Download Sharp Math Geometry Standard 6th 7th 8th M-G

Sharp Math
Geometry
Standard
6th
7th
8th
M-G-1
Standard
Standard
Standard
Find the area of right
Solve problems involving
Verify experimentally the
triangles, other triangles,
scale drawings of
properties of rotations,
special quadrilaterals, and
geometric figures,
reflections, and
polygons by composing
including computing
translations:
into rectangles or
actual lengths and areas
decomposing into triangles
from a scale drawing ando
and other shapes; apply
reproducing a scale
these techniques in the
drawing at a different
context of solving real-
scale.
world and mathematical
a. Lines
are taken to lines, and line
segments to line segments
of the same length.
b. Angles
o
problems.
are taken to angles of the
same measure.
c.
o
Parallel lines are taken to
parallel lines.
Teacher Target
Teacher Target
Teacher Target
Student Target:
Student Target
Student Target
1.
I can compose
and proportions
polygons into
to create scale
triangles and
drawing. (K)
2.
corresponding
area of a triangle
sides of scaled
to the area of the
geometric
composted
figures. (K)
3.
1.
I can define and
identify rotations,
reflections, and
translations. (K)
I can identify
I can compare the
rectangle. (R)
3.
I can use ratios
and decompose
rectangles. (K)
2.
1.
2.
I can identify
corresponding
sides and
corresponding
I can compute
angles. (K)
I can apply the
lengths and areas
techniques of
from scale
composing and/or
drawings using
decomposing to
strategies such as
find the area of
proportions. (K)
describe an
I can solve
image after a
triangles, special
4.
3.
I can use prime
notation to
4.
quadrilaterals
problems
translation,
and polygons to
involving scale
solve
drawings of
reflection, or
mathematical and
geometric figures
real world
using scale
problems. (R)
factors. ®
I can discuss,
5.
rotation. (K)
4.
center of
I can reproduce a
develop and
scale drawing
justify formulas
that is
for triangles and
proportional to a
parallelograms.
given geometric
(R)
figure using a
rotation. (K)
5.
I can identify
direction and
degree of
rotation. (K)
different scale.
(product)
I can identify
6.
I can identify line
of reflection. (K)
7.
I can use physical
models,
transparencies,
or geometry
software to verify
the properties of
rotations,
reflections, and
translations. (R)
M-G-2
Standard Demonstrator
Standard Demonstrator
Standard Demonstrator
Standard
Standard
Standard
Find the volume of a right
Draw (freehand, with
Understand that a two-
rectangular prism with
ruler and protractor, and
dimensional figure is
fractional edge lengths by
with technology)
congruent to another if
packing it with unit cubes
geometric shapes with
the second can be
of the appropriate unit
given conditions. Focus on
obtained from the first by
fraction edge lengths, and
constructing triangles
a sequence of rotations,
show that the volume is
from three measures of
reflections, and
the same as would be
angles or sides, noticing
translations; given two
found by multiplying the
when the conditions
congruent figures,
edge lengths of the prism.
determine a unique
describe a sequence that
Apply the formulas V = l
triangle, more than one
exhibits the congruence
triangle, or no triangle.
between them.
Teacher Target
Teacher Target
Teacher Target
Student Target:
Student Target
Student Target
w h and V = b h to find
volumes of right
rectangular prisms with
fractional edge lengths in
the context of solving
real-world and
mathematical problems.
1.
I can calculate
1.
the volume of a
which conditions
right rectangular
create unique
prism. (K)
2.
than one
volume formulas
triangles, or no
for right
2.
mathematical
problems
based on the
involving
volume of a right
triangle, more
rectangular
than one triangle,
prism with
or no triangle. ®
fractional edge
unit cubes of the
appropriate unit
fraction edge
lengths. (P)
congruency to
write congruent
statements. (R)
4.
3.
I can construct
triangles from
three given angle
measures to
determine when
there is a unique
triangle, more
I can reason that
a two-D figure is
congruent to
another if the
second can be
obtained by a
sequence of
there is a unique
I can model the
I can apply the
concept of
determine when
length. (R)
packing it with
3.
a triangle to
fractional edge
lengths by
congruency. (K)
angles or sides of
prisms with
I can identify
symbols for
three measures of
rectangular
3.
2.
I can analyze
given conditions
I can define
congruency. (K)
triangle.(K)
rectangular
real-world and
1.
triangles, more
I can apply
prisms to solve
I can know
rotations,
reflections,
translation. (R)
5.
