• 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.
  

  Expressions and Equations

  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.

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• 6.RP.A.3.A — Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
  

  Ratios and Proportional Relationships

  6.RP.A.3.A — Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

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• 5.OA.B.3
  

  Operations and Algebraic Thinking

  5.OA.B.3 — Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

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• 6.NS.C.6.C
  

  The Number System

  6.NS.C.6.C — Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

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Jordan is 2 years older than her sister Nora. Let $$j$$ represent Jordan’s age and $$n$$ represent Nora’s age. 

1. Write an equation to represent the relationship between the ages of the two sisters.
2. Create a table of values using your equation.
3. Plot the points in the coordinate plane.

The table below shows the output values for different input values. 

Which equation represents the relationship between the inputs and outputs?

1.   $${x+5=y}$$
2.   $${x+9=y}$$
3.   $${4x+3=y}$$
4.   $${5x+1=y}$$

Zoe is collecting books to donate. She started with 3 books and collects 2 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 books.

1. Name the independent and dependent variables. 
2. Create a table of values and then use it to graph Zoe’s book collection. 

Mara and Evan work at the same company. Mara started working at the company 5 years before Evan started. Let $$m$$ represent the number of years Mara has worked at the company and $$e$$ represent the number of years Evan has worked at the company. 

1. Write an equation to represent the relationship.
2. Create a table of values using your equation.
3. Plot the points in the coordinate plane.