Mathematics
Grade 8 Expressions & Equations


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


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 xcoordinate
changes by an amount A, the output or ycoordinate
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 yintercept) 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.


Analyze and solve linear equations
and pairs of simultaneous linear equations.


Resources



8.EE.7. Solve linear equations in one variable.

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).




Solve
linear equations with rational number coefficients, including equations whose
solutions require expanding expressions using the distributive property and
collecting like terms.



8.EE.8. Analyze and solve pairs of simultaneous linear
equations.

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.




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.




Solve
realworld 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.

As a tech coach, I am always looking for resources and ideas for middle school teachers and students in a onetoone netbook environment. This space is where I share my findings.
Monday, April 16, 2012
4162012 Teching the CCCS  Grade 8 Solving Linear Equations
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