MATHEMATICS STANDARDS
GRADES 6-8
MATH GRADE 8: SOLVE LINEAR EQUATIONS
Mathematics
Grade 8
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Formulate and reason about expressions and
equations, including modeling an association in bivariate data with a linear
equation, and solving linear equations and systems of linear equations
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Students use linear equations and systems of
linear equations to represent, analyze, and solve a variety of problems.
Students recognize equations for proportions (y/x = m or y = mx)
as special linear equations (y = mx + b),
understanding that the constant of proportionality (m) is the slope,
and the graphs are lines through the origin. They understand that the slope (m)
of a line is a constant rate of change, so that if the input or x-coordinate
changes by an amount A, the output or y-coordinate
changes by the amount m·A. Students also use a linear equation to
describe the association between two quantities in bivariate data (such as
arm span vs. height for students in a classroom). At this grade, fitting the
model, and assessing its fit to the data are done informally. Interpreting
the model in the context of the data requires students to express a
relationship between the two quantities in question and to interpret
components of the relationship (such as slope and y-intercept) in
terms of the situation.
Students strategically choose and efficiently
implement procedures to solve linear equations in one variable, understanding
that when they use the properties of equality and the concept of logical
equivalence, they maintain the solutions of the original equation. Students
solve systems of two linear equations in two variables and relate the systems
to pairs of lines in the plane; these intersect, are parallel, or are the
same line. Students use linear equations, systems of linear equations, linear
functions, and their understanding of slope of a line to analyze situations
and solve problems.
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Resources
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Give examples of linear equations in one
variable with one solution, infinitely many solutions, or no solutions. Show
which of these possibilities is the case by successively transforming the
given equation into simpler forms, until an equivalent equation of the
form x = a, a = a, ora = b results
(where a and b are different numbers).
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Solve linear equations with rational number
coefficients, including equations whose solutions require expanding
expressions using the distributive property and collecting like terms.
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Understand that solutions to a system of two
linear equations in two variables correspond to points of intersection of
their graphs, because points of intersection satisfy both equations
simultaneously.
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Solve systems of two linear equations in two
variables algebraically, and estimate solutions by graphing the equations.
Solve simple cases by inspection.
For example, 3x + 2y = 5 and 3x + 2y = 6 have
no solution because 3x + 2y cannot simultaneously be 5 and 6.
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Solve real-world and mathematical problems
leading to two linear equations in two variables. For
example, given coordinates for two pairs of points, determine whether the
line through the first pair of points intersects the line through the second
pair.
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