Please pardon our progress while we refine the look and functionality of our new ALEX site! You can still access the old ALEX site at alex.asc.edu. If you would like to share feedback or have a question for the ALEX Team, you can use the contact form here, or email us directly at administrator@alex.state.al.us.

### Overview

Students will be motivated to learn how to build new linear functions from existing linear functions.  Students will bring pictures of themselves and their parents from home to personally involve them in the lesson.  Students will learn to use the patterns inherent in functions to quickly and accurately graph linear functions.  This lesson will only deal with vertical shifts and the steepness of the line.  Horizontal shifts will be dealt with in future lessons. In addtion, in future lessons  students will transfer this knowledge to also graph exponential, quadratic, and absolute value functions.

This is a College- and Career-Ready Standards showcase lesson plan.

## UP:MA19.A1.17

### Vocabulary

• Function composition

### Knowledge

Students know:
• Techniques to combine functions using arithmetic operations.
• Techniques for combining functions using function composition.

### Skills

Students are able to:
• Accurately develop a model that shows the functional relationship between two quantities.
• Accurately create a new function through arithmetic operations of other functions.
• Present an argument to show how the function models the relationship between the quantities.

### Understanding

Students understand that:
• Arithmetic combinations of functions may be used to improve the fit of a model.

### Primary Learning Objectives

The student will be able to build new functions from existing functions.

### Procedures/Activities

Before:

1. To review and activate prior knowledge students will graph a line (given in slope-intercept form).  Students will use their whiteboards with the coordinate plane and graph y = 3x + 2.  The students will hold up their whiteboards as they finish and the teacher will assess their graphs.

2.  Students will post the pictures that they brought from home at the front of the room (optional).  Students will be given a few minutes to look at the pictures brought in by their classmates.  The teacher will compare the pictures of students and their parents to "parent functions and their babies".  The students can comment on how they are similar to their parents and how they are different from their parents.

During:

3.  Students will use their iPad to search for pictures of baby animals and their parents.  Students will be given five minutes for this activity.  The timer will be projected for students to see.  (See attached PowerPoint 5-down) At the end of the five minutes students will share their favorite pictures.  If students do not have access to an Ipad or computer the teacher may choose to show the PowerPoint "Parents and Their Babies" (attached).

4.  The teacher and students will work through the PowerPoint "It's All in the Family" which will require the student to describe the changes that the functions undergo compared to the parent function.   The PowerPoint concludes with a "one-minute paper" which will be completed and turned in at the end of the period.

5.  Cooperative learning activity- Students will work in pairs.  Students will use their whiteboards with the coordinate plane. (graph paper could also be used)  Each group will be given laminated cards of linear functions.  One student will graph the linear function on the whiteboard and one student will compare the new function to the parent function.  The students will then swap tasks.   The teacher will walk around the room and assess the students understanding. (for suggested problems see attached "Linear Functions")

After:

6.  The students will have one minute to summarize what they have learned about building new functions. (this is found at the end of the PowerPoint "It's All in the Family")

### Assessment Strategies

The students will hold up their whiteboards after graphing the linear function for the teacher to assess their understanding.

The teacher will walk around the room and observe students as they participate in the group activity.

The students will summarize what they have learned with a "one minute paper" which they will turn in at the end of the lesson.

### Acceleration

The lesson could be modified so that students who were already familiar with linear functions could use the same principles and build new exponential, quadratic, and absolute value functions.

### Intervention

Students who need extra assistance will be purposefully paired with another student who can help them with the lesson.

### Total Duration

31 to 60 Minutes

### Background/Preparation

Major concepts to be taught: the effect on the graph of replacing f(x) by f(x) + k, f(kx), and f(x+k), specifically in relation to linear functions.  The teacher should emphasize that new functions can be built from the "parent functions".

Student background- students should be able to graph a line when written in slope intercept form.

Teacher- should be familar with the PowerPoint presentation and work through the examples.

Teacher- prepare a designated place in the classroom for students to put their pictures from home.

### Materials and Resources

The PowerPoint presentation It's All in the Family will be printed and distributed to students so they can participate and make notes during the presentation.

The students will bring a picture from home that includes them and their parents (optional).

Whiteboards with coordinate planes and dry erase markers (if not available provide graph paper to students)

### Technology Resources Needed

PowerPoint presentation "It's All in the Family"

PowerPoint presentation "Parents and Their Babies" (optional)

iPads (optional) for student web search.  If students do not have access to the Internet, the teacher can present the PowerPoint presentation "Parents and Their Babies"