Download Sand Creek Zone Curriculum Map

Sand Creek Zone Curriculum Map
Subject: Geometry
Strand/Concept
Q1 Unit 1
Engage NY Mod 1:A,B
Grade:
Student Expectation
Student Friendly Learning Objective
(SLO)
Quarter:
Level of thinking
G-CO.A.1: Know precise definitions of angle,
circle, perpendicular line, parallel line, and line
segment
I can precisely define angle, perpendicular
line, parallel line, and line segment, based
on the undefined notions of point, line, and
distance along a line.
Knowledge
Angle
Distance
End point
Line
Line segment
Parallel lines
Point
Precision
Perpendicular lines
Ray
Sides of an angle
Undefined notion
Vertex of an angle
G-CO.D.12: Make formal geometric
constructions with a variety of tools and
methods (compass and straightedge, string,
reflective devices, paper folding, dynamic
geometric software, etc.).
I can make formal geometric constructions
with a variety of tools and methods
(compass and straightedge, string, reflective
devices, paper folding, dynamic geographic
software
Application
Compass
Formal geometric
Construction
Straightedge
CG-CO.D.13: Construct an equilateral triangle,
a square, and a regular hexagon inscribed in a
circle.
I can construct an equilateral triangle
Application
Construction
Inscribe
Strand: Congruence
Concept: Experiment
with transformations in
the plane
Strand: Congruence
Concept: Make
geometric constructions
Strand: Congruence
Concept: Make
geometric constructions
Vocabulary
1
Sand Creek Zone Curriculum Map
Subject: Geometry
Strand/Concept
Strand: Congruence
Grade:
Student Expectation
Student Friendly Learning Objective
(SLO)
Quarter:
Level of thinking
G-CO.C.9: Prove theorems about lines and
angles.
I can prove theorems about lines and angles
Analysis
Interior angles
Line
Prove
Theorem
G-CO.A.2: Represent transformations in the
plane
I can represent transformations in the
planning using, e.g., transparencies and
geometry software
Comprehension
Compare
Describe
Distance
Function
Horizontal stretch
Input
Output
Plane
Point
Represent
Transformation
Translation
Concept: Prove
geometric theorems
Q1/2 Unit 2
Engage NY Mod 1:C
Strand: Congruence
I can describe transformations as functions
that take points in the plane as inputs and
give other points as outputs
Concept: Experiment
with transformations in
the plane
Strand: Congruence
Concept: Experiment
with transformations in
the plane
Strand: Congruence
Concept: Experiment
with transformations in
the plane
Vocabulary
G-CO.A.3: Given a rectangle, parallelogram,
trapezoid, or regular polygon, describe the
rotations and reflections that carry it onto itself.
Given a rectangle, parallelogram,
trapezoids, or regular polygon, I can
describe the rotations and reflections that
carry it onto itself
Application
Describe
Polygon
Rectangle
Reflection
Rotation
Trapezoid
G-CO.A.4: Develop definitions of rotations,
reflections, and translations in terms of angles,
circles, perpendicular lines, parallel lines, and
line segments.
I can develop definitions of rotations,
reflections, and translations in terms of
angles, circles, perpendicular lines, parallel
lines, and line segments.
Application
Circle
Describe
Line Segment
Parallel lines
Reflection
Rotation
Translation
2
Sand Creek Zone Curriculum Map
Subject: Geometry
Strand/Concept
Strand: Congruence
Concept: Experiment
with transformations in
the plane
Grade:
Student Expectation
G-CO.A.5: Given a geometric figure and a
rotation, reflection, or translation, draw the
transformed figure
Student Friendly Learning Objective
(SLO)
Given a geometric figure and a rotation,
reflection, or translation, I can draw the
transformed figure, e.g., graph paper, tracing
paper, or geometry software
Quarter:
Level of thinking
Comprehension
Application
Geometric figure
Reflection
Rotation
Sequence of
transformations
Specify
Transform
Application
Comprehension
Congruent
Decide
Geometric description
Rigid motion
Transform
Analysis
Congruent
Corresponding angles
Corresponding sides
Rigid motion
Triangle
I can specify a sequence of transformations
that will carry a given figure onto another
Strand: Congruence
Concept: Understand
congruence in terms of
rigid motions
G-CO.B.6: Use geometric descriptions of rigid
motions to transform figures and to predict the
effect of a given rigid motion on a given figure
I can use geometric descriptions of rigid
motions to transform figures and to predict
the effect of a given rigid motion on a given
figure
Vocabulary
Given two figures, I can use the definition of
congruence in terms of rigid motions to
decide if they are congruent
Q2 Unit 3
Engage NY Mod 1:D
Strand: Congruence
G-CO.B.7: Use the definition of congruence in
terms of rigid motions to show that two triangles
are congruent if and only if corresponding pairs
of sides and corresponding pairs of angles are
congruent.
