ALEX Learning Activity

  

Add Linear Expressions With Rational Coefficients

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  This learning activity provided by:  
Author: YVETTE AKRIDGE
System:Andalusia City
School:Andalusia City Board Of Education
  General Activity Information  
Activity ID: 2859
Title:
Add Linear Expressions With Rational Coefficients
Digital Tool/Resource:
Adding Linear Expressions Worksheet
Web Address – URL:
Overview:

In this learning activity, students will add linear expressions using the properties of operations. The students will also have a chance to practice adding linear expressions on their own, including those that contain integer coefficients and constants as well as expressions that have rational coefficients and constants. This activity includes a review and worksheets ready to print or assign digitally. 

 

This learning activity can be used as a stand-alone activity but is best used as an After Activity. The Before and During Activities can be found in the Tools or Recommendations section.
  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: 7
    Accelerated
    12. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. [Grade 7, 6]
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Factor a linear expression with an integer as the greatest common factor.
    • Interpret the parts of an expression, such as the coefficient, constant, term, and variable, based on the context of problem.
    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.
    Diverse Learning Needs:
    Learning Objectives:

    Student Learning Objectives:

    • I can simplify algebraic expressions by using the distributive property.

    • I can apply properties of real numbers (add, subtract and expand linear expressions).

    • I can simplify algebraic expressions by combining like terms.
      Strategies, Preparations and Variations  
    Phase:
    After/Explain/Elaborate
    Activity:

    1. The teacher will review combining like terms whole-group using the Matching Equivalent Linear Expressions Worksheet. The teacher will display the worksheet whole-group and allow students enough time to complete the matching problems on the worksheet.

    2. After the students have had ample time to work on the review problems on the matching worksheet, the teacher will review the answers.

    3. Once the students have proven they understand combining like terms, the teacher will distribute the Adding Linear Expressions Worksheet.

    4. After the teacher passes out the Adding Linear Expressions Worksheet, he/she will review using the top portion of the worksheet.

    5. The teacher will say, "You can add expressions using the properties of operations. Let’s try it! Simplify (2x − 15) + (–5x + 9). (2x − 15) + (–5x + 9). Identify like terms. [2x + (–5x)] + (–15 + 9). Use the commutative and associative properties to reorder and group like terms. –3x + (–6) Combine like terms. –3x − 6. Rewrite addition as subtraction to simplify the final expression. Try it yourself! Find each sum."

    6. The teacher will instruct the students to complete the worksheet individually for an assessment grade. 

    7. At the end of class, the teacher will bring the students back to a whole-group discussion to determine any problems they faced by applying properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
    Assessment Strategies:

    The teacher will use the Adding Linear Expressions Worksheet as an assessment to check for students' understanding of applying properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
    Advanced Preparation:
    Variation Tips (optional):
    Notes or Recommendations (optional):

    This activity can stand alone or be used as an After/Explain/Elaborate activity for the following learning activities:

    Intro to Combining Like Terms with Rational Coefficients (Before Activity)

    Combining Like Terms with Rational Coefficients (During Activity)
      Keywords and Search Tags  
    Keywords and Search Tags: add, expand, factor, linear expressions, rational coefficients, subtract