6.EE.9: Understanding and Applying Dependent and Independent Variables in Real-World Problems

Grade: 6th Grade

Domain: EE: Expressions and Equations

Standard 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.

Domain Description

Writing and evaluating numerical expressions involving whole-number exponents, as well as writing expressions with numbers and letters as placeholders is essential. It's also important to identify parts of an expression using mathematical terms, such as sum, term, product, factor, quotient, and coefficient. Evaluating expressions with specific values for their variables is also a key process, and can include situations from real-world problems. Other skills include understanding and applying the properties of operations to generate identical expressions and identifying when two expressions are the same.

Understanding how to solve an equation or inequality is crucial, involving a process of identifying which values make the equation or inequality valid. Variables can be used to represent numbers, formulating expressions to solve real-world or mathematical problems. Inequalities can be written to represent real-world constraints or conditions, along with understanding that these inequalities can have infinite solutions.

The use of variables to represent quantities in real-world problems that change in relation to one another is also vital. Equations can be written expressing one variable in terms of another, and relationships between the variables can be analyzed using graphs and tables. This process can be tied back to real-world scenarios, such as motion at a constant speed.