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Partners for Student Success
Accelerated Seventh Grade
Mathematics
Unit 4:
Geometry: Stability and Change
In order for your child to be successful, it is important to be consistent with the mathematical
vocabulary and processes that will be implemented this year in seventh grade. You may find this
resource helpful when supporting your child at home.
Unit Concepts
Concept
Explanation
Supplementary
Angles
Angles that add up to
180 degrees
Example
Angles 1 and 2 are
supplementary
1
Complementary
Angles
Angles that add up to
90 degrees
Vertical
Angles
Angles that share a
vertex and are opposite
each other. Vertical
angles are congruent to
each other
2
4
Angles 3 and 4 are
complementary
3
Angles 1 and 3 are
vertical; Angles 2
and 4 are vertical
1
4
2
Adjacent Angles
Angles that share a
vertex and have a
common side
Alternate
exterior angles
Angles that are on the
outside of a pair of
lines and on opposite
sides of the transversal
Alternate
interior angles
Angles that are in the
inside of a pair of lines
and on opposite sides
of the transversal
Cecil County Public Schools
2015 – 2016
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Angles 3 and 4 are
adjacent; Angles 2 and 3
are adjacent; etc.
1
Accelerated Grade 7
Unit 4 Partners for Student Success
Concept
Explanation
Corresponding
angles
Angles that lie on the
same side of the
transversal and in
corresponding
positions
Converse
Switching the
hypothesis &
conclusion in a
statement
Obtuse Angle
Acute Angle
Right Angle
Parallel Lines
Perpendicular
Lines
Exterior angle
Pythagorean
Theorem
Square roots
Example
Statement: If a figure is a triangle, then it is a
polygon.
Converse: If a figure is a polygon, then it is a
triangle.
NOTE: The converse is not necessarily true.
An angle that
measures greater than
90 degrees
An angle that
measures less than 90
degrees
A 90 degree angle
Two lines that go on
forever and never
intersect
Two lines that
intersect to form right
angles
The exterior angle is
the angle between any
side of a shape, and a
line extended from the
next side
The relationship of
side lengths in a right
triangle, a2 + b2 = c 2; a
and b represent the
length of the
hypotenuse
Right Angle
Obtuse Angle
Acute Angle
Perpendicular
Lines
Parallel Lines
One of two equal
factors of a number
Cecil County Public Schools
2015 – 2016
2
Accelerated Grade 7
Unit 4 Partners for Student Success
Concept
Explanation
Transversal
A line or line segment
that intersects two or
more (often parallel)
lines or line segments
Area of a
Circle
A = p r2
Example
Circumference outside of circle
C= p d
Circumference
Area - inside
of circle
Volume of a rectangular prism = lw
Volume of a triangular prism = Bh
(area of base x height of prism)
Volume
The capacity of a 3D
figure, how many cubic
units it can hold
Volume of a sphere =
4 3
pr
3
Volume of a cylinder = p r 2 h
Volume of a cone =
Surface Area
1 2
pr h
3
The total area of the
surface of a threedimensional figure
How You Can Help

Have your child solve real-world problems finding the area of a circle.
o A circular pizza stone has a diameter of 11 inches. What amount of your oven
will the pizza stone cover, rounded to the nearest hundredth of a square inch?
(Answer: We need to find the area of the pizza stone using the formula A = p r2.
Since radius is half of the diameter, we need to use 5.5 inches for “r” in the
equation. A = p (5.52)= 94.99 in2. The pizza stone will cover 94.99 in2 of the
oven.)
Cecil County Public Schools
2015 – 2016
3
Accelerated Grade 7
Unit 4 Partners for Student Success
How You Can Help (continued)

Have your child solve real-world problems finding the circumference of a circle.
o A backyard gazebo has a diameter of 11 ft. What is the circumference of the
gazebo to the nearest hundredth of a foot? Show how you determined your
answer. (Answer: We need to use the formula C = p d. C = p x 11 = 34.56 ft.
The circumference of the gazebo is 34.56 ft.)

Have your child solve real-world surface area problems.
o You are covering a box with decorative wrapping paper. How much of the
wrapping paper would you use to cover a box with the dimensions below?
Answer:
Find area of each
rectangle.
top: 4x3=12 in2
bottom: 4x3=12 in2
side 1: 7x4=28 in2
side 2: 7x4=28 in2
side 3: 7x4=28 in2
side 4: 7x4=28 in2
Add areas
to get
136 in2
Additional Resources
 www.corestandards.org
o View the math standards your child will be learning this year. Scroll down and
click “Mathematics Standards” to download the pdf document.

www.ixl.com/math/standards/common-core
o Click “Seventh Grade” or “Eighth Grade” to find interactive practice
opportunities aligned with each math standard.

www.studyjams.com
o Using the search bar, find interactive examples and opportunities for practice
for any given concept.
•
www.khanacademy.org
o Using the search bar, find videos and examples on several math concepts
throughout the year.
•
http://www.shmoop.com/common-core-standards/math.html
o Use the dropdown menu to find the common core standard with explanations
and examples
Cecil County Public Schools
2015 – 2016
4
Accelerated Grade 7
Unit 4 Partners for Student Success