Algebra and Functions

1.0 Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs:
1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal descrip­tion (e.g., three less than a number, half as large as area A).

1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2x 25)

1.3 Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the
process used.

1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression, constant) correctly.
1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph.

2.0 Students interpret and evaluate expressions involving integer powers and
simple roots:
2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents.
2.2 Multiply and divide monomials; extend the process of taking powers and extract­ing roots to monomials when the latter results in a monomial with an integer exponent.

3.0 Students graph and interpret linear and some nonlinear functions:
3.1 Graph functions of the form y = nx2 and y = nx3 and use in solving problems.
3.2 Plot the values from the volumes of three-dimensional shapes for various values of
the edge lengths (e.g., cubes with varying edge lengths or a triangle prism with a
fixed height and an equilateral triangle base of varying lengths).
3.3 Graph linear functions, noting that the vertical change (change in y-value) per unit
of horizontal change (change in x-value) is always the same and know that the ratio
(“rise over run”) is called the slope of a graph.
3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the
number of an item, feet to inches, circumference to diameter of a circle). Fit a line to
the plot and understand that the slope of the line equals the quantities.

4.0 Students solve simple linear equations and inequalities over the rational
4.1 Solve two-step linear equations and inequalities in one variable over the rational
numbers, interpret the solution or solutions in the context from which they arose,
and verify the reasonableness of the results.
4.2 Solve multi-step problems involving rate, average speed, distance, and time or a
direct variation.