School District: Lackawanna
GradeAccelerated 7
Updated on: 11/28/2012
Applied Mathematics 2012-2013
Topic 1: Equations
Spiral:
Concepts
Solving Equations
Skills


Solve equations with one
variable that contain more
than one operation
Solve equations in one
variable that contain variables
on both sides.
Common Core Standards
AA22- Solve all types of linear
equations and inequalities in one
variable
AA25- Solve equations and
inequalities involving fractional
expressions
Vocabulary
Equation
Variable
Solution
Integer
Fraction
Topic 2: Geometry Vocabulary and Foundations
Spiral:
Concepts
Geometry Vocabulary
Geometry Foundations
Skills

Common Core Standards

Identify basic geometric
figures
Construct and label geometric
figures
G.CM. 11 Understand and use
appropriate language,
representations, and terminology
when describing objects,
relationships, mathematical
solutions and geometric diagrams


Name and classify angles
Find measures of pairs of
G.PS.5 Choose an effective
approach to solve a problem from
Vocabulary
Point
Line
Plane
Collinear
Segment
Endpoint
Ray
Congruent
Midpoint
Bisect
Angle
Acute
Right
School District: Lackawanna
GradeAccelerated 7
Updated on: 11/28/2012
Applied Mathematics 2012-2013
angles
a variety of strategies.
Obtuse
Straight angle
Complementary
Supplementary
Topic 3: Coordinate Geometry and Transformations
Spiral:
Concepts
Coordinate Geometry


Transformations


Skills
Common Core Standards
Vocabulary
Develop and apply the
formula for midpoint
Use the distance formula to
find the distance between
two points.
Identify reflections,
translations and dilations
Graph transformations in
coordinate plane.
G.G.66 Find the midpoint of a line
segment, given its endpoints
G.G.67 Find the length of a line
segment, given its endpoints
Midpoint formula
Distance formula
Review: midpoint and endpoint
G.G.54 Define, investigate,
justify, and apply isometries in the
Geometry plane (rotations,
reflections, translations, glide
reflection. Note: Use proper
function notation.
G.G.61 Investigate, justify, and
apply the analytical
representations for translations,
rotations about the origin of 90º
and 180º, reflections over the
lines x=0, y=0, and y=x , and
dilations centered at the origin
Reflection
Transformation
Translation
Dilation
Image
Pre-image
School District: Lackawanna
GradeAccelerated 7
Applied Mathematics 2012-2013
Updated on: 11/28/2012
Topic 4: Parallel and Perpendicular Lines
Spiral:
Concepts
Graphing Linear Equations
Skills


Angles formed by parallel lines
and transversals


Perpendicular lines

Common Core Standards
Graph a lines and write their
equations in the proper form
Classify lines as parallel or
perpendicular
Identify the angles formed by
two lines in a transversal
Identify the slope of parallel
lines
Identify the slope of
perpendicular lines
G.G.64 Find the equation of a line,
given a point on the line and the
equation of a line perpendicular
to the given line
G.G.65 Find the equation of a line,
given a point on the line and the
equation of a line parallel to the
desired line
G.G.35 Determine if two lines cut
by a transversal are parallel,
based on the measure of given
pairs of angles formed by the
transversal and the lines
G.G.62 Find the slope of a
perpendicular line, given the
equation of a line
Vocabulary
Point slope form
Slope intercept form
Parallel lines
Transversal
Corresponding angles
Alternate Interior angles
Alternate exterior angles
Same side interior angles
Slope
Perpendicular
Negative reciprocal
Topic 5: Triangles
Spiral:
Concepts
Classifying triangles
Skills


Classify triangles by angle
measurements and side
lengths
Use triangle classification to
Common Core Standards
G.G.30 Investigate, justify, and
apply theorems about the sum of
the measures of the angles of a
triangle
Vocabulary
Acute triangle
Equiangular triangle
Right triangle
Obtuse triangle
School District: Lackawanna
GradeAccelerated 7
Applied Mathematics 2012-2013
find angle measures and side
lengths
Angle relationships

Find the measures of interior
and exterior angles of
triangles
Congruent Triangles

Identify corresponding parts
of congruent triangles
(SSS,SAS, ASA, HL, AAS)
Use properties of congruent
triangles to solve problems

Inequalities In One Triangle

Determine the relationship of
the longest and shortest sides
of a triangle as related to the
largest and smallest angles.
Pythagorean Theorem