I can use the definition of congruence in
terms of rigid motions to show that two
triangles are congruent if and only if
corresponding pairs of sides and
corresponding pairs of angle are congruent
Concept: Understand
congruence in terms of
rigid motions
3
Sand Creek Zone Curriculum Map
Subject: Geometry
Strand/Concept
Strand: Congruence
Concept: Understand
congruence in terms of
rigid motions
Grade:
Student Expectation
G-CO.B.8: Explain how the criteria for triangle
congruence (ASA, SAS, and SSS) follow from
the definition of congruence in terms of rigid
motions.
Student Friendly Learning Objective
(SLO)
I can explain how the criteria for triangle
congruence (ASA, SAS, and SSS) follow
from the definition of congruence in terms of
rigid notions
Quarter:
Level of thinking
Analysis
Vocabulary
ASA (angle-side-angle
postulate)
Congruence
Criteria for triangle
congruence
Explain
Rigid motion
SAS (side-angle-side
postulate)
SSS(Side-side-side
postulate)
Interior angles
Strand: Congruence
Concept: Prove
geometric theorems
Strand: Congruence
Concept: Prove
geometric theorems
G-CO.C.9: Prove1 theorems about 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.
I can prove theorems about lines and angles
Analysis
Line
Prove
Theorem
G-CO.C.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.
I can prove theorems about triangles
Analysis
Interior angle
Prove
Theorem
Triangle
4
Sand Creek Zone Curriculum Map
Subject: Geometry
Strand/Concept
Strand: Congruence
Concept: Prove
geometric theorems
Q3 Unit 4
Engage NY Mod 2:E
Strand: Similarity,
Right Triangles, and
Trigonometry
Grade:
Student Expectation
Student Friendly Learning Objective
(SLO)
Quarter:
Level of thinking
Vocabulary
G-CO.C.11: Prove theorems about
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.
I can prove theorems about parallelograms
Analysis
Prove
Theorem
G-SRT.C.6: Understand that by similarity, side
ratios in right triangles are properties of the
angles in the triangle, leading to definitions of
trigonometric ratios for acute angles.
I can state that by similarity, side ratios in
right triangles are properties of the angles in
the triangle, leading to definitions of
trigonometric ratios for acute angles
Application
Property
Right triangle
Side ratio
Similarity
Triangle
Trigonometric ratio
Understand
G-SRT.C.7: Explain and use the relationship
between the sine and cosine of complementary
angles.
I can explain and use the relationship
between the sine and cosine of
complementary angles
Application
Explain
Complementary angle
Cosine
Relationship
Sine
Concept: Prove
theorems involving
similarity
Strand: Similarity,
Right Triangles, and
Trigonometry
Concept: Define
trigonometric ratios and
solve problems
involving right triangles
5
Sand Creek Zone Curriculum Map
Subject: Geometry
Strand/Concept
Strand: Similarity,
Right Triangles, and
Trigonometry
Grade:
Student Expectation
Student Friendly Learning Objective
(SLO)
Quarter:
Level of thinking
G-SRT.C.8: Use trigonometric ratios and the
Pythagorean Theorem to solve right triangles in
applied problems.
I can use trigonometric ratios and the
Pythagorean Theorem to solve right
triangles in applies problems
Application
Applied problem
Pythagorean theorem
Right triangle
Solve
Trigonometric ration
G-SRT.A.2: Given two figures, use the
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.
