Properties of Rational Functions Investigation Day 1 of 2

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Students will be to identify the features of a rational function.

Big Idea

The group investigation allows students to explore and discuss the structure of rational functions.

Warm up and Homework Review

10 minutes

I include Warm ups with a Rubric as part of my daily routine. My goal is to allow students to work on Math Practice 3 each day. Grouping students into homogenous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative explains this lesson’s Warm Up- Properties of Rational Functions Investigation Day 1 which asks students to explain the reasoning behind the shape of two rational functions.    

I also use this time to correct and record the previous day's Homework

Properties of Rational Function Investigation

38 minutes

In the previous lesson, my students transformed basic rational functions.  This two-day lesson covers the structure of more advanced rational expressions using a group investigation (Math Practice 7).  I begin by showing the students a complex rational function and its graph that doesn't fit the model learned in previous lessons.  I have them do a think-pair-share involving the similarities and differences between this problem and the ones they have seen before. 

Next, I introduce the investigation.  I combine one pair of students with another to create groups of four. Each group receives a packet of rational functions.  They look at the functions as well as any they choose to graph on their calculator to determine which types includes:

  • No y-intercept
  • No x-intercept
  • One Vertical Asymptote
  • Two Vertical Asymptotes
  • Location of the Curves
  • Location of x-intercepts  
  • Horizontal Asymptote at 0
  • Horizontal Asymptote  NOT at 0
  • No Horizontal Asymptote

They are also expected to explain WHY these properties are true for the given functions.   To model what I am looking for, we will look at the first property, no y-intercept together.   The students try to identify what the equations whose graphs that don’t cross the y-axis have in common.  We then discuss it as a class, identifying both the feature in the equation and WHY this feature leads to no y-intercept. 

Before they continue, I let them know how they are going to be assessed.  In the next lesson, I will randomly give each group a property to present to the class (Math Practice 3).  They will have ten minutes to look at their notes from today’s lesson to prepare their presentation.  When it is their turn to present, I will randomly pick one person from each group.  This ensures that each member of each group will be prepared rather than relying on one person.  This presentation will be one half of their grade for this lesson.  The second half will be a summary sheet that they each fill out as they watch the presentations. 

I think this activity provides the best of both worlds when it comes to group presentation and individual responsibility.  All of the students will need to be familiar with each property and have an equal chance of being chosen to present. 

The groups work the remainder of the class on identifying each property (Math Practice 1).  I wander around and provide support as needed as well as keep them working efficiently.  

Please note that the investigation was created using Kuta Software.  This is one of my favorite instructional tools and I would highly recommend it to anyone.  

Exit Ticket

2 minutes

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.  

Today's Exit Ticket asks students to identify which property was easiest to figure out and which was hardest and then explain why.  This lets me know where to provide some extra scaffolding in the next lesson.