ALEX Learning Activity

  

Combining Like Terms With Rational Coefficients

A Learning Activity is a strategy a teacher chooses to actively engage students in learning a concept or skill using a digital tool/resource.

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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: 2848
Title:
Combining Like Terms With Rational Coefficients
Digital Tool/Resource:
Combining Like Terms with Rational Coefficients YouTube
Web Address – URL:
Overview:

In this learning activity, students will learn how to rewrite algebraic expressions by combining like terms. The students will apply properties of operations to add, subtract, factor, and expand linear expressions. The lesson offers a teaching video and additional problems for partner work to check for understanding. 

 

This learning activity can be used as a stand-alone activity but is best used as a core lesson activity. Corresponding 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:
    Mathematics
    MA2019 (2019)
    Grade: 7
    Accelerated
    16. Express and compare very large or very small numbers in scientific notation. [Grade 8, 5]

    a. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used, expressing answers in scientific notation. [Grade 8, 6]

    b. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. [Grade 8, 6a]

    c. Interpret scientific notation that has been generated by technology. [Grade 8, 6b]
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Rewrite numbers using scientific notation.
    • Use use numbers in scientific notation to estimate measurements and values.
    • Use the laws of exponents to multiply and divide expressions containing numbers written in scientific and decimal notation to solve real-world problems.
    • Compare numbers written in scientific notation and express the multiplicative relationship between the numbers.
    Teacher Vocabulary:
    • Multiplicative relationship
    • Scientific Notation
    Knowledge:
    Students know:
    • That scientific notation is formed using base ten system and is the reason a 10 is used as the base number.
    • Raising or lowering an exponent is has an effect on the place value of the decimal expansion.
    • That scientific notation is formed using a base ten system.
    • how to apply laws for multiplying and dividing exponents
    Skills:
    Students are able to:
    • Write numbers in standard notation in scientific notation.
    • Convert numbers from scientific notation back to standard form.
    • Use information given in scientific notation to estimate very large or small quantities given in real-world contexts.
    • Perform multiplication and division with numbers expressed in scientific notation to solve real-world problems, including problems where both scientific and decimal notation are used.
    • Choose between appropriate units of measure when determining solutions or estimating
    Understanding:
    Students understand that:
    • The movement of decimals in converting between scientific and standard notation is a function of an exponent.
    • Every decimal place represents a power of ten (this is a connection many students have not made yet when thinking about place value).
    • Scientific notation has real-world applications for very large and very small quantities found in many disciplines.
    • performing scientific notation operations are another application of integer exponent operations.
    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, factor, and expand linear expressions).

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

    Procedure:

     

    Introduction: (5 minutes, whole group)

    • The teacher will start the lesson by reviewing that simple addition is adding all the numbers together to get a sum. In algebra, numbers are sometimes attached to variables and we need to make sure that the variables are alike before we add or subtract the numbers.

    • The teacher will say, "In this lesson, we will be practicing simplifying expressions with rational coefficients. Does anyone remember what it means if a number is a rational number? Does anyone know what the word coefficient means? (The teacher will allow students to answer the questions.)

     

    During (20 minutes, whole group)

    • The teacher will begin the lesson portion of the learning activity by showing the Combining Like Terms with Rational Coefficients video.

    • The teacher will review the steps taught in the video using the following examples:

    • The teacher will say, "We will now work on a few examples to review what the video taught us.  First, we need to identify the coefficients, constant terms, and like terms in the following examples. Next, we will need to apply appropriate properties:

    1) x + 4 - 2x - 10

    2) 5(w - 4) + w + 8

    3) -3.6 - 1.9x + 1.2 + 5.1x

    4) 11/12 - 1/6h + 5/6h - 1/3

    5) 2/5b + 4/3 − 4/5b + 1/3

    6) ¾(12x + 20) − 6x − 8

     

    Conclusion (10 minutes, partner work)

    • The teacher will ask the students if they understand the material taught in the video and if he/she needs to work on any additional examples.

    • Once the students confirm they understand the material that has been taught, the teacher will assign the combining like terms with rational coefficients practice. (The practice will be assigned digitally.)

    • The teacher will allow students to work in pairs to solve the combining like terms with rational coefficients practice. This will allow the students who are afraid to ask questions the opportunity to learn from peer-tutoring.
    Assessment Strategies:

    As the students are working on the practice problems, the teacher should be watching and listening to the students' responses to ensure the students understand the learning objective. 
    Advanced Preparation:

    • The teacher will need to review the video prior to the lesson.

    • If the teacher does not have a Khan Academy account, he/she will need to create a free Khan Academy account so that he/she may assign the practice problems.

    • The teacher will need to assign the practice problems through a digital platform. 

    • The students will need to have prior knowledge of combining fractions.

    • The teacher may need to predetermine student groupings.
    Variation Tips (optional):

    • The students can work on the additional problems individually instead of with a partner.

    • The teacher could use the practice problems as a graded assessment.
    Notes or Recommendations (optional):

    This activity can stand alone or be used as a During/Explore/Explain activity for the following learning activities:

     

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

    Add Linear Expressions with Rational Coefficients  (After Activity)
      Keywords and Search Tags  
    Keywords and Search Tags: add, expand, factor, linear expressions, rational coefficients, subtract