21 6.EE.C.9 6.EE.C.9 Math.6.EE.9 6.EE.C.9 6.EE.9 6.EE.9 6.EE.9 6.EE.C.9 6.EE.C.9 CC.2.2.6.B.3 M06.B-E.3.1.1 M06.B-E.3.1.2

Represent Relationships [2 variables] 6th Grade

Alabama Course of Study Standards: 21
Identify, represent, and analyze two quantities that change in relationship to one another in real-world or mathematical situations. Use tables, graphs, and equations to represent the relationship between independent and dependent variables.
Arkansas Academic Standards: 6.EE.C.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another: Write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation For example: In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Note: The independent variable is the variable that can be changed; the dependent variable is the variable that is affected by the change in the independent variable.
Arizona - K-12 Academic Standards: 6.EE.C.9
Use variables to represent two quantities that change in relationship to one another to solve mathematical problems and problems in real-world context. Write an equation to express one quantity (the dependent variable) in terms of the other quantity (the independent variable). Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
Common Core State Standards: Math.6.EE.9 or 6.EE.C.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
Mississippi College- and Career-Readiness Standards: 6.EE.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another. Write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
North Carolina - Standard Course of Study: 6.EE.9
Represent and analyze quantitative relationships by: Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs).
New York State Next Generation Learning Standards: 6.EE.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another. e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times. Given a verbal context and an equation, identify the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. e.g., Given the equation d = 65t to represent the relationship between distance and time, identify t as the independent variable and d as the dependent variable.
Tennessee Academic Standards: 6.EE.C.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another. For example, Susan is putting money in her savings account by depositing a set amount each week (50). Represent her savings account balance with respect to the number of weekly deposits (s = 50w, illustrating the relationship between balance amount s and number of weeks w). Write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
Wisconsin Academic Standards: 6.EE.C.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
Pennsylvania Core Standards: CC.2.2.6.B.3
Represent and analyze quantitative relationships between dependent and independent variables.
Pennsylvania Core Standards: M06.B-E.3.1.1
Write an equation to express the relationship between the dependent and independent variables
Pennsylvania Core Standards: M06.B-E.3.1.2
Analyze the relationship between the dependent and independent variables using graphs and tables and/or relate these to an equation

If a relationship exists between two values, say x and y, such that one value, say y, is dependent on the other value, x, then x is referred to as the independent variable, and y is referred to as the dependent variable.

Consider a known relationship, such as the relationship between inches and feet.
There are 12 inches in 1 foot.
What if we want to know the number of inches in a given number of feet?
Then, the number of inches is dependent on the number of feet.
This relationship could be represented by the equation 12x = y, where x is the number of feet, and y is the number of inches.
In this situation, x is the independent variable and y is the dependent variable.

What if we want to know the number of feet in a given number of inches?
Then, the number of feet is dependent on the number of inches.
This relationship could be represented by the equation

\frac{1}{12}

x = y, where x is the number of inches and y is the number of feet.
In this situation, x is the independent variable and y is the dependent variable.

Note that while you will often see the letters x and y used for the independent and dependent variables, respectively, it is the mathematical language and/or situation which dictates independent and dependent - not the letter used for the variable.

Mathematical relationships are often represented by equations, tables, and/or graphs.

Represent Relationships [2 variables]

Alabama Course of Study Standards: 21

Identify, represent, and analyze two quantities that change in relationship to one another in real-world or mathematical situations.
Use tables, graphs, and equations to represent the relationship between independent and dependent variables.

Arkansas Academic Standards: 6.EE.C.9

Arizona - K-12 Academic Standards: 6.EE.C.9

Common Core State Standards: Math.6.EE.9 or 6.EE.C.9

Mississippi College- and Career-Readiness Standards: 6.EE.9

North Carolina - Standard Course of Study: 6.EE.9

Represent and analyze quantitative relationships by:
Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another.
Analyze the relationship between quantities in different representations (context, equations, tables, and graphs).

New York State Next Generation Learning Standards: 6.EE.9

Tennessee Academic Standards: 6.EE.C.9

Wisconsin Academic Standards: 6.EE.C.9

Pennsylvania Core Standards: CC.2.2.6.B.3

Represent and analyze quantitative relationships between dependent and independent variables.

Pennsylvania Core Standards: M06.B-E.3.1.1

Write an equation to express the relationship between the dependent and independent variables

Pennsylvania Core Standards: M06.B-E.3.1.2

Analyze the relationship between the dependent and independent variables using graphs and tables and/or relate these to an equation

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