Lesson 3 | Exponents and Exponential Functions | 9th Grade Mathematics

Objective

Multiply polynomials using properties of exponents and properties of operations.

Common Core Standards

Core Standards

The core standards covered in this lesson

A.APR.A.1 — Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Arithmetic with Polynomials and Rational Expressions

A.APR.A.1 — Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Foundational Standards

The foundational standards covered in this lesson

7.EE.A.1

Expressions and Equations

7.EE.A.1 — Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
8.EE.A.1

Expressions and Equations

8.EE.A.1 — Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² × 3<sup>-5</sup> = 3<sup>-3</sup> = 1/3³ = 1/27.
8.EE.C.7

Expressions and Equations

8.EE.C.7 — Solve linear equations in one variable.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Apply the distributive property to multiply a monomial by a polynomial.
Apply the distributive property more than once to multiply a polynomial by a polynomial.
Use precision when simplifying polynomial expressions; multiply coefficients of terms and add the exponents of like bases (Standard for Mathematical Practice 6).

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

Find the product.

$${4y^2(-3y+6y^5-4)}$$

Guiding Questions

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Problem 2

Find the product.

$${(y+1)(y^3-2y+5)}$$

Guiding Questions

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Problem 3

Simplify the expression. Write your answer in standard form.

$${2x^3(3x^4-x^2+x)-(2x^5-x^7)}$$

Guiding Questions

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Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Problem 1

Must the product of three polynomials again be a polynomial?

References

EngageNY Mathematics Algebra I > Module 1 > Topic B > Lesson 9 — Exit Ticket, Question #1

Algebra I > Module 1 > Topic B > Lesson 9 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem 2

Find $${(w^2+1)(w^3-w+1)}$$.

References

EngageNY Mathematics Algebra I > Module 1 > Topic B > Lesson 9 — Exit Ticket, Question #2

Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Kuta Software Free Algebra 1 Worksheets Multiplying Polynomials
EngageNY Mathematics Algebra I > Module 1 > Topic B > Lesson 9 — Problem Set

Lesson 2

Lesson 4

Lesson Map

Topic A: Exponent Rules, Expressions, and Radicals

Use exponent rules to analyze and rewrite expressions with non-negative exponents.

8.EE.A.1

Add and subtract polynomial expressions using properties of operations.

A.APR.A.1

Multiply polynomials using properties of exponents and properties of operations.

A.APR.A.1

Solve mathematical applications of exponential expressions.

8.EE.A.1

Use negative exponent rules to analyze and rewrite exponential expressions.

8.EE.A.1 A.SSE.A.2

Define rational exponents and convert between rational exponents and roots.

N.RN.A.1 N.RN.A.2

Write equivalent radical and rational exponent expressions. Identify quantities as rational or irrational.

N.RN.B.3

Simplify radical expressions.

N.RN.A.2

Multiply and divide rational exponent expressions and radical expressions.

N.RN.A.2 N.RN.B.3

Add and subtract rational exponent expressions and radical expressions.

N.RN.A.2 N.RN.B.3

Topic B: Arithmetic and Geometric Sequences

Describe and analyze sequences given their recursive formulas.

F.BF.A.2 F.IF.A.2 F.IF.A.3

Write recursive formulas for sequences, including the Fibonacci sequence.

F.BF.A.2 F.IF.A.2 F.IF.A.3

Define arithmetic and geometric sequences, and identify common ratios and common differences in sequences.

F.BF.A.2 F.LE.A.2

Write explicit rules for arithmetic sequences and translate between explicit and recursive formulas.

F.BF.A.2 F.IF.A.3 F.LE.A.2

Write explicit rules for geometric sequences and translate between explicit and recursive formulas.

F.BF.A.2 F.IF.A.3 F.LE.A.2

Topic C: Exponential Growth and Decay

Compare rates of change in linear and exponential functions shown as equations, graphs, and situations.

A.SSE.A.1 F.IF.C.9 F.LE.A.1 F.LE.A.3

Write linear and exponential models for real-world and mathematical problems.

A.SSE.A.1 F.LE.A.1 F.LE.A.2 F.LE.B.5

Graph exponential growth functions and write exponential growth functions from graphs.

F.BF.B.3 F.IF.C.7.E

Write exponential growth functions to model financial applications, including compound interest.

F.IF.C.8.B F.LE.A.2 F.LE.B.5

Write, graph, and evaluate exponential decay functions.

F.BF.B.3 F.IF.C.7.E F.IF.C.8.B F.LE.A.1.C

Identify features of exponential decay in real-world problems.

F.IF.C.8.B F.LE.A.1.C

Solve exponential growth and exponential decay application problems.

F.IF.C.8.B F.LE.A.1 F.LE.A.2

Exponents and Exponential Functions

Objective

Common Core Standards

Core Standards

Arithmetic with Polynomials and Rational Expressions

Foundational Standards

Expressions and Equations

Expressions and Equations

Expressions and Equations

Criteria for Success

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Target Task

Problem 1

References

Problem 2

References

Additional Practice

Lesson Map

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