Download 7th Math Accelerated Unit 4 - Livingston County School District

Livingston County Schools
Seventh (7th) Grade PRE-ALGBRA Unit 4
Math: ACCELERATED
Unit Overview
Unit 4: Creating, Comparing, and Analyzing Geometric Figures
Students use geometric construction, as well as solve real-world and mathematical problems involving area, surface area, and volume of 2 and 3
dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. They draw, construct, and describe geometrical
figures and describe the relationships between them. They solve real-life and mathematical problems involving angle measure, area, surface
area, and volume. They understand congruence and similarity using physical models, transparencies, or geometry software. They solve
problems involving volume of cylinders, cones, and spheres.
Length of unit: 39 days
KY Core Academic
Standard
7.G.1
Solve problems involving
scale drawings of
geometric figures,
including computing
actual lengths and areas
from a scale drawing and
reproducing a scale
drawing at a different
scale.
Learning Target
K
Use ratios and proportions to
create scale drawing
X
Identify corresponding sides of
scaled geometric figures
X
Compute lengths and areas from
scale drawings using strategies
such as proportions.
X
Solve problems involving scale
drawings of geometric figures
using scale factors.
R
S
P
Critical Vocabulary
Scale Drawings
Scale Factors
Corresponding Sides
Corresponding Angles
Congruent Figures
X
Texts/Resources/Activities
Geometric Solids Lab
Proportion
Proportional
Straightedge
Protractor
Compass
Ruler
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7th Grade PRE-ALGEBRA Unit 4
Parallel
Reproduce a scale drawing that is
proportional to a given geometric
figure using a different scale.
7.G.2
Draw (freehand, with
ruler and protractor, and
with technology)
geometric shapes with
given conditions. Focus
on constructing triangles
from three measures of
angles or sides, noticing
when the conditions
determine a unique
triangle, more than one
triangle, or no triangle.
I can state the conditions which
create unique triangles, more
than one triangle, or no triangle.
I can analyze given conditions
based on the three measures of
angles or lengths of sides of a
triangle to determine when there
is a unique triangle, more than
one triangle, or no triangle.
X
Perpendicular
X
X
I can construct triangles from
three given angle measures to
determine when there is a
unique triangle, more than one
triangle or no triangle using
appropriate tools (freehand,
rulers, protractors, and
technology).
X
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
(freehand, rulers, protractors,
X
Point
Ray
Line
Line Segment
Endpoint
Midpoint
Supplementary Angles
Complementary Angles
Adjacent Angles
Vertical Angles
Acute Angles
Obtuse Angles
Straight Angles
Right Angles
Acute triangle
Equiangular triangle
Right Triangle
Obtuse Triangle
Scalene Triangle
Isosceles Triangle
Equilateral Triangle
Regular Polygon
Cross-Section
No-D
1-D
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7th Grade PRE-ALGEBRA Unit 4
and technology).
7.G.3
Describe the twodimensional figures that
result from slicing threedimensional figures, as in
plane sections of right
rectangular prisms and
right rectangular
pyramids.
I can define slicing as making a
cross-section of a 3D figure.
X
I can describe the twodimensional figures that result
from slicing a three-dimensional
figure such as a right rectangular
prism or pyramid.
X
7.G.4
Know the formulas for
the area and
circumference of a circle
and use them to solve
problems; give an
informal derivation of
the relationship between
circumference and area
of a circle.
I can identify the parts of a
circle including radius,
diameter, area, circumference,
center, and chord.
Analyze three-dimensional
shapes by examining two
dimensional cross-sections.
I can identify and approximate
X
X
π
X
I can state the formulas for area
and circumference of a circle
X
Given the circumference of a
circle, I can find its area.
X
Given the area of a circle, I can
find its circumference.
X
2-D
3-D
Base
Face
Lateral Face
Length, width, height
Cube
Pyramid
Prism
Cone
Cylinder
Sphere
Polygon
Quadrilateral
Parallelogram
Trapezoid
Rectangle
Rhombus
Square
Pentagon
Hexagon
Septagon
Octagon
Nonagon
Decagon
Undecagon
Dodecagon
n-gon
Circle
Radius
Diameter
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7th Grade PRE-ALGEBRA Unit 4
I can justify that π can be
derived from the circumference
and diameter of a circle.
X
π
I can apply circumference or
area formulas to solve
mathematical and real-world
problems
X
I can justify the formulas for
area and circumference of a
circle and how they relate to π
X
I can informally derive the
relationship between the
circumference and area of a
circle.
7.G.5
Use facts about
supplementary,
complementary, vertical,
adjacent angles in a
multi-step problem to
write and solve simple
equations for an
unknown angle in a
figure.
I can identify and recognize
types of angles: supplementary,
complementary, vertical, and
adjacent.
I can determine complements
and supplements of a given
angle.
I can determine unknown angle
measures by writing and solving
Center
Chord
Tangent
X
X
Circumference
Perimeter
Area
Lateral Surface Area
Surface Area
Volume
Linear Units
Square Units
Cubic Units
Rotation
Reflection
Translation
Prime Notation
Image
Center of Rotation
Direction of Rotation
Degree of Rotation
Line of Reflection
Dilation
Scale Factor of Dilation
Coordinates of transformed image
X
Similar
X
Interior angle of a triangle
Exterior angle of a triangle
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7th Grade PRE-ALGEBRA Unit 4
Remote interior angle of a triangle
algebraic equations based on
relationships between angles.
7.G.6
Solve real-world and
mathematical problems
involving area, volume,
and surface area of twoand three-dimensional
objects composed of
triangles, quadrilaterals,
polygons, cubes, and
right prisms.
I can state the formulas for area
(triangle, rectangle, circle) and
volume (right prisms)
X
I can find surface area (right
prisms).
