Combining Like Terms With Rational Coefficients

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

7

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. 

Phase

During/Explore/Explain
Mathematics (2019) Grade(s): 7

MA19.7.6

Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

UP:MA19.7.6

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.
    Mathematics (2019) Grade(s): 7 - Grade 7 Accelerated

    MA19.7A.12

    Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. [Grade 7, 6]

    UP:MA19.7A.12

    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.
    Mathematics (2019) Grade(s): 7 - Grade 7 Accelerated

    MA19.7A.16

    Express and compare very large or very small numbers in scientific notation. [Grade 8, 5]

    UP:MA19.7A.16

    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.

    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.

    Activity Details

    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. 

    Variation Tips

    • 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.

    Background / 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.

    Learning Activity (Before)

    Intro to Combining Like Terms With Rational Coefficients

    Learning Activity (During)

    Combining Like Terms With Rational Coefficients

    Learning Activity (After)

    Add Linear Expressions With Rational Coefficients
    Combining Like Terms with Rational Coefficients YouTube
    https://www.youtube.com/watch?v=ZqdUtxzj7Dc.

    Approved Date

    Owner (Author)

    yvetteakridge
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