MA.912.AR.1.4

Divide a polynomial expression by a monomial expression with rational number coefficients.

Clarifications

Clarification 1: Within the Algebra 1 course, polynomial expressions are limited to 3 or fewer terms.
General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Algebraic Reasoning
Status: State Board Approved

Benchmark Instructional Guide

• Monomial
• Polynomial

Vertical Alignment

Previous Benchmarks

Next Benchmarks

Purpose and Instructional Strategies

In middles grades, students added, subtracted and multiplied linear expressions. In Algebra I, students perform operations on polynomials limited to 3 or fewer terms and divide polynomials by a monomial. In later courses, students will perform operations on all polynomials.
• Instruction includes the connection to addition, subtraction and multiplication of polynomials to develop the understanding of closure, and the connection to properties of exponents.
• Instruction includes proper vocabulary and terminology, keeping in mind that when dividing, the word “cancel” can become a misconception for students. A number or an expression divided by itself is equivalent to 1 and does not disappear (see Appendix D).
• Instruction includes the use of manipulatives, like algebra tiles, and various strategies, like the area model, properties of exponents and decomposing fractions.
• Decomposing fractions
•  The expression can be written as   . Students can then   perform the division with  each fraction to determine the difference.

Common Misconceptions or Errors

• Students may not understand the meaning of closure (although not directly discussed in this benchmark, polynomials are not closed under division).
• Students may not understand like terms.

Strategies to Support Tiered Instruction

• Teacher provides examples showing that polynomials are closed under the operations of addition, subtraction and multiplication, but not under division.
• For example, when subtracting or multiplying polynomials (as shown below), the result is always a polynomial.
7$x$ +5−(3$x$ + 8) = 4$x$ − 3
(7$x$ + 5)(3$x$ + 8) = 21$x$2 + 71$x$ + 40
• For example, when dividing polynomials (as shown below), the result may or may not be a polynomial.

Instructional Task 1 (MTR.3.1, MTR.4.1, MTR.5.1)
• Part A. Determine the quotient of ($\frac{\text{1}}{\text{3}}$$a$4 − 3$a$3 + $\frac{\text{1}}{\text{2}}$$a$2) and 3$a$3
• Part B. Discuss with your partner the strategy used. How do your quotients compare to one another?

• Part A. Determine the quotient of $x$ + $x$and $x$-1
• Part C. What happens when you divide $x$ + $x$2 by the expression $x$$\frac{\text{1}}{\text{2}}$ (which is not a monomial)?

Instructional Items

Instructional Item 1
• What is the quotient of the expression

Instructional Item 2
• What is the quotient of the expression

Instructional Item 3
•  What is the quotient of the expression

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

Related Courses

This benchmark is part of these courses.
1200310: Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200320: Algebra 1 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200380: Algebra 1-B (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912090: Access Algebra 1B (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))
1200315: Algebra 1 for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200385: Algebra 1-B for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912075: Access Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.912.AR.1.AP.4: Divide a polynomial expression by a monomial expression with integer coefficients.

Related Resources

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Student Resources

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