelogram
7.4 Properties of
Special
Parallelograms
7.5 Properties of
Trapezoids and
kites
8. Similarity
8.1 Similar Polygons
8.2 Proving Triangle
Similarity by AA
7
KCCRS
Standards
G-CO.C.11
G-SRT.B.5
G-MG.A.1, 3
G-SRT.A.2, 3
G-MG.A.1, 3
G-SRT.B.4, 5
G-GPE.B.5, 6
Vocabulary
Diagonal
Equilateral polygon
Equiangular polygon
Regular polygon
Parallelogram
Rhombus
Rectangle
Square
Trapezoid
Bases of a trapezoid
Base angles of a
trapezoid
Legs of a trapezoid
Isosceles trapezoid
Midsegment of a
trapezoid
kite
Corresponding parts
of similar polygons
Corresponding lengths
of similar polygons
Essential Questions Resources
I Can…
are any two sides of a triangle
related to the third side?
Inequality
Theorem.
If the two sides of one triangle
are congruent to two sides of
another triangle, what can you
say about the third sides of
the triangles?
What is the sum of the
measures of the interior
angles of a polygon?
…write indirect
proofs.
What are the properties of
parallelograms?
How can you prove that a
quadrilateral is a
parallelogram?
What are the properties of the
diagonals of rectangles,
rhombuses, and squares?
What are some properties of
trapezoids and kites?
How are similar polygons
related?
What can you conclude about
two triangles when you know
…find and use
the interior and
exterior angle
measures of
polygons.
…use properties
of
parallelograms
and special
parallelograms.
…prove that a
quadrilateral is a
parallelogram.
…identify and
use properties
of trapezoids
and kites.
…use AA, SSS,
and SAS
Similarity
Theorems to
Notes
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Geometry
Unit/Chapter
KCCRS
Standards
8.3 Proving Triangle
Similarity by SSS
and SAS
8.4 Proportionality
Theorems
9. Right Triangles and
Trigonometry
9.1 The Pythagorean
Theorem
8
G-SRT.B.4, 5
G-SRT.C.6, 7, 8
G-SRT.D.9, 10, 11
G-MG.A.1, 3
Vocabulary
Essential Questions Resources
Perimeters of similar
polygons theorem
Areas of similar
polygons theorem
Angle-Angles (AA)
similarity theorem
Side-Side-Side (SSS)
similarity theorem
Side-Angle-Side (SAS)
similarity theorem
Triangle
proportionality
theorem
Converse of the
Triangle
proportionality
theorem
Three Parallel Lines
Theorem
Triangle angle bisector
theorem
that two pairs of
corresponding angles are
congruent?
Pythagorean triple
Geometric mean
Trigonometric ratio
Tangent
Angle of elevation
Sine
How can you prove the
Pythagorean Theorem?
What are two ways to use
corresponding sides of two
triangles to determine that
the triangles are similar?
What proportionally
relationships exist in a triangle
intersected by an angle
bisector or by a line parallel to
one of the sides?
I Can…
prove triangles
are similar.
…decide
whether
polygons are
similar.
…use similarity
criteria to solve
problems about
lengths,
perimeters, and
areas.
…prove the
slope criteria
using similar
triangles.
What is the relationship
among the side lengths of 45°-
…use the
Triangles
Proportionality
Theorem and
other similar
proportionality
theorems.
…use the
Pythagorean
Theorem and
the Converse of
the Pythagorean
Theorem.
Notes
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Geometry
Unit/Chapter
KCCRS
Standards
9.2 Special Right
Triangles
9.3 Similar Right
Triangles
9.4 The Tangent Ratio
9.5 The Sine and
Cosine Ratios
9.6 Solving Right
Triangles
9.7 Laws of Sines and
Cosines??
Vocabulary
Cosine
Angle of depression
Inverse tangent
Inverse sine
Inverse cosine
Solve a right triangle
Law of Sines
Law of Cosines
Essential Questions Resources
45°-90° triangles? 30°-60°-90°
triangles?
How are altitudes and
geometric means of right
triangles related?
How is a right triangle used to
find the tangent of an acute
angle? Is there a unique right
triangle that must be used?
How is a right triangle used to
find the sine and cosine of an
acute angle? Is there a unique
right triangle that must be
used?
When you know the lengths of
the sides of a right triangle,
how can you find the
measures of the two acute
angles?
I Can…
…use geometric
means.
…find side
lengths and
solve real-life
problems
involving special
right triangles.
…find the
tangent side,
sine, and cosine
ratios and use
them to solve
real-life
problems.
…use the Law of
Sines and Law of
Cosines to solve
triangles.
What are the Law of Sines and
the Law of Cosines?
10. Circles
10.1 Lines and
Segments That
Intersect Circles
9
G-CO.A.1
G-C.A.1, 2, 3, 4
G-MG.A.1, 3
G-CO.D.13
G-GPE.A.1
Circle
Center
Radius
Chord
Diameter
Secant
What are the definitions of
the lines and segments that
intersect a circle?
How are circular arcs
measures?
