Digital Unit Plan Template

Unit Title: Interpreting Functions Name: Lawrence Lam

Content Area: Algebra II Grade Level: 10-12

CA Content Standard(s)/Common Core Standard(s):

Algebra II

Analyze functions using different representations. [Focus on using key features to guide selection of appropriate type of model function.]

7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

b.Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

9. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Big Ideas:

How many different ways can we represent a function? How do functions with square roots, cube roots, piecewise, or absolute value functions look? Can a function be rewritten to a different form and yet have the same value? Why would we rewrite a function into another form if they will have the same values?

A2

Unit Goals and Objectives:

1. Students will expand their ability in creating graphs representing more difficult functions, such as polynomial functions. As well as being able to find the amplitude, endpoints and other aspects of the graph representation. Also allowing students to become more skilled when identifying suitable factorizations in polynomial functions.

2. Students will be able to understand that a function can be rewritten in different forms of the original function and understand that it will still have the same value. (ex factoring)

3. Students will become more familiar with the different representations of functions algebraically(whether the function is in terms of any given variable) and geometrically(when functions are graphed how they look and how rewritten functions algebraically will look the same on a graph).

Unit Summary:

After completion of this course, students will become more experienced with their knowledge of function representation. Students will be able to graph more difficult graphs with tables. Students will locate and describe aspects of graphs such as endpoints, amplitude, periods, and midpoints. As well as being able to rewrite functions to a different but equivalent form and knowing the purpose of rewriting functions. They will be able to identify and visualize the geometric representations of functions and vice versa.

Assessment Plan:

Entry-Level: Students will be given an online survey to

demonstrate their knowledge to the core concepts of this unit.

Formative: Students will form groups of 2 and

complete the assignment containing 5 questions by means of the easiest method possible.

Students will be asked to complete a webercise using the notes from the presentation as a reference.

Students will be given a list of functions and will be asked to graph these functions. They will also be asked to label key components to these functions such as intercepts.

Students will be given a online quiz on Quizlet to demonstrate their knowledge of the unit.

Summative: Students will be given an exam to truly test

their knowledge of the unit. Students are required to obtain a score of no less then 70%.

Students will also partake in a group project with the purpose of creating a presentation about the quadratic formula. Students will be graded based on the accuracy, the content and as well as their creativity.

Lesson 1

Student Learning Objective: Acceptable Evidence: Instructional Strategies: Communication

Lesson Activities:Before jumping into graphing square roots, cubed, etc, the teacher will begin

Students will become more experienced in their ability to graph functions by moving on to more difficult functions; square roots, cubed roots, piecewise-defined functions, and polynomial functions.

Graphs on homework/quiz/ exams are precise and accurate.

Being able to explain how they were able to get such a figure on their graph(mostly from tables)

Collection Collaboration Presentation Organization Interaction

by reviewing graphing simple functions by tables. When students have been warmed up with basic graphs the teacher will then ask the class how would function with a square root look, what restrictions would it have and why would it have restrictions if it as any. The teacher will then explain the relation between a algebraically expressed function and a geometrically expressed function and how the restrictions on one is also displayed on a graph.

Examples of common functions and their graphs will be presented to give students a basic idea of what similar function or more detailed function would look like. The teacher will then provide real life example polynomial functions in order to allow students to further understand the purpose of graphing more difficult functions.

Lesson 2

Student Learning Objective:

Students will be able to locate and describe aspects of graphs, such as their periods, amplitudes, endpoints..etc mostly from trigonometric functions.

Acceptable Evidence:

Having students explain how they were able to identify certain amplitudes and periods of graphs.

Pop-quizzes involving students being asked to describe the graph's amplitudes, period...etc

Instructional Strategies: Communication Collection Collaboration Presentation Organization Interaction

Lesson Activities:Students now will be introduced to more trigonometric functions. They will be given examples of each trig function and their geometrically representation. They will be given the restrictions and how it affects their geometrically representation. With these restrictions, students will then be introduced to the properties of graphs, such as the functions amplitude, period, midpoint,...etc and what this tells us about the graph.

Pop-quizzes will be given out for students to keep their skills in both graphing and knowledge of trig functions and properties in check. These quizzes will ask students graph and to identify amplitudes and periods of a function if there is any. This will allow students to carefully think and understand the function they are working with.

Worksheets will also be given in order for students to step away from quizzes and work with other students to collaborate on how they will find the aspects of graphs.

Lesson 3

Student Learning Objective:

Students will now learn about the relations between algebraic expressed functions and their geometrically expressed forms. They will understand how a function can be rewritten to a different form and both be graphed the same. Students

Acceptable Evidence:

Students should be able to rewrite a function correctly and explain how they got the new expression.

Students will be able to define a graph's function and its rewritten form.

Students will form groups

Instructional Strategies: Communication Collection Collaboration Presentation Organization Interaction

Lesson Activities:

The teacher will begin the class by asking students if there is only one form for expressed functions. Following the questions the teacher will then begin to ask what if we wanted to find out the zeroes of functions, or the vertex of the function. The teacher will then provide examples of functions that can be rewritten by the method of factoring. More difficult examples will be provided for students to become more comfortable and more exposed to difficult functions. Students will then be asked what if you can't factor, how else can you possibly rewrite a function to another form? Then the teacher will introduce students to "completing the square". Students will also then be asked to graph both the original and the rewritten function and only to

will also understand why function have to be rewritten and the purpose of rewriting expressed functions.

of 4 to rewrite as many expressed functions as they can in 20min

realize that they will come out the same. The teacher will then explain why the graphs are the same and later will ask the students to explain the algebraic and geometric properties of rewriting functions.

Students will then form groups of 4 and will be given a total of 10 functions. They will be asked for the next 20minutes to rewrite as many expressions as they can. Some functions can be rewritten in a few possible ways and the group that can come up with the most rewrites in the given time win.

Unit Resources:

McDougal Littell Algebra II (1st Edition) By Ron Larson

Useful Websites:

Khan Acadamy:

https://www.khanacademy.org/

Graphing Calculator

https://www.desmos.com/calculator

Quizlet

http://quizlet.com/29532324/57-completing-the-square-flash-cards/