ALGEBRA OVERVIEW: Solving Linear Equations
Grade 7
Grade 8
SEEING STRUCTURE IN EXPRESSIONS
Interpret the structure of expressions
Functions &  Describe using words and symbols and  Identify and use variables and determine an
relationships
make sense of algebraic expressions and appropriate set of values for the
equations/inequalities and understand
independent (domain) and dependent
how they relate to the contexts
(range) variables.
(mathematical and real-world) they
model.
SEEING STRUCTURE IN EXPRESSIONS
Write expressions in equivalent forms to solve problems
Equivalent
a. Use models, tables, graphs, and
expressions
properties of numbers and operations
to reason about the equivalence of
expressions
b. Rewrite linear expressions in
equivalent forms by
expanding/factoring (distributive
property) and combining like terms,
connecting models of these expressions
with symbolic representations (e.g.
area models, algebra tiles).
c. Evaluate expressions given values of
the variables.
a. Develop rules for manipulating
symbolic expressions in ways that
are both connected to and
independent from arithmetic
operations (e.g., partial products,
combining integers), tabular,
graphical and contextualized
reasoning.
b. Recognize applications of the
distributive, associative, and
commutative properties.
Algebra
Beyond
a. Determine and explain whether a

relationship (given in contextual,
symbolic, tabular, or graphical form)
is a function and identify its domain
and range.
b. Recognize and use functions that may
be defined by different expressions
over different intervals of their
domain; such functions are piecewise
defined.
c. Identify the intervals where the values
of a function/relation are positive or
negative, and describe the behavior of
a function as x approaches positive or
negative infinity, given the symbolic
and graphically representations.
(linear, quadratic, exponential,
inverse, cubic)
Identify the intervals where the values of a
function are positive or negative, and
describe the behavior of a function as x
approaches positive or negative infinity,
given the symbolic and graphically
representations. (polynomials,
trigonometric, rational, etc.)
 Review and strengthen their understanding
of the conventional order of operations
rules and number properties in the contexts
of practical problems and evaluating
expressions.
ALGEBRA OVERVIEW: Solving Linear Equations
Version 2.0 December 6, 2010
REASONING WITH EQUATIONS AND INEQUALITIES
Understand solving equations as a process of reasoning and explaining the reason
Solve equations and inequalities in one variable
Solve systems of equations
Represent and solve equations and inequalities graphically
Solve
Model
a. Estimate or find solutions to linear
equations and inequalities by
inspecting their graphs and tables
and interpret the meaning of the
solution in the real-world context.
b. Use concrete models and
“doing/undoing” and “balancing”
methods to solve simple linear
equations and inequalities and to
answer questions about the contexts
they represent.
c. Begin to develop strategies for
solving linear functions of the form
y = mx + b symbolically.
d. Recognize and solve problems
involving proportional relationships
making connections to strategies
used to solve other linear problems
(tables, graphs and symbols) and
connecting to unit rate, scale factor
and equivalent fractions strategies.
 Use estimation (e.g., spaghetti) to find a
line of best-fit model for a set of data
and answer questions about the context
represented by the data.
a. Connect the concrete models and
ideas of “doing/undoing” and
“balancing” methods used to solve
linear equations to solve equations in
other function classes and to routinize
methods for solving equations
symbolically.
b. Solve multi-step linear
equations/inequalities symbolically
and interpret the meaning of the
solution in the real-world context.
c. Set up and solve systems of two linear
equations/inequalities and interpret
the meaning of the solution in the
real-world context (using graphing,
substitution, and combination)
including systems with no solutions or
infinitely many solutions.
d. Recognize and solve problems
involving inversely proportional
relationships making connections to
strategies used to solve other
problems (tables, graphs and
symbols).

a. Write a linear equation in a variety of
forms and translate among the various
forms (point-slope, y-intercept, and
standard) and reason about which
form is most useful for a particular
context.
b. Set up and solve systems of up to
three linear equations/inequalities
with three unknowns and interpret the
meaning of the solution in the realworld context (using graphing,
substitution, and combination).
c. Solve a formula for one variable.
d. Set-up and solve compound
inequalities with a single variable and
interpret the meaning of the solution
in a real-world context.
e. Set-up and solve absolute value
equations and inequalities and
interpret the meaning of the solution
in a real-world context.
a.
b.
c.
d.
e.
Find the nth term in arithmetic
sequences.
Find and make sense of the zero’s of
polynomial function from its linear
factors.
Use a calculator or computer
software to set up and solve systems
of linear equations and/or
inequalities and other functions and
interpret the meaning of the solutions
in real-world contexts.
Analyze simple rational expressions
and equations and understand the
relationship between the zeros of the
numerator and denominator, and the
function’s intercepts, asymptote, and
domain.
Apply given transformations to
parent functions and represent
symbolically.
Use a calculator or computer software to
find the linear regression model for a set of
data and answer questions about the
context represented by the data.
ALGEBRA OVERVIEW: Solving Linear Equations
Version 2.0 December 6, 2010