Given two figures, I can use the definition of
similarity in terms of similarity
transformations to decide if they are similar
Application
I can 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
Comprehension
Corresponding angles
Corresponding sides
Decide
Equality
Explain
Proportion
Similar
Similarity transformation
Triangle
G-SRT.A.3: Use the properties of similarity
transformations to establish the AA criterion for
two triangles to be similar.
I can use the properties of similarity
transformations to establish the AA criterion
for two triangles to be similar.
Analysis
Concept: Define
trigonometric ratios and
solve problems
involving right triangles
Strand: Similarity,
Right Triangles, and
Trigonometry
Concept: understand
similarity in terms of
similarity
transformations
Strand: Similarity,
Right Triangles, and
Trigonometry
Concept: understand
similarity in terms of
similarity
transformations
Vocabulary
AA criterion (angle-angle)
Properties of similarity
transformations
Similar
Triangle
6
Sand Creek Zone Curriculum Map
Subject: Geometry
Strand/Concept
Strand: Similarity,
Right Triangles, and
Trigonometry
Grade:
Student Expectation
Student Friendly Learning Objective
(SLO)
Quarter:
Level of thinking
G-SRT.B.5: Use congruence and similarity
criteria for triangles to solve problems and
prove relationships in geometric figures.
I can use congruence and similarity criteria
for triangles to solve problems and prove
relationships in geometric figures.
Analysis
Prove
Solve
Geometric figure
Relationship
Similarity criteria
Triangle
G-MG.A.1: Using geometric shapes, their
measures, and their properties to describe
objects (e.g., modeling a tree trunk or a human
torso as a cylinder)
I can use geometric shapes, their measures,
and their properties to describe objects (e.g.,
modeling a tree trunk or a human torso as a
cylinder)
Application
Cylinder
Describe
Geometric
Measure
Model
Property
Shape
G-GMD.A.1: Give an informal 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.
I can five and informal argument for the
formulas for the circumference of a circle
Analysis
Argument
Circle
Circumference
Formula
Informal
Concept: Prove
theorems involving
similarity
Strand: Modeling with
Geometry
Concept: Apply
geometric concepts in
modeling situations
Q3 Unit 5
Engage NY Mod 3:A,B
Strand: Geometric
Measurement and
Dimension
Vocabulary
Context: Explain
volume formulas and
use them to solve
problems
7
Sand Creek Zone Curriculum Map
Subject: Geometry
Strand/Concept
Strand: Geometric
Measurement and
Dimension
Grade:
Student Expectation
Student Friendly Learning Objective
(SLO)
Quarter:
Level of thinking
G-GMD.A.3: Use volume formulas for
cylinders, pyramids, cones and spheres to
solve problems.
I can use volume formulas for cylinders,
pyramids, cones and spheres to solve
problems.
Application
Cone
Cylinder
Solve
Pyramid
Sphere
Volume formula
G-GMD.B.4: Identify the shapes of twodimensional cross-sections of threedimensional objects, and identify threedimensional objects generated by rotations of
I can identify the shapes of two-dimensional
cross-sections of three-dimensional objects,
Application
Cross section
Generate
Identify
Rotation
Three-dimensional
Two-dimensional
Shape
G-GMD.A.1: Give an informal 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.
I can five and informal argument for the
formulas for the circumference of a circle
Analysis
Context: Explain
volume formulas and
use them to solve
problems
Strand: Geometric
Measurement and
Dimension
Concept: Visualize
relationships between
two-dimensional and
three-dimensional
objects
Strand: Geometric
Measurement and
Dimension
Concept: Visualize
relationships between
two-dimensional and
three-dimensional
objects
Vocabulary
8
Sand Creek Zone Curriculum Map
Subject: Geometry
Strand/Concept
Strand: Geometric
Measurement and
Dimension
Grade:
Student Expectation
Student Friendly Learning Objective
(SLO)
Quarter:
Level of thinking
G-GMD.A.3: Use volume formulas for
cylinders, pyramids, cones and spheres to
solve problems.
I can use volume formulas for cylinders,
pyramids, cones and spheres to solve
problems.