I can describe the
sequence of
rotations,
reflections,
translations that
exhibits the
congruence
between 2-D
figures using
words. (R)
than one triangle
or no triangle
using
appropriate tools.
(Performance)
4.
I can construct
triangles from
three given side
measures to
determine when
there is a unique
triangle, more
than one triangle
or no triangle
using
appropriate tools.
(Preformace)
M-G-3
Standard Demonstrator
Standard Demonstrator
Standard Demonstrator
Standard
Standard
Standard
Draw polygons in the
Describe the two-
Describe the effect of
coordinate plane given
dimensional figures that
dilations, translations,
coordinates for the
result from slicing three-
rotations, and reflections
vertices; use coordinates
dimensional figures, as in
on two-dimensional
to find the length of a side
plane sections of right
figures using coordinates.
joining points with the
rectangular prisms and
same first coordinate or
right rectangular
the same second
pyramids.
coordinate. Apply these
techniques in the context
of solving real-world and
mathematical problems.
Teacher Target
Teacher Target
Teacher Target
Student Target:
Student Target
Student Target
1.
2.
3.
I can draw
1.
I can define
polygons in the
slicing as the
coordinate plane.
cross-section of a
(K)
3-D figure. (K)
I can use
2.
1.
dilations as a
reduction or
enlargement of a
I can describe the
coordinates to
two-dimensional
find the length of
figures that result
a side of a
from slicing a
polygon. (K)
three-
I can apply the
dimensional
techniques of
figure such as a
using coordinates
right rectangular
to find the length
prism or
of a side of a
pyramid. (K)
I can define
figure. (K)
2.
I can identify
scale factor of the
dilation. (K)
3.
I can describe the
effects of
dilations,
I can analyze
translations,
in the coordinate
three-
plane to solve
dimensional
rotations, and
real-world and
shapes by
mathematical
examining two-
problems. (R)
dimensional
polygon drawn
3.
reflections on 2D figures using
coordinates. (R)
cross-sections.
(R)
M-G-4
Standard Demonstrator
Standard Demonstrator
Standard Demonstrator
Standard
Standard
Standard
Represent three-
Know the formulas for the
Understand that a two-
dimensional figures using
area and circumference of
dimensional figure is
nets made up of
a circle and use them to
similar to another if the
rectangles and triangles,
solve problems; give an
second can be obtained
and use the nets to find
informal derivation of the
from the first by a
the surface area of these
relationship between the
sequence of rotations,
figures. Apply these
circumference and area of
reflections, translations,
techniques in the context
a circle.
and dilations; given two
of solving real-world and
similar two-dimensional
mathematical problems.
figures, describe a
sequence that exhibits the
similarity between them.
Teacher Target
Teacher Target
Teacher Target
Student Target:
Student Target
Student Target
1.
I can identify that
1.
3-D figures can
2.
3.
I can identify the
area of rectangles
and
and triangles to a
circumference of
net, and combine
the areas for each
answer
4.
5.
similarity
statements. (R)
4.
a 2-D figure is
I can identify the
another if the
similar to
second can be
obtained by a
sequence of
rotations,
involving surface
circumference
area using nets.
and diameter of a
(R)
6.
reflections,
translations, or
I can justify that
from the
problems
I can reason that
a circle. (K)
π can be derived
mathematical
I can apply the
concept of
(K)
figure. (R)
world and
similar. (K)
3.
circumference.
3-dimensional
I can recognize
symbol for
given its
surface area of a
I can solve real-
2.
area of a circle,
representing the
4.
I can identify π.
proportional. (K)
formulas for area
calculating the
shape into one
sides are
(K)
triangles. (R)
knowledge of
corresponding
chord. (K)
figures using nets
I can apply
congruent and
center, and
dimensional
3.
angles are
circumference,
three-
rectangles and
corresponding
diameter, area,
I can represent
I can define
similar figures as
including radius,
nets. (K)
made up of
1.
parts of a circle
be represented by
2.
I can identify the
dilations. (R)
5.
I can describe the
sequence fo
rotations,
reflections,
circle. (R)
translations, or
I can apply
exhibits the
circumference or
dilations that
similarity
between 2-D
area formula to
figures using
solve
words and/or
mathematical
symbols. (R)
and real-world
problems. (R)
7.
I can justify the
formulas for area
and
circumference of
a circle and how
they relate to π.
(R)
8.