Use the Pythagorean theorem
to find missing sides of right
triangles
G.G.32 Investigate, justify, and
apply theorems about geometric
inequalities, using the exterior
angle theorem
G.G.30 Investigate, justify, and
apply theorems about the sum of
the measures of the angles of a
triangle
G.G.29 Identify corresponding
parts of congruent triangles
G.G.28 Determine the
congruence of two triangles by
using one of the five congruence
techniques (SSS, SAS, ASA, AAS,
HL), given sufficient information
about the sides and/or angles of
two congruent triangles
G.G.34 Determine either the
longest side of a triangle given the
three angle measures or the
largest angle given the lengths of
three sides of a triangle
G.G.48 Investigate, justify, and
apply the Pythagorean theorem
and its converse
Updated on: 11/28/2012
Equilateral triangle
Isosceles triangle
Scalene triangle
Interior angle
Exterior angle
Remote interior angle
SSS
SAS
ASA
AAS
HL
Hypotenuse
Pythagorean triples
Radical
School District: Lackawanna
GradeAccelerated 7
Similar Triangles
Applied Mathematics 2012-2013


Identify similar triangles (AA,
SAS, SSS)
Apply properties of similar
triangles to solve problems
G.G.44 Establish similarity of
triangles, using the following
theorems: AA, SAS, and SSS
G.G.45 Investigate, justify, and
apply theorems about similar
triangles
Updated on: 11/28/2012
Similar
Ratio
Topic 6: Polygons & Quadrilaterals
Spiral:
Concepts
Properties of polygons
Skills


Properties of Parallelograms
Properties of Special
Parallelograms

Common Core Standards
G.G.36 Investigate, justify and
Classify polygons based on
apply theorems about the sums of
size and angles
Find and use the measures of the measures of the interior and
interior and exterior angles of exterior angles of polygons
G.G.37 Investigate, justify, and
polygons
apply theorems about each
interior and exterior angle
measure of regular polygons
G.G.38 Investigate, justify, and
 Apply properties of
apply theorems about
parallelograms to solve
parallelograms involving their
problems
angles, sides, and diagonals
G.G.41 Justify that some
quadrilaterals are parallelograms,
rhombuses, rectangles, squares,
or trapezoids
G.G.39 Investigate, justify, and
Apply properties of
apply theorems about special
rectangles, rhombuses and
parallelograms (rectangles,
squares to solve problems
rhombuses, squares) involving
Vocabulary
Polygon
Vertex
Parallelogram
Quadrilaterals
Rectangle
Rhombus
Square
School District: Lackawanna
GradeAccelerated 7
Properties of trapezoids
Applied Mathematics 2012-2013

Use properties of trapezoids
to solve problems
their angles, sides, and diagonals
G.G.41 Justify that some
quadrilaterals are parallelograms,
rhombuses, rectangles, squares,
or trapezoids
G.G.40 Investigate, justify, and
apply theorems about trapezoids
(including isosceles trapezoids)
involving their angles, sides,
medians, and diagonals
G.G.41 Justify that some
quadrilaterals are parallelograms,
rhombuses, rectangles, squares,
or trapezoids
Updated on: 11/28/2012
Trapezoid
Topic 7: Solid Geometry
Spiral:
Concepts
Skills
Common Core Standards
Area and Perimeter
(Review)

Utilize area and perimeter
formulas to solve problems
AG1 Find the area and perimeter
of figures composed of polygons
and circles or sectors of a circle
Surface area and volume of
prisms, cylinders, pyramids and
cones

Find the surface area of 3-d
shapes
Find the volume of 3-d shapes
G.G.13 Apply the properties of a
regular pyramid, including: lateral
edges are congruent lateral faces
are congruent isosceles triangles
volume of a pyramid equals onethird the product of the area of
the base and the altitude

Vocabulary
Area
Perimeter
Circumference
Composite figure
Diameter
Radius
Prism
Cylinder
Cone
Pyramid
School District: Lackawanna
GradeAccelerated 7
Applied Mathematics 2012-2013
Updated on: 11/28/2012
G.G.14 Apply the properties of a
cylinder, including: bases are
congruent volume equals the
product of the area of the base
and the altitude lateral area of a
right circular cylinder equals the
product of an altitude and the
circumference of the base
G.G.15 Apply the properties of a
right circular cone, including:
lateral area equals one-half the
product of the slant height and
the circumference of its base
volume is one-third the product
of the area of its base and its
altitude
Topic 8: Circles
Spiral:
Concepts
Circles in the coordinate plane
Skills


Write equations and graph
circles in the coordinate plane
Use the equation and graph
of a circle to solve problems
Common Core Standards
G.G.70 Solve systems of equations
involving one linear equation and
one quadratic equation
graphically
G.G.71 Write the equation of a
circle, given its center and radius
or given the endpoints of a
diameter
G.G.72 Write the equation of a
circle, given its graph Note: The
center is an ordered pair of
integers and the radius is an
Vocabulary
Linear
Center
Quadratic
Intersection
School District: Lackawanna
GradeAccelerated 7
Solving Systems
Applied Mathematics 2012-2013

Determine the solution of one
linear and quadratic equation
graphically
Updated on: 11/28/2012
integer
G.G.73 Find the center and radius
of a circle, given the equation of
the circle in center-radius form
G.G.74 Graph circles of the form
(x-h)^2 + (y-k)^2 = r^2
G.G.70 Solve systems of equations Solution of systems
involving one linear equation and
one quadratic equation
graphically