Operations with Polynomials Day 2 of 2

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Objective

Students will be able to add and subtract polynomial equations graphically and algebraically.

Big Idea

Students explore and make conclusions about functions operations using graphing technology.

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 homogeneous pairs provides an opportunity for appropriately differentiated math conversations. This lesson’s Warm Up- Operations with Polynomials Day 2 asks students to determine whether two polynomials have been added correctly.

I also use this time to correct and record any past Homework

Exploring Operations with Polynomial using Graphing Technology

20 minutes

This is the second day of a two day lesson. We now move on to exploring functions with TI-84 graphing calculators.  Please see the Calculator Notes in slide #2 from the PowerPoint for specific instructions on using TI-84s. 

I have students look first at Two Quadratics and then at a Quadratic and a Cubic to explore the effect on the degree of the sum or the difference of the polynomials (Math Practice 7).  As they learn to accurately predict the degree of the resulting polynomial functions under addition or subtraction, I ask them to create their own polynomials whose sum or difference produces a specific characteristic.  For example, I might ask them to identify two cubic functions whose sum produces a line function.   In my video I describing another problem and getting students to think outside of the box a bit (Math Practice 1).  Depending on my remaining time, I may ask specific students to write their functions on a note card so the class can see and discuss multiple solutions.  This is a great, non-threatening way of allowing the students to analyze each other’s work (Math Practice 3).  

Lesson Summary

17 minutes

The concluding activity has the students do two things.

  1. Summarize the outcome when you find the sum or difference of polynomial functions with the same degree.
  2. Summarize the outcome when you find the sum or difference of polynomial functions with different degrees.

I have the students work on these in pairs and then we discuss it as a class.  

Exit Ticket

3 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 find the sum of two functions.

Assignment

My Operations with Polynomial Functions assignment provides the students with an opportunity to find the sum and difference of polynomial functions both graphically and algebraically.  It also assesses their understanding of the outcomes when adding polynomials (Math Practice 7).  Finally, it provides them with a profit modeling exercise (Math Practice 4).  

 

note: I have students tape the half-sheet into their notebooks and work on separate paper. You can reformat the handout if you wanted to have students work directly on it.