Adding and Subtracting Polynomials

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Objective

SWBAT Add and subtract polynomial expressions.

Big Idea

When polynomial expressions are added the result is another polynomial expression.

Opening

10 minutes

Each pair of students will be given an envelope and asked to group the contents (see add_subtract_polynomials_open) into four groups of four.  Usually students will be able to pick up on the fact that they should be grouping the individual terms by like terms.  I like to use a document camera to show what a particular group has done so that all students can compare their groups (I have a group do their work under the doc cam).  

Then I ask each pair of students to think about what the sets of like terms add up to. (You may want to clarify that we are asking them to only sum the like terms not all of the terms). Using the group whose terms are under the document camera to demonstrate, have other pairs of students verbalize how the group came up with their answers.  Having multiple groups share about the same set of like terms will allow the others in the class to see the range of options for combining like terms.

For example: I will hear one group say that, "We added -4y + 3y and got -1y.  Then we added that to -y and got -2y.  Last we added that to 5y and got 3y."  Another pair might say, "We noticed that -1y and -4y would give us -5y which cancelled out 5y.  So our answer was 3y."  Let students take some time to express their ideas here and allow other students to respond MP3.

Investigation

15 minutes

As they explore today's investigation, students will answer a series of questions which require them to think more deeply about adding and subtracting polynomial expressions.  The word "degree" is used in this investigation.  I will usually put a few examples of polynomials on the board and talk about the degree of each.  This is a fairly straight-forward vocabulary word that students often pick up on easily.

Question #5 will require students to solve a non-routine problem (MP1), thinking outside of the box of basic addition and subtraction.  In working on this task students need to make use of structure to come up with a reasonable answer (MP7). If time permits, I like to have students put some answers up on the board to the different parts of Question 5 to show the range of possibilities.  

Reciprocal Teaching

15 minutes

This add_subtract_polynomials_practice is a reciprocal teaching activity asks students to apply the understanding that they have just constructed through the investigation to teach a peer. When participating in a reciprocal teaching activity, students work in pairs and there are two forms (in this case A and B).  The answers for A are on form B and vice-versa.  The key to facilitating is encouraging students to attend to their partner carefully and respectfully.  Explain to students that they should NEVER be writing at the same time. When one student is working, the other is watching and coaching and helping them arrive at the correct answer.  Then they switch roles and the other person completes a question.  Explain to the students that quality is more important than quantity.  If they do not finish all of the questions, that is okay.

While students are working, I will use the time to assess student progress by watching individual students work through problems.  I try to let the partners do most of the coaching and helping. I think that you can learn a great deal by just watching the students work.  I suggest having a class roster to make notes of who is understanding the material and who is struggling. This will be important information to have before moving onto equation solving in the next portion of the unit.