Beaverton School District Geometry Long-term and Supporting Learning Targets

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Oct 10, 2013 (3 years and 6 months ago)

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M
A.
HS.
G
E
.ALT.0
1: I can demonstrate my understanding

of the foundations of
geometry.


M
A.
HS.GE.AST.0
1.1: I can translate between vocabulary, symbols and/or a
diagram to communicate.

M
A.
HS.GE.AST.0
1.2: I can demonstrate my understanding of the und
efined terms.

M
A.
HS.GE.AST.0
1.3: I can use definitions
,

postulates
, and theorems

to build and
defend a logical argument.

M
A.
HS.GE.AST.0
1.4: I can apply inductive and deductive reasoning to build and
defend a logical argument.



M
A.
HS.
G
E
.ALT.0
2
: I can pr
ove and apply congruence theorems dealing with
angles

and
lines to solve problems and justify my solutions.


M
A.
HS.GE.AST.0
2
.1: I can apply and prove theorems and use properties dealing
with vertical angles and a linear pair of angles.

M
A.
HS.GE.AST.0
2
.2:

I can apply and prove theorems and use properties dealing
with complementary and supplementary angles.

M
A.
HS.GE.AST.0
2
.3: I can apply and prove theorems and use properties dealing
with parallel and perpendicular lines.

M
A.
HS.GE.AST.0
2
.4: I can use angle

measures to prove that lines are parallel or
perpendicular.



M
A.
HS.GE.ALT.0
3
: I can connect linear algebra and coordinates to geometric
situations and use it to prove geometric theorems. (CCSS
-
G
-
GPE
-
4
-
7)


M
A.
HS.GE.AST.0
3
.1: I can use coordinates to pr
ove 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)

M
A.
HS.GE.AST.0
3
.2: I can prove the slope criteria for parallel and perpendicular
lines and use them to solve geometric problems.



For example
, find the equation of a line parallel or perpendicular to a given line that
passes through a given point.



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 a point).

B
eaverton School District

Geometry

Long
-
term and Supporting Learning Targets

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/
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Given a diagram, determine if two lines are parallel, perpendicular, or neither.

M
A.
HS.GE.AST.0
3
.3: I can find the point on a line segment between two given
points that divides the segm
ent in a given ratio (1/2, ¼, 1/8…).



Use midpoint theorem.

M
A.
HS.GE.AST.0
3
.4: I can prove theorems about quadrilaterals
(opposite sides
are congruent, o
pposite angles are congruent, the diagonals of a parallelograms
with congruent diagonals.



M
A.
HS.
GE.AL
T
.0
4
: I can prove and apply congruence theorems dealing with triangles
to solve problems and justify my solutions.


M
A.
HS.GE.AST.0
4.1: I can use a diagram that marks the congruent segments and
angles and
determine

if two triangles are congruent.

M
A.
HS.GE.A
ST.0
4.2: I can use a diagram that marks the congruent segments and
angles and
formally prove

if two triangles are congruent.

M
A.
HS.GE.AST.0
4.3: I can use Corresponding Parts of Congruent Triangles
Theorem to determine and prove other statements.

M
A.
HS.GE
.AST.0
4.4: I can apply the congruence of polygons to solve problems.



M
A.
HS.
GE
.ALT.0
5
: I am able to use a variety of tools and methods to construct basic
geometric figures.


M
A.
HS.GE.AST.0
5
.1: I can draw formal geometric constructions with a variety o
f
tools and methods, which could include, but not limited to, the following;
compass and straightedge, string, reflective devices, and dynamic geometric
software.




Formal Geometric Constructions should include: Copying a segment; copying an angle;
bisectin
g a segment; bisecting an angle; constructing perpendicular lines, including the
perpendicular bisector of a line segment; and constructing a line parallel to a given line
through a point not on the line.

M
A.
HS.GE.AST.0
5
.2: I can apply and construct trian
gle properties including
medians, centroids, circumcenters, orthocenters, and incenters.

M
A.
HS.GE.AST.0
5
.3: I can construct an equilateral triangle, a square and a regular
hexagon inscribed in a circle.

M
A.
HS.GE.AST.0
5
.4: I can construct the inscribed an
d circumscribed circles of a
triangle.



