7 lessons, 14 PowerPoints, 7 Videos

P.6

Rational Expressions (2 – Day Lesson)

1.2

Linear Equations and Rational Equations (2 – Day Lesson)

1.3

Models and Applications (1 – Day Lesson)

3.5

Rational Functions and their Graphs (2 – Day Lesson)

Learning Goals

·Learning Goal 12: Students will be able to perform operations on rational expressions

·Learning Goal 13: Students will be able to write and solve rational equations.

·Learning Goal 14: Students will be able to graph and interpret key features of rational functions.

MAFS Standards

MAFS.912.A-APR.4.7
Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

MAFS.912.A-REI.1.2
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

MAFS.912.A-REI.1.1
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

MAFS.912.A-CED.1.3
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

MAFS.912.A-CED.1.1
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute.

MAFS.912.A-CED.1.4
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohms law V = IR to highlight resistance R

MAFS.912.F-IF.3.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

MAFS.912.F-IF.2.4
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity

MAFS.912.F-IF.2.5
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

MAFS.912.A.APR.4.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.