ALEX Lesson Plan

     

Color this Polynomial Simplified

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  This lesson provided by:  
Author:Elizabeth Thompson
System: Blount County
School: Blount County Board Of Education
The event this resource created for:GEMS
  General Lesson Information  
Lesson Plan ID: 23833

Title:

Color this Polynomial Simplified

Overview/Annotation:

This lesson helps students of all levels visualize the process of polynomial simplification and replicate it with ease. Three alternate forms of assessment are given to accomodate any school's level of technology (Podcasting. Powerpoints or Poster Presentations).
This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.

 Associated Standards and Objectives 
Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 7
6. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use properties of operations to produce combined and re-written forms of the expressions that are useful in resolving mathematical and contextual problems.
Teacher Vocabulary:
Term
  • like terms
  • Constant
  • Factor
  • Expression
  • Rational coefficient
  • Knowledge:
    Students know:
    • how to add, subtract, multiply, and divide rational numbers.
    • A(b + c) = ab + ac.
    • how to find the greatest common factor of two or more terms.
    Skills:
    Students are able to:
    • apply properties of operations as strategies to add and subtract linear expressions with rational coefficients.
    • Apply properties of operations as strategies to factor linear expressions with rational coefficients.
    • Apply properties of operations as strategies to expand linear expressions with rational coefficients.
    Understanding:
    Students understand that:
    • only like terms can be combined, e.g., x + y = x + y but x + x = 2x.
    • To factor an expression, one must factor out the greatest common factor.
    • There are many different ways to write the same expression.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.7.6.1: Define linear expression, rational, coefficient, and rational coefficient.
    M.7.6.2: Simplify an expression by dividing by the greatest common factor (Ex. 18x + 6y= 6(3x + y).
    M.7.6.3: Simplify expressions with parentheses (Ex. 5(4 + x) = 20 + 5x).
    M.7.6.4: Recognize the property demonstrated in a given expression.
    M.7.6.5: Combine like terms of a given expression.
    M.7.6.6: Recall how to find the greatest common factor.
    M.7.6.7: Give examples of the properties of operations including distributive, commutative, and associative.

    Prior Knowledge Skills:
    • Apply properties of operations for addition and subtraction.
    • Define equivalent, simplify, term, distributive property, associative property of addition and multiplication, and the commutative property of addition and multiplication.
    • Simplify expressions with parentheses (Ex. 5(4 + x) = 20 + 5x).
    • Combine terms that are alike of a given expression.
    • Recognize the property demonstrated in a given expression.
    • Simplify an expression by dividing by the greatest common factor.
      Example: 18x + 6y = 6(3x + y).
    • Determine the greatest common factor.

    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.7.5 Solve multiplication problems up to fifteen with whole number factors.


    Mathematics
    MA2019 (2019)
    Grade: 9-12
    Algebra I with Probability
    7. Add, subtract, and multiply polynomials, showing that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Use the repeated reasoning from prior knowledge of properties of arithmetic on integers to progress consistently to rules for arithmetic on polynomials.
    • Accurately perform combinations of operations on various polynomials.
    Teacher Vocabulary:
    • Polynomials
    • Closure
    • Analogous system
    Knowledge:
    Students know:
    • Corresponding rules of arithmetic of integers, specifically what it means for the integers to be closed under addition, subtraction, and multiplication, and not under division.
    • Procedures for performing addition, subtraction, and multiplication on polynomials.
    Skills:
    Students are able to:
    • Communicate the connection between the rules for arithmetic on integers and the corresponding rules for arithmetic on polynomials.
    • Accurately perform combinations of operations on various polynomials.
    Understanding:
    Students understand that:
    • There is an operational connection between the arithmetic on integers and the arithmetic on polynomials.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    ALGI.7.1: Combine like terms of a given expression
    ALGI.7.2: Define monomial, term, binomial, trinomial and polynomial.
    ALGI.7.3: Multiply polynomial expressions (quadratic).
    ALGI.7.4: Multiply polynomial expressions (linear).
    ALGI.7.5: Subtract polynomial expressions.
    ALGI.7.6: Add polynomial expressions.
    ALGI.7.7: Use order of operations to evaluate and simplify algebraic and numerical expressions.
    ALGI.7.8: Identify the terms in a polynomial expressions.
    ALGI.7.9: Explain the distributive property.