M
A.
HS.GE.ALT.0
6
: I can apply the laws of similarity to solve problems and prove my
solutions


M
A.
HS.GE.AST.0
6
.1: I can apply the similarity of polygons to solve problems

M
A.
HS.GE.AST.0
6
.2: I can apply the triangle

similarity theorems to solve
problems, write and complete proofs.

M
A.
HS.GE.AST.0
6
.3: I can prove whether or not two shapes are similar.


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/12


M
A.
HS.GE.ALT.0
7
: I can solve for unknown lengths and angles in right triangles and
justify my solutions. (CCSS
-
G
-
SR
T
-
6
-
8)


M
A.
HS.
G
E.AST.0
7
.1: Given three side lengths, I can determine and justify whether
a triangle can be created.

M
A.
HS.
G
E.AST.0
7
.2: I can use the Pythagorean Theorem to find unknown lengths
of right triangles and determine if a triangle is right, obtus
e, or acute.

M
A.
HS.
G
E.AST.0
7
.3: I can demonstrate and use properties of special right
triangles.



30
-

60
-
90 triangles



45
-
45
-
90 triangles

M
A.
HS.
G
E.AST.0
7
.4: I can use trigonometric ratios (sine, cosine and tangent) to
find unknown lengths in right triangle
s.



Explain and use the relationship between the sine and cosine of complementary angles.



Understand that by similarity, side ratios in right triangles are properties of angles in
the triangle, leading to definitions of trigonometric ratios for acute angle
s.

M
A.
HS.
G
E.AST.0
7
.5: I can use trigonometric ratios (sine, cosine, and tangent) to
find the unknown angles in right triangles.



Explain and know the differences between; sin, sin
-
1 , cos, cos
-
1 , tan, tan
-
1 and when to
use them.

M
A.
HS.
G
E
.AST.0
7
.6: In ap
plied problems I can use trigonometric ratios and the
Pythagorean Theorem to solve right triangles.



M
A.
HS.GE.ALT.0
8
: I can prove theorems and utilize the properties to solve problems
of two
-
dimensional polygons, including real
-
world applications. (CCSS
-
G
-
CO
-
10
-
11,
CCSS
-
G
-
MG
-
1
-
3)


M
A.
HS.GE.AST.0
8
.1: I can classify polygons based on characteristics.



Triangle classifications: right, acute, obtuse, scalene, equilateral, isosceles.



Quadrilateral classifications: trapezoid, rectangle, square, kite, parall
elogram, and
rhombus.



General classifications: by number of sides, by properties of quadrilaterals, equilateral,
equiangular, regular, convex, concave.

M
A.
HS.GE.AST.0
8
.2: I can find the perimeter and area of a variety of polygons,
including applications
.



Including: regular polygons, quadrilaterals, triangles, composite shapes, and shaded
regions.



Use coordinates to compute perimeters of polygons and areas of triangles and rectangles
(e.g. using the distance formula)



Apply concepts of density based on ar
ea and volume in modeling situations (ex: person
per square mile)

M
A.
HS.GE.AST.0
8
.3: I can find the unknown sides and angles of a variety of
polygons, including
applications.




Given area or perimeter of a polygon, find a missing dimension.



Given a diagra
m or information, find a missing angle.

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M
A.
HS.GE.AST.0
8
.4: Given similar figures, I can compare and compute their
respective areas and volumes. *Can be taught in 2
-
D and 3
-
D.


M
A.
HS.GE.ALT.0
9
: I can apply properties of circles to solve problems and justi
fy my
solutions. (CCSS
-
G
-
C
-
1
-
5)


M
A.
HS.GE.AST.0
9
.1: I can apply properties of angles formed by chords, tangents
and secants to solve problems.



This includes the use of congruent circles, concentric circles, radius, chord, diameter,
tangent, point of tange
ncy, central angle, inscribed angle.

M
A.
HS.GE.AST.0
9
.2: I can prove that all circles are similar.

M
A.
HS.GE.AST.0
9
.3: I can state and use precise definitions of circles, arcs,
degrees, radians, arc measure, arc length, and areas of sectors.

M
A.
HS.GE.AST.
0
9
.4: I can derive the formula for the area of a sector of a circle.

M
A.
HS.GE.AST.0
9
.5: I can give an informal argument for the circumference of a
circle, and for the area of a circle.

