Operations with Polynomials Day 1 of 2

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Students will be able to add and subtract polynomials graphically and algebraically.

Big Idea

Students get the opportunity to explore and make conclusions about operations with polynomials 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. The resource Video specifically explains this lesson’s Warm Up- Operations with Polynomial Functions asks students to come up with three real-life examples of slope, as a rate of change.  

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

Finding Sums and Differences Graphically and Algebraically

15 minutes

This is the first of a two day lesson.  My goal for this lesson is to extend my students’ view of functions into the realm of operations with function.  We will not only look at how to add and subtract polynomials, we will also analyze the effects of adding different types of polynomial functions together.

I begin with a quick review of the terminology that will be important to the discussions in today’s lesson. 

Next, I hand out a copy of the graph of the first two linear functions which my students visually add and then subtract.  We discuss the new function for each operation and then connect how the graphical and algebraic methods of addition and subtraction produce the same results.  Detailed notes are included in the PowerPoint.

We then look at another pair of linear functions whose slopes are opposite.  These produce a sum that is horizontal.  The third example provides the students with a parabola and a line.  The students predict the shape of the sum and difference and then find their solutions graphically (Math Practice 7).  

Exploring Operations using Graphing Technology

15 minutes

I have included this portion of the lesson because it is always important to have more to do than not enough.  Each class is different and may end in separate places.  

We now move on to exploring functions with TI-84 graphing calculators.  Please see the notes in slide #11 of the PowerPoint for detailed instructions on using the calculators. 

I have them look at two quadratics and then at a quadratic and a cubic to explore the effect of the degree of the sum or the difference of different types of polynomials (Math Practice 7).  As they learn to accurately predict the types of polynomial functions that will occur, I ask them to create their own polynomials whose sum or difference produces a specific characteristic.  For example, I ask them to identify two cubic functions that produce a line when added together.  Depending on the remaining time, I may choose some examples to write on the board for the class to discuss.  This is a great, non-threatening way of allowing the students to analyze each other’s work (Math Practice 3).  

Exit Ticket

2 minutes

I use an exit ticket each day to provide a quick formative assessment to judge the success of the lesson.  Today's exit ticket , asks the students to find to find the sum of two linear functions.