Pre-calculus 11 Pacing Guide - This pacing guide replaces the previous yearly plan. It has been updated to reflect removed outcomes and provide flexibility for responsive instruction.
Pre-calculus 11 Desmos Activity Collection - A collection of online student Desmos activities organized by unit.
AN01 Students will be expected to demonstrate an understanding of the absolute value of real numbers.
AN01.01 Determine the distance of two real numbers of the form ± a , a ∈ R, from 0 on a number line, and relate this to the absolute value of a (|a|).
AN01.02 Determine the absolute value of a positive or negative real number.
AN01.03 Explain, using examples, how distance between two points on a number line can be expressed in terms of absolute value.
AN01.04 Determine the absolute value of a numerical expression.
AN01.05 Compare and order the absolute values of real numbers in a given set.
RF02 Students will be expected to graph and analyze absolute value functions (limited to linear and quadratic functions) to solve problems.
RF02.01 Create a table of values for y = |f(x)|, given a table of values for y = f(x).
RF02.02 Generalize a rule for writing absolute value functions in piecewise notation.
RF02.03 Sketch the graph of y = |f(x)|; state the intercepts, domain, and range; and explain the strategy used.
RF02.04 Solve an absolute value equation graphically, with or without technology.
RF02.05 Solve, algebraically, an equation with a single absolute value, and verify the solution.
RF02.06 Explain why the absolute value equation |f(x)| < 0 has no solution.
RF02.07 Determine and correct errors in a solution to an absolute value equation.
RF02.08 Solve a problem that involves an absolute value function.
RF11 Students will be expected to graph and analyze reciprocal functions (limited to the reciprocal of linear and quadratic functions).
RF11.01 Compare the graph of y = 1/f(x) to the graph of y = f(x).
RF11.02 Identify, given a function f(x), values of x for which y = 1/f(x) will have vertical asymptotes; and describe their relationship to the non-permissible values of the related rational expression.
RF11.03 Graph, with or without technology, y = 1/f(x), given y = f(x) as a function or a graph, and explain the strategies used.
RF11.04 Graph, with or without technology, y = f(x), given y = 1/f(x) as a function or a graph, and explain the strategies used.
Additional Resources and Activities for AN01 and RF02 (absolute value functions):
How Old is Tiger Woods? - Have students guess a variety of celebrities (or teachers at your school?) ages and then ask them to determine who the best "age guesser" was. You'll quickly realize the necessity for absolute value. This activity is also available as a Desmos Activity "How Old Is?".
Absolute Value Project - Ask students to guess the number of items in a container. Collect the estimates from the class and then compare to the actual value. This data will give you an absolute value graph to discuss.
Absolute Value Translations Desmos Activity - In this activity, students use a blended approach (paper and pencil, as well as Desmos) to explore the effects of horizontal and vertical translations on absolute value graphs.
Absolute Value Marbleslides Desmos Activity - Total imitation of the Marble-slides activities created by the Desmos team - Just with Absolute Value equations.
Which One Doesn’t Belong: Absolute Value Functions (number 42) - The WODB number routine encourages mathematical thinking, reasoning and promotes discourse in the classroom that includes all students.
Open Middle Question - Ask students to create an absolute value equation such that x = – 2 is an extraneous solution (extraneous solutions are invalid and do not solve the original equation). One example is |3x – 4| = 5x.
Additional Resources and Activities for RF11 (reciprocal functions):
Which One Doesn’t Belong: Reciprocal Functions (number 12 and 35) - The WODB number routine encourages mathematical thinking, reasoning and promotes discourse in the classroom that includes all students.
Reciprocal Function Investigation on Desmos Activity Builder from David Petro - This is meant to be an introductory activity when looking at reciprocal functions of linear and quadratic functions. This is part of a larger unit on rational functions from David.
Functions Cumulative Review Activity
Functions SET Game - The game of SET is a great game for logical reasoning. Tina created a deck of cards for students to create sets using function characteristics. There are not set rules for what makes a set, just: "Make a set, but be able to explain why these 3 can make a set." This could be used as a cumulative review for all the functions in the course.