 ## Inverse Functions Lesson I like teaching inverse functions. This inverse functions lesson plan will help you find connections with your students. With the real world context, students understand this concept well by the end of class. I love working on the ideas of computers, maps, and math puzzles. Be sure to stay to the end for your free copy of the inverse functions worksheet set.

### Standard: CCSS.MATH.CONTENT.HSF.BF.B.4.A

Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2x3 or f(x) = (x+1)/(x-1) for x ≠ 1.

### I Can Statement for the Inverse Functions Lesson Plan

I can find the inverse of a linear function.

This introduction is our students first experience with inverse functions, and while the full standard also incorporates the inverse of exponential and rational functions, we are beginning with linear functions during this lesson.

### Essential Questions About Inverse Functions

Why is the idea of "inverse" so important in mathematics?

I like this question. It forces the students to think critically and evaluate their understanding of the concept.

### Bellringer Worksheet

The bellringer worksheet consists of 4 questions asking students to create a linear equation from a table. This bellringer should reinforce their understanding of linear relationships and functions before beginning the day's lesson. ### Understanding Inverse Functions Activity

The activity for today helps our students understand the essential question. We take a look at some direction to our friend Tracy's home, and we ask the student to give the directions back. This activity is not only ideal for understanding inverses but also this is an excellent technical writing exercise as well. We can then connect that activity to a math question. Students may have seen this before, and they are stumped that a teacher could know what number they started with after doing some silly calculations. But now they will know the magic trick. ### Practice - Inverse Functions Worksheet

The practice sheets are designed to give students a contextual, algebraic, and graphical understanding of inverse functions. The inverse function worksheets build upon themselves and will allow students the opportunity to ask questions and work through the work using math vocabulary. ### Exit Slip - Formative assessment for Inverse Functions

The exit slip is two relatively simple inverse questions that will allow you to quickly assess your students to determine if anyone is falling behind. The first question will give you a glimpse into their algebraic ability to manipulate the equation, while they second problem will give you a look at their understanding of inverse functions.  ## F.IF.1 Understanding Functions

Wow! What a big and open topic. I look at the examples given at Illustrative Mathematics

and it was not what I would have

come up with.

Katy is told that the cost of producing x DVDs is given by C(x)=1.25x+2500. She is then asked to find an equation for C(x)x,  the average cost per DVD of producing x DVDs.

She begins her work:
C(x)x=1.25x+2500x

and finishes by simplifying both sides to get:

C=1.25+2500x

Is Katy's answer correct? Explain.

### Dig Deeper

So I dig deeper into the meaning and I reread. I see how their example fits the standard, but I want to be able to see this and create it myself.

I believe that all most teachers are in this same boat. We are immobilized by the unknown. For so long we have understood exactly what our kiddos need to do well. We know what the tests look like. We understand the standards. And now.... There is too much unknown. It is overwhelming.

### Breaking it Down

And so I begin breaking everything down. By Unit, by week, by standard, by assessment question.It gives me order and control and I feel a bit better. But I want to be careful not to forget the big picture of the Mathematical Practices. That is why I added them to my main unit pages. It is an instant reminder of the bigger picture.

I do not want to fall back into task teaching, although kids need to understand tasks. More importantly, I want to teach kids how to think, analyze and problem solve for their lives, not just in my class. If we can remember the big picture and focus on our big goals for our kids and apply it to Interpreting Functions we can achieve success for ourselves and most importantly our students. So lets jump in....

Interpreting Functions

Understand the concept of a function and use function notation.

1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

## Where to begin teaching functions to Algebra 1 students?

I love the idea of teaching functions at the beginning of Algebra 1 and weaving them into the curriculum to cement the concept into the minds of my students. There are functions everywhere. And if we can teach kids to see them, it will go a long way to connect them to the math.  It is the perfect way to begin the year, connecting Algebra to their middle school years.

## Planning

As I have begun the idea of creating a plan for next year, I have started with the scope and sequence created by the Mathematics Common Core Toolbox. And now I am searching for the best lesson plans I can find that will engage and develop an understanding of functions. Some great sites go beyond the repeated questions and algorithms and help students relate math to the real world. This will truly force understanding about what they are doing with the mathematics.

## What I want my students to learn in Unit 1

(Common Core Objectives or my Core Common Standards)

• Can they identify a function, do they understand the definition of a function
• Can compare two functions, even if they are represented in different ways (i.e., table, graph, or situation)
• Evaluate the function of a given variable
• Create equations in two variables and graph
• Give an appropriate domain for a function
• Find inverse functions

## Keep getting better (Never finished)

I am looking forward to a great year. And the more I prepare and take the great ideas I find and organize them as I find them, the less likely I am going to be regretting finding that awesome lesson a week after I have taught it. I want to force my students to work harder than I do.
I want them doing the work, processing, and thinking!