Intro to Combining Like Terms With Rational Coefficients

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

7

Overview

In this learning activity, the students will be reminded that in simple addition they learned to add all the numbers together to get a sum. In algebra, numbers are sometimes attached to variables. The students will learn that they need to make sure that the variables are alike before they can add the numbers. This learning activity can be used as a stand-alone activity but is best used as an introductory activity. Corresponding activities are available.

Phase

Before/Engage
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

    The students will apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

    Activity Details

    1. The teacher will review combining like terms with the students using the Combining Like Terms video.
    2. The teacher will then use the Combining Like Term practice whole group to check for understanding of combining like terms.
    3. The teacher will allow students to work in pairs to solve additional problems using the Combining Like Terms with Negative Coefficients & Distribution practice.

    Assessment Strategies

    As the students are working on the additional 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 or with a partner.
    • The teacher could use the practice problems as a graded assessment.

    Background / Preparation

    • The teacher will need to review the video and the practice problems prior to the lesson.
    • The teacher will need to create a free Khan Academy account if he/she does not have an account already.
    • The teacher will need to assign the practice problems through a digital platform. 
    • The students will need to have prior knowledge of the distributive property.
    • 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
    Khan Academy Video
    https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:foundation-algebra/x…

    Approved Date

    Owner (Author)

    yvetteakridge
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