…identify
chords,
diameters, radii,
secants, and
tangents of
circles.
Notes
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Geometry
Unit/Chapter
10.2 Finding Arc
Measures
10.3 Using Chords
10.4 Inscribed
Angles and
Polygons
10.5 Angle
Relationships in
Circles
10.6 Segment
Relationships in
circles
10.7 Circles in the
Coordinate plane??
11. Circumference ,
Area, and Volume
10
KCCRS
Standards
G-GPE.B.4
G-GMD.A.1,2, 3
G-GMD.B.4
G-C.B.5
Vocabulary
Tangent
Point of tangency
Tangent circles
Concentric circles
Common tangent
Central angle
Minor arc
Major arc
Semicircle
Measure of a minor
arc
Measure of a major
arc
Adjacent arcs
Congruent circles
Congruent arcs
Similar arcs
Inscribed angle
Intercepted arc
Subtend
Inscribed polygon
Circumscribed circle
Circumscribed angle
Segments of a chord
Tangent segment
Secant segment
External segment
Standard equation of
a circle
Circumference
Arc length
Radian
Population density
Essential Questions Resources
What are two ways to
determine when a chord is a
diameter of a circle?
How are inscribed angles
related to their intercepted
arcs? How are the angles of an
inscribed quadrilateral related
to each other?
When a chord intersects a
tangent line or another chord,
what relationships exist
among the angles and arcs
formed?
What relationships exist
among the segments formed
by two intersecting chords or
among segments of two
secants that intersect outside
a circle?
I Can…
…find angle and
arc measures.
…use inscribed
angles and
polygons and
circumscribed
angles.
…use properties
of chords,
tangents, and
secants to solve
problems.
…write and
graph equations
of cirlces.
What is the equation of a
circle with center (h, k) and
radius r in the coordinate
plane?
How can you find the length of
a circular arc?
…measure
angles in
radians.
Notes
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Geometry
Unit/Chapter
11.1 Circumference
and Arc Length
11.2 Areas of Circles
and Sectors
11.3 Areas of
Polygons
11.4 ThreeDimensional
Figures
11.5 Volumes of
Prisms and
Cylinders
11.6 Volumes of
Pyramids
11.7 Surface Areas
and Volumes of
Cones
11.8 Surface areas
and Volumes of
Spheres
12. Probability
12.1 Sample Space
and Probability
12.2 Independent
and Dependent
Events
11
KCCRS
Standards
G-CO.A.1
G-MG.A.1, 2, 3
G-C.B.5
S-CP.A.1, 2, 3, 4, 5
S-CP.B. 6, 7, 8, 9
Vocabulary
Sector of a circle
Center of a regular
polygon
Radius of a regular
polygon
Apothem of a regular
polygon
Central angle of a
regular polygon
Polyhedron
Face
Edge
Vertex
Cross section
Solid of revolution
Axis of revolution
Volume
Cavalieri’s Principle
Density
Similar solids
Lateral surface of a
cone
Chord of a sphere
Great circle
Essential Questions Resources
How can you find the area of a
sector of a circle?
How can you find the area of a
regular polygon?
What is the relationship
between the numbers of
vertices V, edges E, and faces
F of a polyhedron?
How can you find the volume
of a prism or cylinder that is
not a right prism or right
cylinder?
How can you find the volume
of a pyramid?
How can you find the surface
area and the volume of a
cone?
How can you find the surface
area and the volume of a
sphere?
How can you list the possible
outcomes in the sample space
of an experiment?
Probability
experiment
Outcome
Event
Sample space
How can you determine
Probability of an event whether two evens are
Theoretical probability independent or dependent?
I Can…
…find arc
lengths and
areas of sectors
of circles.
…find areas of
rhombuses,
kites, and
regular
polygons.
…find and use
volumes of
prisms,
cylinders,
pyramids,
cones, and
spheres.
…describe crosssections and
solids of
revolution.
…find the
experimental
and theoretical
probability of an
event.
Notes
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Geometry
Unit/Chapter
12.3 Two-way
tables and
Probability
12.4 Probability of
Disjoint and
Overlapping Events
12.5 Permutations
and Combinations
12.6 Binomial
Distributions
12
KCCRS
Standards
Vocabulary
Geometric probability
Experimental
probability
Independent events
Dependent events
Conditional
probability
Two-way table
Joint frequency
marginal frequency
joint relative
frequency
marginal relative
frequency
conditional relative
frequency
compound event
overlapping events
disjoint events
mutually exclusive
events
permutation
n factorial
combination
random variable
probability
distribution
binomial distribution
binomial experiment
Essential Questions Resources
How can you construct and
interpret a two-ways table?
How can you find probabilities
of disjoint and overlapping
events?
How can a tree diagram help
you visualize the number of
ways in which two or more
events can occur?
How can you determine the
frequency of each outcome of
an event?
I Can…
…find
probabilities of
independent
and dependent
events.
…use
conditional
relative
frequencies to
find conditional
probabilities.
…use formulas
for the number
of permutations
and the number
of
combinations.
…construct and
interpret
probability
distributions
and binomial
distributions.
Notes