Building
upon knowledge and skills gained in preceding
grades,
by the end of Grade 8, students will:
Standard 4.2
(Geometry
and Measurement) All students will develop
spatial sense and the ability to use geometric
properties, relationships, and measurement
to model, describe and analyze phenomena.
Standard 4.2.8.A
Geometric
Properties
Standard 4.2.8.A.1
Understand
and apply concepts involving lines, angles, and
planes.
· Complementary and supplementary angles
· Vertical angles
· Bisectors and perpendicular bisectors
· Parallel, perpendicular, and intersecting
planes
· Intersection of plane with cube, cylinder,
cone, and sphere
Standard 4.2.8.A.2
Understand
and apply the Pythagorean theorem.
Standard 4.2.8.A.3
Understand
and apply properties of polygons.
· Quadrilaterals, including squares, rectangles,
parallelograms, trapezoids, rhombi
· Regular polygons
· Sum of measures of interior angles of a
polygon
· Which polygons can be used alone to generate
a tessellation and why
Standard 4.2.8.A.4
Understand
and apply the concept of similarity.
· Using proportions to find missing measures
· Scale drawings
· Models of 3D objects
Standard 4.2.8.A.5
Use
logic and reasoning to make and support conjectures
about geometric objects.
Standard 4.2.8.B
Transforming
Shapes
Standard 4.2.8.B.1
Understand
and apply transformations.
· Finding the image, given the pre-image,
and vice-versa
· Sequence of transformations needed to map
one figure onto another
· Reflections, rotations, and translations
result in images congruent to the pre-image
· Dilations (stretching/shrinking) result
in images similar to the pre-image
Standard 4.2.8.B.2
Use
iterative procedures to generate geometric patterns.
· Fractals (e.g., the Koch Snowflake)
· Self-similarity
· Construction of initial stages
· Patterns in successive stages (e.g., number
of triangles in each stage of Sierpinski’s
Triangle)
Standard 4.2.8.C
Coordinate
Geometry
Standard 4.2.8.C.1
Use
coordinates in four quadrants to represent geometric
concepts.
Standard 4.2.8.C.2
Use
a coordinate grid to model and quantify transformations
(e.g., translate right 4 units).
Standard 4.2.8.D
Units
of Measurement
Standard 4.2.8.D.1
Solve
problems requiring calculations that involve
different
units of measurement within a measurement system
(e.g., 4’3" plus 7’10" equals
12’1").
Standard 4.2.8.D.2
Use
approximate equivalents between standard and metric
systems to estimate measurements (e.g., 5 kilometers
is about 3 miles).
Standard 4.2.8.D.3
Recognize
that the degree of precision needed in calculations
depends on how the results will be used and the
instruments used to generate the measurements.
Standard 4.2.8.D.4
Select
and use appropriate units and tools to measure quantities
to the degree of precision needed in a particular
problem-solving situation.
Standard 4.2.8.D.5
Recognize
that all measurements of continuous quantities are
approximations.
Standard 4.2.8.D.6
Solve
problems that involve compound measurement units,
such as speed (miles per hour), air pressure (pounds
per square inch), and population density (persons
per square mile).
Standard 4.2.8.E
Measuring
Geometric Objects
Standard 4.2.8.E.1
Develop
and apply strategies for finding perimeter and area.
· Geometric figures made by combining triangles,
rectangles and circles or parts of circles
· Estimation of area using grids of various
sizes
· Impact of a dilation on the perimeter and
area of a 2-dimensional figure
Standard 4.2.8.E.2
Recognize that the volume of a pyramid or cone is
one-third of the volume of the prism or cylinder
with the same base and height (e.g., use rice to
compare volumes of figures with same base and height).
Standard 4.2.8.E.3
Develop
and apply strategies and formulas for finding the
surface area and volume of a three-dimensional figure.
· Volume - prism, cone, pyramid
· Surface area - prism (triangular or rectangular
base), pyramid (triangular or rectangular base)
· Impact of a dilation on the surface area
and volume of a three-dimensional figure
Standard 4.2.8.E.4
Use
formulas to find the volume and surface area of
a sphere.
