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 x-coordinate
changes by an amount A, the output ory-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.
| |||
Expressions and Equations work with
radicals and integer exponents.
|
Resources
|
||
8.EE.1. Know
and apply the properties of integer exponents to generate equivalent
numerical expressions.
|
For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.
|
||
8.EE.2. Use
square root and cube root symbols to represent solutions to equations of the
form x2 =p and x3 = p,
where p is a positive rational number.
Evaluate square roots of small perfect squares and cube roots of small
perfect cubes. Know that √2 is irrational.
|
|||
8.EE.3. Use
numbers expressed in the form of a single digit times a whole-number power of
10 to estimate very large or very small quantities, and to express how many
times as much one is than the other.
|
For example, estimate the population of the
United States as 3 times 108 and the population of the world
as 7 times 109, and determine that the world population is more
than 20 times larger.
|
||
8.EE.4. Perform
operations with numbers expressed in scientific notation, including problems
where both decimal and scientific notation are used. Use scientific notation
and choose units of appropriate size for measurements of very large or very
small quantities. Interpret scientific notation that has been generated by
technology.
|
(e.g., use millimeters per year for seafloor spreading)
|
||
No comments:
Post a Comment