Sorting Polynomial Equations and Identities

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Objective

Students will be able to identify whether polynomial equations have one solution, no solutions or many solutions.

Big Idea

Students master the ability to differentiate identities from linear and quadratic equations in this sorting activity lesson.

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 Warm Up- Sorting Equations and Identities asks students to determine whether the equation (x + 2)(y + 2) = xy + 4 is always, sometime or never true.  

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

Introduction

7 minutes

I am a huge fan of the Math Assessment Project (MAP) lessons and activities.  They are centered on both the Common Core math and practice standards.  The lesson I am doing with my students today has students analyze equations to determine whether they are identities (Math Practice 7).  It also addresses many of the common errors found in students’ algebraic manipulation.  The lesson on the MAP website offers a complete lesson plan, therefore, I will be addressing how I enact this lesson in my class rather than repeating its exact contents. 

I had my students complete a pre-assessment several days ago and it drives my questioning today.  The MAP lesson offers an excellent question guide on page four of their lesson plan based on the issues noted in the pre-assessment. 

The warm up today is the first question in this introduction.  I pull up the visual representation of (x + 2)(y + 2) = xy + 4 and ask them to re-evaluate and discuss with their partner where this is always, sometimes or never true.  The lesson plan suggests the use of personal white boards but I have chosen not to use them today.  Please look in the lesson plan on the MAP website for specific questioning techniques that guides students to the realization that this is sometimes true. 

We then look at the equation (x + 2)(x − 2) = x2 +4 and have a class discussion on whether this equation is always, sometimes or never true

Always, Sometimes or Never Sorting Activity

20 minutes

In pairs, the students will be given a large piece of paper, a set of cards, and a glue stick.  They will divide the paper into three columns with the headings Always, Sometimes, and Never.   As a team, they will then sort the cards into the appropriate columns.  One big key here is that they discuss and agree on the placement of each card (Math Practice 3).  I walk around providing support as needed.  The lesson plan on the website offers specific questions that are helpful which I have included in the Introduction.  For example, "You have shown the statement is true for this specific value of x. Now convince me it is always true for every number!"

Class Discussion

10 minutes

The final portion of class will be spent concluding the activity.  The MAP lesson suggests that each group shares one of their responses; however, there isn’t time for that in my class period.  This activity was based on 60 minutes and my classes are only 50 minutes.  A way around this is to have pairs share with another pair of students and then have volunteers share out any particularly interesting pieces of information that they found.  

I have included the guidance on specific questions to use during Group Discussion from the MAPS website.

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 write a definition of a identity.

Homework

I pass back their original pre-assessment along with a new copy and ask them to improve their original work.