Application
Cylinder
Describe
Geometric
Measure
Model
Property
Shape
G-GMD.B.4: Identify the shapes of twodimensional cross-sections of threedimensional objects, and identify threedimensional objects generated by rotations of
two- dimensional objects.
I can identify the shapes of two-dimensional
cross-sections of three-dimensional objects,
Application
Cross section
Generate
Identify
Rotation
Three-dimensional
Two-dimensional
Shape
G-GPE.B.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).
I can use coordinates to prove simple
geometric theorems algebraically
Concept: Visualize
relationships between
two-dimensional and
three-dimensional
objects
Strand: Modeling with
Geometry
Concept: Apply
geometric concepts in
modeling situations
Q4 Unit 7
Engage NY Mod 4
Strand: Expressing
Geometric Properties
and Equations
Vocabulary
I can identify three-dimensional objects
generated by rotations of two- dimensional
objects
Concept: Use
coordinates to prove
simple geometric
theorems algebraically
9
Sand Creek Zone Curriculum Map
Subject: Geometry
Strand/Concept
Strand: Expressing
Geometric Properties
and Equations
Concept: Use
coordinates to prove
simple geometric
theorems algebraically
Strand: Expressing
Geometric Properties and
Equations
Grade:
Student Expectation
Student Friendly Learning Objective
(SLO)
Quarter:
Level of thinking
Vocabulary
G-GPE.B.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).
I can 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).
Analysis
G-GPE.B.6: Find the point on a directed line
segment between two given points that
partitions the segment in a given ratio.
I can find the point on a directed line
segment between two given points that
partitions the segment in a given ratio.
Application
Directed line segments
Partition
Point
Ratio
G-GPE.B.7: Use coordinates to compute
perimeters of polygons and areas of triangles
and rectangles, e.g., using the distance formula
I can use coordinates to compute perimeters
of polygons e.g., using the distance formula
Application
I can compute areas of triangles and
rectangles e.g., using the distance formula
Application
Compute
Coordinate
Perimeter
Polygon
Rectangle
Triangle
Application
Equation
Geometric problem
Line
Parallel lines
Point
Prove
Slope criteria Solve
Concept: Use
coordinates to prove
simple geometric
theorems algebraically
Strand: Expressing
Geometric Properties and
Equations
Concept: Use
coordinates to prove
simple geometric
theorems algebraically
10
Sand Creek Zone Curriculum Map
Subject: Geometry
Strand/Concept
Q4 Unit 6
Engage NY Mod 5:all
Strand: Circles
Concept: Understand
and apply theorems to
circles
Strand: Circles
Concept: Understand
and apply theorems to
circles
Strand: Circles
Concept :Find arc
lengths and areas of
sectors of circles
Grade:
Student Expectation
Student Friendly Learning Objective
(SLO)
Quarter:
Level of thinking
G-C.A.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.
I can identify and describe relationships
among inscribed angles, radii, and chords.
Comprehension
I can describe relationships among inscribed
angles, radii, and chords.
Application
G-C.A.3: Construct the inscribed and
circumscribed circles of a triangle, and prove
properties of angles for a quadrilateral inscribed
in a circle..
I can construct the inscribed ad
circumscribed circles of a triangle
Application
I can prove properties of angles for a
quadrilateral inscribed in a circle
Analysis
G-C.B.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.
I can derive using similarity the fact that the
length of the arc intercepted by an angle is
proportional to the radius
Analysis
I can define the radian measure of the angle
as the constant of proportionality
Comprehension
I can derive the formula for the area of
sector
Analysis
Vocabulary
Chord
Describe
Diameter
Identify
Inscribe
Inscribed angle
Radius
Relationship
Circle
Circumscribed circle of a
triangle
Construct
Inscribe
Inscribed circle of a
triangle
Prove
Quadrilateral
Arc
Constant of proportionality
Define
Derive
Formula
Intercept
Proportion
Radian
Radius
Sector
Similarity
11
Sand Creek Zone Curriculum Map
Subject: Geometry
Strand/Concept
Grade:
Student Expectation
Student Friendly Learning Objective
(SLO)
Quarter:
Level of thinking
Vocabulary
G-C.A.1: Prove that all circles are similar
12
COMMON CORE AND COLORADO ACADEMIC STANDARDS
13