    Prior Knowledge Skills:
    • Identify properties of exponents.
    • Give examples of the properties of operations including distributive, commutative, and associative.
    • Recall how to find the greatest common factor.
    • Combine like terms of a given expression.
    • Recognize the property demonstrated in a given expression.
    • Simplify expressions with parentheses (Ex. 5(4 + x) = 20 + 5x).
    • Simplify an expression by dividing by the greatest common factor (Ex. 18x + 6y= 6(3x + y).
    • Define linear expression, rational, coefficient, and rational coefficient.
    • Combine terms that are alike of a given expression.

    Local/National Standards:

    NCTM: Algebra: Represent and analyze mathematical situations and structures using algebraic symbols Problem Solving: apply and adapt a variety of appropriate strategies to solve problems. Communication: organize and consolidate their mathematical thinking through communication; communicate their mathematical thinking coherently and clearly to peers, teachers, and others

    Primary Learning Objective(s):

    The student will learn to identify like terms in a polynomial expression. The student will learn to simplify the polynomial expression.

    Additional Learning Objective(s):

    Students will explore a method of communication that is becoming more popular in our global society (addressing communication as a societal issue).

     Preparation Information 

    Total Duration:

    91 to 120 Minutes

    Materials and Resources:

    Colored Pencils/Crayons for entire class Worksheets of increasing difficulty for practice. Samples of completed problems (enlarged to hang around the room) If an overhead projector is used: Colored markers and/or squared of transparent colored film will be needed. If Posterboard Project is chosen: Posterboard will be needed.

    Technology Resources Needed:

    Interwrite Board (Dry Erase Board or Overhead Projector works fine) Sample problems on computer (or transparency for overhead) Podcasting equipment (if this method of assessment is chosen) MS Paint/ Computer access (if an alternate method of assessment is chosen

    Background/Preparation:

    Scan or type sample problems of increasing difficulty to use with your Interwrite board (or create a transparency). Practice worksheets (increasing difficulty). Watch the PowerPoint and print notespages. Colored pencils/crayons available for all students Reserve lab-time if the bonus assignment is used (or assign it for homework). Have an area to display student work.

      Procedures/Activities: 
    1.)Print a copy of the PowerPoint notepages to view teacher notes during presentation. View the PowerPoint prior to class (note 'fly-ins').

    2.)View the web attachments: (1) An intro to podcasts , (2) Podcasting in the classroom . Two alternate forms of assessment are offered in the 'Polynomial Assessment' attachment for schools with different levels of technology.

    3.)In Class: Explain the objective (to simplify polynomials). Using an Interwrite Pad/Dry-erase board or overhead, quicky offer a sample of what the student will be expected to simplify at the end of the lesson (1-2 days). This approach typically makes students receptive to an outlined method (offered in the PowerPoint).

    4.)Use the PowerPoint sample ‘Color this Polynomial Simplified’ to explain the visualization process.

    5.)Using your Interwrite Board (or overhead), open some sample problems. Use the highlight function to shade over like terms increasing the difficulty level with each problem and allowing students to help you through the process.

    6.)Pass out sample problems (worksheet) and give students time to practice.

    7.)After the completion of multiple problems, the students should be able to forgo the color process.

    8.)Homework/Lab Assignment: Place students into groups of 2-3. Give each group a challenging problem to be solved (see attachement - Polynomial Assignment Options).


    Attachments:
    **Some files will display in a new window. Others will prompt you to download.
      Assessment  

    Assessment Strategies

    Tradiational grades (right/wrong) can be used on practice worksheets. Rubrics are provided for the alternative assessments (Podcasting, PowerPoint and/or Poster Project). See the attachment.

    Acceleration:

    Students can apply this concept to solving multi-step equations (a new concept).

    Intervention:

    Use a calculator for adding/subtracting integers within the Polynomial to be simplified. Review operations on integers (add, subtract, multiply and divide).


    View the Special Education resources for instructional guidance in providing modifications and adaptations for students with significant cognitive disabilities who qualify for the Alabama Alternate Assessment.