Introduction
Enclosed is a complete list of the seventh grade
Extended Mathematics objectives. The seventh
grade extended curriculum includes all eighth
grade and some of the seventh grade objectives
from the Standards of Learning (SOLs) set by
the State of Virginia. Students in this course will
take the Grade 8 SOL test in the spring.
The content of the mathematics standards
supports the following five goals for students:
 becoming mathematical problem solvers,
 communicating mathematically both orally
and in writing,
 reasoning mathematically,
 making mathematical connections, and
 representing ideas mathematically.
Concepts are introduced and developed through
the use of various models and representations.
Students apply the concepts and skills through a
wide variety of problem-solving experiences.
Instruction in the process of problem solving is
integrated early and continually throughout the
mathematics curriculum strands.
The Prince William County Curriculum contains
six content strands:
 Number and Number Sense
 Computation and Estimation
 Measurement
 Geometry
 Probability and Statistics
 Patterns, Functions, and Algebra
More detailed descriptions of the expectations of
students are included in the essential knowledge
and skills section of the PWCS mathematics
curriculum guide, which can be found at:
http://pwcs.math.schoolfusion.us/
Mathematics Vision Statement
The Prince William County Schools
Mathematics program promotes an
environment in which students
develop a comprehensive and
enduring understanding of the
concepts of mathematics. Students
learn to effectively apply these
concepts and use a variety of
problem solving strategies. The
program nurtures a productive
disposition toward mathematics,
challenges all learners, and
supports further investigations
in this field.
Because mathematics has its own language, the
acquisition of specialized mathematics vocabulary
and language patterns is crucial to a student’s
understanding and appreciation of mathematics.
Students are expected to correctly use and apply
the concepts, skills, symbols, and vocabulary
identified throughout this curriculum.
The complete curriculum guide and other
resources for students and parents are online at
the Prince William County Mathematics Web
Site: http://pwcs.math.schoolfusion.us/
7th Grade
Extended
Mathematics
Teacher’s Name
School’s Name
School’s Address
School’s Phone Number
Other Websites for Parents
http://www.figurethis.org/index.html/
http://www.doe.virginia.gov/
http://www.aplusmath.com/
http://www.nlvm.org
http://www.c3.lanl.gov/mega-math/index.html
http://www.nctm.org
http://www.math.com/students/practice.html
Parent Edition
Number and Number Sense
8.1 The student will
a) simplify numerical expressions involving
positive exponents, using rational numbers,
order of operations, and properties of
operations with real numbers; and
b) compare and order decimals, fractions,
percents, and numbers written in scientific
notation.
8.2 The student will describe orally and in writing the
relationships between the subsets of the real
number system.
Computation and Estimation
7.4 The student will solve single-step and multi-step
practical problems, using proportional reasoning.
8.3 The student will
a) solve practical problems involving rational
numbers, percents, ratios, and proportions;
b) determine the percent increase or decrease
for a given situation.
8.6 The student will
a) verify by measuring and describe the
relationships among vertical angles, adjacent
angles, supplementary angles, and
complementary angles; and
b) measure angles of less than 360°.
7.8 The student, given a polygon in the coordinate
plane, will represent transformations (reflections,
dilations, rotations, and translations) by graphing
in the coordinate plane.
Geometry
8.7 The student will
a) investigate and solve practical problems
involving volume and surface area of prisms,
cylinders, cones, and pyramids; and
b) describe how changing one measured
attribute of a figure affects the volume and
surface area.
8.8 The student will
a) apply transformations to plane figures; and
b) identify applications of transformations.
8.4 The student will apply the order of operations to
evaluate algebraic expressions for
given replacement values of the variables.
8.9 The student will construct a three-dimensional
model, given the top or bottom, side, and front
views.
8.5 The student will
a) determine whether a given number is a
perfect square; and
b) find the two consecutive whole numbers
between which a square root lies.
8.10 The student will
a) verify the Pythagorean Theorem; and
b) apply the Pythagorean Theorem.
Measurement
7.5 The student will
a) describe volume and surface area of
cylinders;
b) solve practical problems involving the volume
and surface area of rectangular prisms and
cylinders; and
c) describe how changing one measured
attribute of a rectangular prism affects its
volume and surface area.
7.6 The student will determine whether plane figures
(quadrilaterals and triangles) are similar and write
proportions to express the relationships between
corresponding sides of similar figures.
8.11 The student will solve practical area and
perimeter problems involving composite plane
figures.
Probability and Statistics
7.9 The student will investigate and describe the
difference between the experimental probability
and theoretical probability of an event.
8.12 The student will determine the probability of
independent and dependent events with and
without replacement.
8.13 The student will
a) make comparisons, predictions, and
inferences, using information displayed in
graphs; and
b) construct and analyze scatterplots.
Patterns, Functions, and Algebra
7.12 The student will represent relationships with
tables, graphs, rules, and words.
7.13 The student will
a) write verbal expressions as algebraic
expressions and sentences as equations
and vice versa; and
b) evaluate algebraic expressions for given
replacement values of the variables.
7.14 The student will
b) solve practical problems requiring the
solution of one- and two-step linear
equations.
7.16 The student will apply the following properties of
operations with real numbers:
a) the commutative and associative properties
for addition and multiplication;
b) the distributive property;
c) the additive and multiplicative identity
properties; and
d) the additive and multiplicative inverse
the multiplicative property of zero.
8.14 The student will make connections between any
two representations (tables, graphs,
words, and rules) of a given relationship.
8.15 The student will
a) solve multistep linear equations in one
variable with the variable on one and two
sides of the equation;
b) solve two-step linear inequalities and graph
the results on a number line; and
c) identify properties of operations used to
solve an equation.
8.16 The student will graph a linear equation in two
variables.
8.17 The student will identify the domain, range,
independent variable, or dependent variable in
a given situation.