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

Common Core Standards Represent Relationships [2 variables]
Grade:	6th Grade
Standard:	CC.2.2.6.B.3
Description:	Represent and analyze quantitative relationships between dependent and independent variables.
Standard:	M06.B-E.3.1.1
Description:	Write an equation to express the relationship between the dependent and independent variables
Standard:	M06.B-E.3.1.2
Description:	Analyze the relationship between the dependent and independent variables using graphs and tables and/or relate these to an equation
Standard:	Math.6.EE.9 or 6.EE.C.9
Description:	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.

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.

Common Core Standards

Represent Relationships [2 variables]

CC.2.2.6.B.3

Represent and analyze quantitative relationships between dependent and independent variables.

M06.B-E.3.1.1

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

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

Math.6.EE.9 or 6.EE.C.9

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