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7-A-3-1

Page history last edited by Christine Koerner 1 year, 10 months ago

7.A.3.1 Write and solve problems leading to linear equations with one variable in the form px+q=r and p(x+q)=r, where p,q, and r are rational numbers.

In a Nutshell

Write equations based where the constant of proportionality is a rational number. Identify the constant rational number in the situation. Isolate a single variable to solve the written equation for that variable. The distributive property should be utilized to identify equivalent equations.

Student Actions	Teacher Actions
Develop a deep and flexible conceptual understanding of linear equations with one variable, by selecting which forms of single variable equation represents a given real-world situation. Develop accurate and appropriate procedural fluency by manipulating expressions, using arithmetic and algebraic properties, given in various forms that lead to linear equations with one variable. Develop mathematical reasoning of equivalent equations utilizing the distributive property. Develop an accurate and appropriate procedural fluency of solving equations with one variable.	Use and connect mathematical representations of linear equations and how they relate to real-world situations. Implement tasks that allow students to represent and solve real-world situations mathematically using linear equations. Pose purposeful questions about equivalent equations and other representations of a given real-world situation.
Key Understandings	Misconceptions
Operations on an equation must be done in the correct order. Write equations by identifying the proportional rate of change as well as a constant value from a real-world situation. To solve an equation, a single variable should be isolated. Students should understand how to use the distributive property to identify equivalent equations. Ability to work with variables in a variety of contexts and formats of the initial equation.	Student may divide a factor from one side of an equation without dividing each term by the factor. Students may solve 2 step equations in the wrong order (i.e. 3x + 6 = 12, students will try to divide both sides by 3 first instead of subtracting both sides by 6). Students may forget to distribute first if the equation requires distributing (i.e. 3(x + 2) = 8). Students may only distribute to one term inside the parentheses. Students may see problems rigidly and not seek to understand the relationships among the numbers and variables before attempting to isolate the variable. Often, this leads to students approaching a problem in a less familiar structure (i.e., q+px=r) without considering how the structure might impact their approach.

Depth of Knowledge Level 1 Example

Solve: 2x-2=8

Credit: OSDE Regional Math Workshop, February 2019 and openmiddle.com

Depth of Knowledge Level 2 Example

Jeffrey solved the equation 2x-2 = 8 by using the steps below. Were his steps correct? If so, explain how you know his work is correct. If his steps were not correct, explain what he did incorrectly and what he should have done instead:

Jeffrey's work:

2x - 2 = 8

/2 /2

x - 2 = 4

+2 +2

x = 6

Depth of Knowledge Level 3 Example

Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to find the largest (or smallest) possible values for the sum of x and y.