Equivalent Quadratic Expressions

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

8, 9, 10, 11, 12

Overview

This video lesson transitions students from reasoning concretely and contextually about quadratic functions to reasoning about their representations in ways that are more abstract and formal (MP2).

In earlier grades, students reasoned about multiplication by thinking of the product as the area of a rectangle where the two factors being multiplied are the side lengths of the rectangle. In this lesson, students use this familiar reasoning to expand expressions such as (x + 4)(x + 7), where x + 4, and x + 7 are side lengths of a rectangle with each side length decomposed into x and a number. They use the structure in the diagrams to help them write equivalent expressions in expanded form, for example, x2 + 11x + 28 (MP7). Students recognize that finding the sum of the partial areas in the rectangle is the same as applying the distributive property to multiply out the terms in each factor.

The terms “standard form” and “factored form” are not yet used and will be introduced in an upcoming lesson, after students have had some experience working with the expressions.

Mathematics (2019) Grade(s): 09-12 - Algebra I with Probability

MA19.A1.5
Use the structure of an expression to identify ways to rewrite it.

Vocabulary

Terms
Linear expressions
Equivalent expressions
Difference of two squares
Factor
Difference of squares

Knowledge

Students know:

Algebraic properties.
When one form of an algebraic expression is more useful than an equivalent form of that same expression.

Skills

Students are able to:

Use algebraic properties to produce equivalent forms of the same expression by recognizing underlying mathematical structures.

Understanding

Students understand that:

Generating equivalent algebraic expressions facilitates the investigation of more complex algebraic expressions.

Mathematics (2019) Grade(s): 09-12 - Algebra I with Probability

MA19.A1.24
Distinguish between situations that can be modeled with linear functions and those that can be modeled with exponential functions.

Vocabulary

Linear functions
Exponential functions
Constant rate of change
Constant percent rate of change
Intervals
Percentage of growth
Percentage of decay

Knowledge

Students know:

Key components of linear and exponential functions.
Properties of operations and equality

Skills

Students are able to:

Accurately determine relationships of data from a contextual situation to determine if the situation is one in which one quantity changes at a constant rate per unit interval relative to another (linear).
Accurately determine relationships of data from a contextual situation to determine if the situation is one in which one quantity grows or decays by a constant percent rate per unit interval relative to another (exponential).

Understanding

Students understand that:

Linear functions have a constant value added per unit interval, and exponential functions have a constant value multiplied per unit interval.
Distinguishing key features of and categorizing functions facilitates mathematical modeling and aids in problem resolution.

CR Resource Type

Audio/Video

Resource Provider

PBS

License Type

CUSTOM

https://aptv.pbslearningmedia.org/resource/im20-math-ep7-68/equivalent-quadrati…

Custom License Type (URL)

https://creativecommons.org/licenses

Comments or Notes

This resource has student task statements and practice problem worksheets.

Approved Date

2022-09-13

Design by Adaptive Theme