I can informally
derive the
relationship
between
circumference
and area of a
circle. (R)
M-G-5
Standard Demonstrator
Standard Demonstrator
Standard Demonstrator
Standard
Standard
Standard
Use facts about
Use informal arguments
supplementary,
to establish facts about the
complementary, vertical,
angle sum and exterior
and adjacent angles in a
angle of triangles, about
multi-step problem to
the angles created when
write and solve simple
parallel lines are cut by a
equations for an unknown
transversal, and the
angle in a figure.
angle-angle criterion for
similarity of triangles. For
example, arrange three
copies of the same triangle
so that the sum of the
three angles appears to
form a line, and give an
argument in terms of
transversals why this is so.
Teacher Target
Teacher Target
Teacher Target
Student Target
Student Target
Student Target
1.
I can identify
1.
and recognize
similar triangles.
types of angles:
(K)
supplementary,
complementary,
2.
transversals. (K)
(K)
I can determine
3.
when parallel
supplements of a
line is cut by
given angle. (K)
I can determine
unknown angle
transversal. (K)
4.
interior angles
writing and
equals 180. (R)
solving algebraic
on relationships
I can justify that
the sum of
measures by
equations based
I can identify
angles created
complements and
3.
I can define and
identify
vertical, adjacent.
2.
I can define
5.
I can justify that
the exterior angle
between angles.
of a triangle is
(R)
equal to the sum
of the two remote
interior angles.
(R)
6.
I can use AngleAngle Criterion
to prove
similarity among
triangles. (R)
M-G-6
Standard Demonstrator
Standard Demonstrator
Standard Demonstrator
Standard
Standard
Standard
Solve real-world and
Explain a proof of the
mathematical problems
Pythagorean Theorem and
involving area, volume
its converse.
and surface area of twoand three-dimensional
objects composed of
triangles, quadrilaterals,
polygons, cubes, and right
prisms.
Teacher Target
Teacher Target
Teacher Target
Student Target
Student Target
Student Target
1.
I can explain the
1.
vocabulary:
formulas for area
square, root,
and volume and
Pythagorean
then procedure
Theorem, right
for finding
angle, legs a &b,
surface area and
hypotenuse, sides,
when to use them
right triangle,
converse, base,
in real-world
and math
problems for two
height, proof. (K)
2.
and hypotenuse
dimensional
of a right
objects composed
quadrilaterals,
I can be able to
identify the legs
and three
of triangles,
I can define key
triangle. (K)
3.
I can explain a
proof of a
polygons, cubes,
Pythagorean
and right prisms.
Theorem. (K)
(K)
2.
4.
I can explain a
proof of the
converse of the
I can solve real-
Pythagorean
world and
Theorem. (K)
mathematical
problems
involving area,
surface area and
volume of two
and threedimensional
objects composed
of triangles,
quadrilaterals,
polygons, cubes,
and right prisms.
(R)
M-G-7
Standard Demonstrator
Standard Demonstrator
Standard Demonstrator
Standard
Standard
Standard
Apply the Pythagorean
Theorem to determine
unknown side lengths in
right triangles in realworld and mathematical
problems in two and three
dimensions.
Teacher Target
Teacher Target
Teacher Target
Student Target
Student Target
Student Target
1.
I can recall the
Pythagorean
Theorem and its
converse. (K)
2.
I can solve basic
mathematical
Pythagorean
Theorem
problems and its
converse to find
missing lengths
of sides of
triangles in two
and threedimensions. (R)
3.
I can apply
Pythagorean
Theorem in
solving realworld problems
dealing with two
and threedimensional
shapes. (R)
M-G-8
Standard Demonstrator
Standard Demonstrator
Standard Demonstrator
Standard
Standard
Standard
Apply the Pythagorean
Theorem to find the
distance between two
points in a coordinate
system.
Teacher Target
Teacher Target
Teacher Target
Student Target
Student Target
Student Target
1.
I can determine
how to create a
right triangle
from two points
on a coordinate
graph. (R)
2.
I can use the
Pythagorean
Theorem to solve
for the distance
between the two
points. (R)
M-G-9
Standard Demonstrator
Standard Demonstrator
Standard Demonstrator
Standard
Standard
Standard
Know the formulas for the
volumes of cones,
cylinders, and spheres and
use them to solve realworld and mathematical
problems.
Teacher Target
Teacher Target
Teacher Target
Student Target
Student Target
Student Target
I can calculate the area
and circumference of a
circle needed for surface
area.
I can use formulas to find
the volume of prisms and
cylinders.
I can use formulas to find
the surface area of prisms
and cylinders.
Standard Demonstrator
Standard Demonstrator
Standard Demonstrator