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.)

**Grade:**912

**Strand:**Algebraic Reasoning

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

- 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 subtracting or multiplying polynomials (as shown below), the
result is always a polynomial.

- For example, when dividing polynomials (as shown below), the result may or may not be a polynomial.

### Instructional Tasks

*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?

Instructional Task 2 (

Instructional Task 2 (

*MTR.3.1, MTR.4.1, MTR.5.1*)- Part A. Determine the quotient of $x$ + $x$
^{2 }and $x$^{-1}. - Part B. What do you notice about your answer and the Laws of Exponents?
- 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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## Parent Resources

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