M
A.
HS.GE.AST.0
9
.6: I can use coordinates to prove that a point lies
on a circle
and circumscribed and inscribed circles.

M
A.
HS.GE.AST.0
9
.7: I can prove properties of angles for a quadrilateral inscribed
in a circle.



M
A.
HS.GE.ALT.
10
: I can apply the characteristics and properties of Three
-
Dimensional

figures to solve pr
oblems, including applications and justify my
solutions. (CCSS
-
G
-
GMD
-
1
-
3, CCSS
-
G
-
MG
-
1
-
3)


M
A.
HS.GE.AST.
10
.1: I can identify and classify 3
-
D figures from a model, a net,
and different perspectives.




Recognize face, vertex, edge, diagonal, lateral face,
base, altitude.



Use geometric shapes, their measures, and their properties to describe objects (e.g.,
modeling a tree trunk or a human torso as a cylinder)

M
A.
HS.GE.AST.
10
.2: I can find the surface area of 3
-
Dimensional figures including
applications.



Giv
en the surface area of 3
-
Dimensional figures, I can find missing measures.



Applications situations should specifically address concepts of density and optimization
as well as other situations.

M
A.
HS.GE.AST.
10
.3: I can find the volume of 3
-
Dimensional figu
res, including
applications.



Give an informal argument for the volume of a cylinder, pyramid and cone.



Give an informal argument using Cavalieri’s principle for the formulas for the volume of
a sphere and other solid figures.




Given the volume area of 3
-
D
imensional figures, I can find missing measures.



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)

M
A.
HS.GE.AST.
10
.4: I can visualize relationships between 2
-
D and 3
-
D figures.



Identify the shapes of 2
-
dimensional cross
-
sections of 3
-
dimensional objects, and identify
3
-
dimensional objects generated by rotations of 2
-
dimensional objects.

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/12


M
A.
HS.GE.ALT.
12:

I can use
independence and conditional probability formally to
interpret data and compute the probabilities of compound events. (CCSS
-
S
-
CP
-
1
-
7)


M
A.
HS.
G
E
.AST
.
12
.1
:

I can describe events as subsets of a sample space (the set of
outcomes) using characteristics (or cat
egories) of the outcomes, or as unions,
intersections, or complements of other events (“or”, “and”, “not”).

M
A.
HS.GE.AST.
12
.2
:

I can demonstrate that two events A and B are independent
of the probability of A and B occurring together is the products of the
ir
probabilities, and use this characterization to determine if they are independent.

M
A.
HS.GE.AST.
12
.3
:

I can use the general formula to compute the conditional
probability of A given B as P(A and B)/P(B).

M
A.
HS.GE.AST.
1
2.4:

I can use a two
-
way table as a

sample space to decide if
events are independent and to approximate conditional probabilities.

M
A.
HS.GE.AST.
12.5:

I can recognize and explain the concepts of conditional
probability and independent in every day language and every day situations.

M
A.
HS.GE
.AST.
12.6:

I can model conditional probability of an event through Venn
Diagrams and Factor Trees.

M
A.
HS.GE.AST.
12.7:

I can 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.



Due to a reduction
to the number of student contact days for 2012
-
13, it is recommended
that this target be included only if time allows or it is naturally integrated with another
target or targets.



MA.
HS.
G
E.ALT 11
: I can apply and analyze transformations of figures. (CCS
S
-
G
-
CO
-
2
-
5)


MA.
HS.
G
E.AST.
11
.1: I can identify lines of symmetry and distinguish between
rotation and reflection symmetries given a rectangle, parallelogram, trapezoid, or
regular polygon,

MA.
HS.
G
E.AST.
11
.2: I can identify and draw rigid transformations

of 2
-
dimensional figures on and off the coordinate plane.



Transformations should include translations, reflections across either axis, or y = +/
-

x,
and rotations about the origin in multiples of 90 degrees.



Students can use graph paper, tracing paper,
or geometry software to represent rigid
transformations.

MA.
HS.
G
E.AST.
11
.3: I can identify and apply non
-
rigid transformations of
geometric figures on and off the coordinate plane.

Transformatio
ns should address scale factor, dilations including origin centered dilations,
and similarity
.