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Multi-Step Problems in the Real World


Videos to help Grade 6 students learn how to analyze an equation in two variables, choose an independent variable and a dependent variable, make a table and make a graph for the equation.

New York State Common Core Math Module 4, Grade 6, Lesson 32

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Lesson Plans and Worksheets for Grade 6

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Common Core For Grade 6

Lesson 32 Student Outcomes

Students analyze an equation in two variables, choose an independent variable and a dependent variable, make a table and make a graph for the equation by plotting the points in the table. For the graph, the independent variable is usually represented by the horizontal axis and the dependent variable is usually represented by the vertical axis.

Opening Exercise

Xin is buying beverages for a party which are individually packaged and come in packs of 8. Let p be the number of packages Xin buys and t be the total number of beverages. The equation t = 8p can be used to calculate the total number of beverages when the number of packages is known. Determine the independent and dependent variable in this scenario. Then make a table using whole number values of p less than 6.

Example 1

Make a graph for the table in the Opening Exercise.

Example 2

Use the graph to determine which variable is the independent variable and which is the dependent variable. Then state the relationship between the quantities represented by the variables.


1. Each week Quentin earns $30. If he saves this money, create a graph that shows the total amount of money Quentin has saved from week 1 through week 8. Write an equation that represents the relationship between the number of weeks that Quentin has saved his money (w) and the total amount of money he has saved (s). Then name the independent and dependent variable. Write a sentence that shows this relationship.


2. Zoe is collecting books to donate. She started with 3 and collects two more each week. She is using the equation b = 2w + 3, where b is the total number of books collected and w is the number of weeks she has been collecting. Name the independent and dependent variables. Then create a graph to represent how many books Zoe has collected when w is 5 or less.

3. Eliana plans to visit the fair. She must pay $5 to enter the fair grounds and an additional $3 rrper ride. Write an equation to show the relationship between r, the number of rides, and t, the total cost. State which variable is dependent and which is independent. Then create a graph that models the equation.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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