X
I can use area, surface area, and
volume in real-world problems
for two- and three-dimensional
objects composed of triangles,
quadrilaterals, polygons, cubes,
and right prisms.
X
I can solve real-world problems
involving area, surface area and
volume of two- and threedimensional objects composed
of triangles, quadrilaterals,
polygons, cubes, and right
prisms.
8.G.1 a b c
Verify experimentally the
properties of rotations,
reflections, and
translations:
Transversal
Parallel Lines
Interior Angles
Exterior Angles
Alternate Exterior Angles
Alternate Interior Angles
Corresponding Angles
Adjacent Angles
Supplementary Angles
Vertical Angles
X
Define & identify rotations,
reflections, and translations.
X
Identify corresponding sides &
corresponding angles.
X
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7th Grade PRE-ALGEBRA Unit 4
a. Lines are taken to
lines, and line segments
to line segments of the
same length.
Understand prime notation to
describe an image after a
translation, reflection, or
rotation.
X
b. Angles are taken to
angles of the same
measure.
Identify center of rotation.
X
Identify direction and degree of
rotation.
X
Identify line of reflection.
X
c. Parallel lines are taken
to parallel lines.
Use physical models,
transparencies, or geometry
software to verify the properties
of rotations, reflections, and
translations (ie. Lines are taken to
lines and line segments to line
segments of the same length,
angles are taken to angles of the
same measure, & parallel lines
are taken to parallel lines.)
8.G.2
Understand that a twodimensional figure is
congruent to another if
the second can be
obtained from the first
by a sequence of
X
Define congruency.
X
Identify symbols for
congruency.
X
Apply the concept of
congruency to write congruent
X
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rotations, reflections,
and translations; given
two congruent figures,
describe a sequence that
exhibits the congruence
between them.
statements.
X
Reason that a 2-D figure is
congruent to another if the
second can be obtained by a
sequence of rotations,
reflections, translation.
Describe the sequence of
rotations, reflections,
translations that exhibits the
congruence between 2-D
figures using words.
8.G.3
Describe the effect of
dilations, translations,
rotations, and reflections
on two-dimensional
figures using coordinates.
X
Define dilations as a reduction
or enlargement of a figure.
X
Identify scale factor of the
dilation.
X
Describe the effects of dilations,
translations, rotations, &
reflections on 2-D figures using
coordinates.
8.G.4
Understand that a twodimensional figure is
similar to another if the
second can be obtained
Define similar figures as
corresponding angles are
congruent and corresponding
sides are proportional.
X
X
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from the first by a
sequence of rotations,
reflections, translations,
and dilations; given two
similar two-dimensional
figures, describe a
sequence that exhibits
the similarity between
them.
8.G.5
Use informal arguments
to establish facts about
the angle sum and
exterior angle of
triangles, about the
angles created when
parallel lines are cut by a
transversal, and the
angle-angle criterion for
similarity of triangles. For
example, arrange three
copies of the same
Recognize symbol for similar.
X
Apply the concept of similarity to
write similarity statements.
X
Reason that a 2-D figure is similar
to another if the second can be
obtained by a sequence of
rotations, reflections, translation,
or dilation.
X
Describe the sequence of
rotations, reflections,
translations, or dilations that
exhibits the similarity between 2D figures using words and/or
symbols.
X
Define similar triangles
X
Define and identify transversals
X
Identify angles created when
parallel line is cut by transversal
(alternate interior, alternate
exterior, corresponding,
vertical, adjacent, etc.)
Justify that the sum of interior
angles equals 180. (For
example, arrange three copies
X
X
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7th Grade PRE-ALGEBRA Unit 4
triangle so that the three
angles appear to form a
line, and give an
argument in terms of
transversals why this is
so.
8.G.9
Know the formulas for
the volumes of cones,
cylinders, and spheres
and use them to solve
real-world and
mathematical problems.
of the same triangle so that the
three angles appear to form a
line.)
X
Justify that the exterior angle of
a triangle is equal to the sum of
the two remote interior angles.
Use Angle-Angle Criterion to
prove similarity among
triangles. (Give an argument in
terms of transversals why this is
so.)
Identify and define vocabulary:
cone, cylinder, sphere, radius,
diameter, circumference, area,
volume, pi, base, height
Know formulas for volume of
cones, cylinders, and spheres.
X
X
X
Compare the volume of cones,
cylinders, and spheres.
X
Determine and apply appropriate
volume formulas in order to solve
mathematical and real-world
problems for the given shape.
X
Given the volume of a cone,
cylinder, or sphere, find the radii,
X
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height, or approximate for π.
Common Assessments Developed (Proposed Assessment
Dates):
Learning Check # 4 (Last day before Summer Break)
HOT Questions:
 What does area mean?
 What does volume mean?
 What are two approximations for pi? How would you decide when to
use each? What is the exact and approximate circumference of a
circle with a diameter of 7 meters? …10 feet? Show all work.
 Find the circumference of a circle with radius 4 centimeters. John
used the formula C=2 π r. Susy used the formula C=
correct? Explain.







πd.
Who was
Solve C= πd for pi. Use your solution to define pi. What does that
mean? How would you use the solution to graphical represent pi?
Compare and contrast pyramids, prisms, cones, and cylinders.
Make a polygon flowchart/venn diagram.
The answer is two-dimensional. What are the questions?
Compare the volume of cones, cylinders, and spheres.
Describe the effect of dilations, translations, rotations, and
reflections on two-dimensional figures using coordinates.
Is the statement sometimes true, always true, or never true?
Justify your answer.
a) Vertical angles are congruent.
b) Alternate interior angles are congruent.
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7th Grade PRE-ALGEBRA Unit 4