ALEX Lesson Plan


How Do Functions Behave?

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  This lesson provided by:  
Author:Michelle Russell
System: Florence City
School: Florence High School
  General Lesson Information  
Lesson Plan ID: 33045


How Do Functions Behave?


In this lesson, students will conduct a collaborative investigation to independently discover the leading term test for end behavior. They will work with their classmates to discover the principles governing the end behavior of polynomials. They will present their findings concerning end behavior and will be asked to justify their conclusions.  Students will create an Educreations video to present and record their findings.

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

 Associated Standards and Objectives 
Content Standard(s):
MA2015 (9-12) Precalculus
18. Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [F-IF7]
a. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. [F-IF7b]
b. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. [F-IF7c]
c. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. [F-IF7d]
d. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. [F-IF7e]

Local/National Standards:

Math Practice Standard #7

Look for and make use of structure

Primary Learning Objective(s):

The students will be able to develop the rules for the end behavior of polynomial functions.

Additional Learning Objective(s):

 Preparation Information 

Total Duration:

31 to 60 Minutes

Materials and Resources:

Big chart paper for groups to summarize findings


Technology Resources Needed:

  • iPad (if students do not have access to an iPad they can create a foldable in place of the video) 
  • Educreations App (free)
  • Projector
  • Graphing Calculator (if no graphing calculators are available, students can graph the functions)


Educreations App will need to be downloaded on the iPad prior to the lesson.

Prerequisite learning - Students should be able to identify and know the meaning of x and y intercepts of a polynomial function as well as the domain and range. If not, students will need to be given these vocabulary words to be defined.

The teacher makes graphing calculators available for the students. (optional)

  1. Connect students to prior knowledge by reviewing key features of polynomial functions (x and y intercepts, domain, and range). Please see attached document: Key Features of a Graph.
  2. Class/group activity - students will collaborate with classmates to create the rules governing the end behavior of polynomials. The teacher will give students four functions to examine and the students will try to discover the rules governing end behavior. The teacher will put a 5-minute timer (see attachment below for a timer) on the overhead for the students. At the end of 5 minutes the timer can be reset if necessary. (Please see attached document: End Behavior)
  3. Students will create a summary of their findings and justify their results.
  4. Students will create a video summarizing their results using the Educreations App.

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Assessment Strategies

The teacher will walk around the room and listen to the group discussions. 

The teacher will assess the students as they create their findings.

The teacher will assess the videos students create using a rubric. (Please see attached document: Rubric Leading Term Test)




Students can be shown how to demonstrate end behavior with their arms. For example: Positive and even: both arms up. Negative and even: both arms down. Odd and positive: left arm down right arm up. Odd and negative: left arm up and right arm down.

Each area below is a direct link to general teaching strategies/classroom accommodations for students with identified learning and/or behavior problems such as: reading or math performance below grade level; test or classroom assignments/quizzes at a failing level; failure to complete assignments independently; difficulty with short-term memory, abstract concepts, staying on task, or following directions; poor peer interaction or temper tantrums, and other learning or behavior problems.

Presentation of Material Environment
Time Demands Materials
Attention Using Groups and Peers
Assisting the Reluctant Starter Dealing with Inappropriate Behavior
Be sure to check the student's IEP for specific accommodations.