Essential Math Mapping

Algebra and Functions Module

 

Lesson 1

Writing and Simplifying Expression

                

AF 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).

AF 1.2 Use the correct order of operations to evaluate algebraic expressions such as
3(2x + 5)2.

Lesson 2

Interpreting Graphs

AF 1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph.

 

Lesson 3

Solving Equations and Inequalities

 

AF 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.

 

Lesson 4

Operations with Monomials

AF 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.

 

AF 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.

Lesson 5

Linear Equations

 

AF 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.

 

Lesson 6

Direct Variation

 

AF 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 a line equals the [ratio of the] quantities.

AF 4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation.

Lesson 7

Graphing Quadratic and Cubic Equations

AF 3.1 Graph functions of the form y = nx2 and y = nx3 and use in solving problems.

 

Lesson 8

Mathematical Reasoning

MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.

MR2.1 Use estimation to verify the reasonableness of calculated results.

MR2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.