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Current Unit: Unit 8

Polynomials and Factoring

This unit will introduce students to solving polynomials through adding, subtracting, multiplying and dividing. Following practices of performing basic operations on polynomials, including applying the laws of exponents, students will gain skills in recognizing different techniques for solving polynomial expressions and equations. In addition to performing operations, students will learn techniques for factoring different kinds of polynomials in order to apply them to real-world examples. This unit will ultimately prepare students for solving quadratic functions and equations, and solving rational expressions and functions.

 

The SOLs addressed in this unit are:

 

A.2b:   The student will perform operations on polynomials, including adding, , multiplying, and dividing polynomials.

 

A.2c:   The student will perform operations on polynomials, including factoring completely first- and second-degree binomials and trinomials in one or two variables. Graphing calculators will be used as a tool for factoring and for confirming algebraic factorizations.

 

Resource Links for this unit:

http://www.mathsisfun.com/algebra/polynomials.html

https://www.khanacademy.org/math/algebra-basics/quadratics-polynomials-topic

https://ca.ixl.com/math/grade-9/add-and-subtract-polynomials

https://www.ixl.com/math/algebra-1/factor-polynomials

https://app.nearpod.com/#/presentation?pin=976BC88CCEB5B6901D6B718616080A39-1

GOALS

The student will:

 

Develop skills in adding, subtracting, multiplying, and dividing polynomials.

 

Develop skills in factoring polynomials.

 

Apply different kinds of polynomials to real world examples.

 

Recognize when to use certain techniques to different kinds of polynomials

ESSENTIAL VOCABULARY

Polynomial/Binomial/Trinomial

Punnett Square/Area Model

Factoring

Distributive property

Substitution

FOIL

Trial and error

Difference of squares

Zeros/Roots

Functions

Parabola

Sum of cubes

Greatest Common Factor

Synthetic Division

ESSENTIAL SKILLS/CONTENT

Factoring, Graphing, Order of Operations

 

TSW use manipulatives to determine how to find the area of square and rectangular shapes.

TSW apply square area to multiplication.

TSW demonstrate their understanding of the FOIL method for multiplying binomials.

TSW practice multiplying different kinds of polynomials.

TSW practice different techniques for factoring polynomials.

TSW find the zeros of polynomial functions and graph the solutions.

ASSESSMENT/EVALUATION

Pretest/Posttest: Pretest  involving some vocabulary, operations on polynomial expressions (add/subtract/mult/dividd). Posttest will have multiplying, dividing and factoring polynomials to see progress.

Project: Alone or with partner; apply graphs to real world problems (may use computer).

Presentation: Present projects

Audience Responses: Assess presentations and possibly rate peers on performance.

 

 

 

 

 

 

 

 

 

POSSIBLE ACTIVITIES FOR THIS UNIT

  • Pretest

  • Multiply/find area using manipulatives to lead to multiplying polynomials

  • Model factoring polynomials

  • Activity involving different factoring techniques

  • Math Relays (game where students sit in rows and the student at the front is given a problem to solve; student will complete ONE step and pass it to the student behind them to also complete ONE step; if student makes a change to work done by previous student, that counts as their step and they must pass it back; the last student in the row must complete the problem where it ends once it gets to them; once problem is solved students must pass paper forward, all the way to the first student. The row that finishes first, when the front student has the paper back, with the correct solution wins!)

  • Project (involving real world application to polynomials)

  • Posttest

     

     

     

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