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Transition Unit
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Number
and Number Relations: In problem-solving investigations, students demonstrate
an understanding of the real number system and communicate the relationships
within that system using a variety of techniques and tools.
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N-1-M.
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demonstrating
that a rational number can be expressed in many forms, and selecting an
appropriate form for a given situation (e.g., fractions, decimals, and
percents)
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M-GLE-8-1.
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Compare
rational numbers using symbols (i.e., <, £ , =, ³, >) and position on a number
line (N-1-M) (N-2-M)
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M-GLE-8-2.
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Use
whole number exponents (0-3) in problem-solving contexts (N-1-M) (N-5-M)
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N-2-M.
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demonstrating
number sense and estimation skills to describe, order, and compare rational
numbers (e.g., magnitude, integers, fractions, decimals, and percents)
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M-GLE-8-3.
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Estimate
the answer to an operation involving rational numbers based on the original
numbers (N-2-M) (N-6-M)
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N-3-M
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reading,
writing, representing, and using rational numbers in a variety of forms (e.g.,
integers, mixed numbers, and improper fractions)
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M-GLE-8-4.
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Read
and write numbers in scientific notation with positive exponents (N-3-M)
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N-4-M
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demonstrating
a conceptual understanding of the meaning of the basic arithmetic operations
(add, subtract, multiply and divide) and their relationships to each other
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M-GLE-8-5.
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Simplify
expressions involving operations on integers, grouping symbols, and whole
number exponents using order of operations (N-4-M)
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N-8-M
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demonstrating
a conceptual understanding and applications of proportional reasoning (e.g.,
determining equivalent ratios, finding a missing term of a given proportion)
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M-GLE-8-8.
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Solve
real-life problems involving percentages, including percentages less than 1 or
greater than 100 (N-8-M) (N-5-M)
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3D Transformations
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Unit Description
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Students
are introduced to volume as a measure of filling and to surface area as a
measure of wrapping. After
developing strategies for measuring the surface areas and volumes of
rectangular prisms, students use their new knowledge to develop strategies for
measure the surface are and volumes of cylinders, cones, spheres, and
irregular solids. They
also study the relationships between surface area and volume.
This
unit will also stimulate and sharpen students’ awareness of symmetry and to
begin to develop their understanding of the underlying mathematics.
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Enduring Understandings
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Essential Questions
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As
the dimensions of a prism and cylinder change, so does the volume and surface
area.
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Strategies
for finding volume of any three dimensional figure will work for any similar
three dimensional figure.
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Patterns
can be used to predict attributes of design.
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Designs
can change position without changing shape.
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The
angles formed by a transversal passing through parallel lines have a distinct
relationship.
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Which
system of measurement is most appropriate for situations?
Why?
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Is
there a constant relationship between the dimensions and volumes of different
shapes? If
so, why? If
not, why not?
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How
can the relationship between the angles formed by parallel lines and a
transversal be determined?
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Is
the angle relationship formed parallel lines and a transversal consistent?
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In
transformations, what changes? What
remains the same? Why?
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How
do I know that a shape has symmetry? Congruence?
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Students will know…
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Volume
(the amount of space inside of a figure measured in cubic units)
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Surface
area (the sum of the areas of all surfaces and side surfaces of a three
dimensional figure.
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Circumference
(the length of a circle, measured by multiplying the radius by 2 and pi.)
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Prism
(a solid with two bases that are formed by congruent polygons that lie in
parallel planes.)
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Cone
(a solid with a base, a vertex not contained in the same plane as the base,
and a lateral surface area composed of all points in the segments connecting
the vertex to the edge of the base.
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Symmetry
(shows congruence of a shape when folded about a center point.)
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Translation
(slides figures the same distance in the same direction.)
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Relationship
of angles formed by parallel lines and a transversal (corresponding, vertical,
alternate interior, alternate exterior, supplementary, complementary)
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Students will be able to…
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Conceptualize
volume as a measure of filling an object.
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Discover
that strategies for finding the volume and surface area of a rectangular prism
will work for any prism.
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Reason
about problems involving the surface area and volumes of rectangular prisms,
cylinders, cones, and spheres.
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Determine
which rectangular prism has the least (greatest) surface area for a fixed
volume.
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Estimate
the volume of an irregular shape by measuring the amount of water displaced by
the solid.
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Understand
the relationship between a cubic centimeter and a milliliter.
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Recognize
and describe symmetries of figures.
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Create
figures with specified symmetries.
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Give
precise mathematical directions for performing reflections, rotations, and
translations.
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Determine
angle measures formed by parallel lines and a transversal by measuring only
one angle.
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Grade-Level
Expectations
(List
Number, Text, and Benchmark Codes)
17)
Determine
the volume and surface area of prisms and cylinders. (M-1-M) (G-7-M)
19)
Demonstrates
an intuitive sense of the relative sizes of common units of volume in relation
to real-life applications and use this sense when estimating (M-2-M0 (G-7-M)
20)
Identify
and select appropriate units for measuring volume. ( M-3-M)
21)
Compare
and estimate measurements of volume and capacity within and between the U.S.
and metric systems (M-4-M) (G-1-M)
22)
Convert
units of volume/capacity within systems for U.S. and metric units (M-5-M)
23)
Define
and apply the terms measure, distance, midpoint, bisect, bisector, andperpendicular
bisector
(G-2-M)
24)
Demonstrate
conceptual and practical understanding of symmetry, similarity, and congruence
and identify similar and congruent figures. (G-2-M)
25)
Predict,
draw, and discuss the resulting changes in lengths, orientation, and angle
measures, and coordinates when figures are translated, reflected across
horizontal or vertical lines, and rotated on a grid. (G-3-M) (G-6-M)
26)
Predict,
draw, and discuss the resulting changes in lengths, orientation, and angle
measures that occur in figures under a similarity transformation (dilation).
(G-3-M) (G-6-M)
27)
Construct
polyhedra using 2-dimensional patterns (nets).
(G-4-M)
30)
Construct,
interpret, and use scale drawings in real-life situations (G-5-M) (M-6-M)
(N-8-M)
32)
Model
and explain the relationship between the dimensions of a rectangular prism and
its volume (i.e., how scale change in linear dimensions(s) affects volume.)
(G-5-M)
48)
Illustrate
patterns of change in dimension(s) and corresponding changes in volumes of
rectangular solids. (P-3-M)
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