Getting Started 
Misconception/Error The student is unable to use the equation to make a table of values and/or graph. 
Examples of Student Work at this Level The student makes an incorrect table/graph.Â Consequently, the student is unable to correctly describe the relationship between the independent and dependent variables.
Â Â Â
Â Â Â

Questions Eliciting Thinking How did you calculate the values for T in the chart? Did you use the equation?
What does the variable T represent? What does the variable w represent? 
Instructional Implications Show the student that the equation TÂ = 5wÂ + 10 can be used to calculate values of T for chosen values of w. Guide the student to select reasonable values of w such as 0, 1, 2, 3, and 4 and make explicit that these values represent numbers of weeks. Then ask the student to evaluate the expression 5w + 10 for each given value of w. Model calculating a value of T and remind the student to apply the order of operations rules when evaluating expressions. Ask the student to calculate the remaining values of T. Guide the student to relate each value of T to its associated value of w. Model explaining the meaning of a coordinate pair [e.g., (3, 25) means that after three weeks, Latasha has saved $25]. Point out that the value of T depends on the value of w. Review the terms dependent and independent if needed. Clarify that because both are variables, they both can change. Change in the dependent variable depends on the change in the independent variable. It may be helpful to use the terms input and output.
Consider implementing the CPALMS Lesson Plan From Tables to Graphs and Back! (ID 31597), which addresses multiple representations of the relationship between dependent and independent variables. 
Moving Forward 
Misconception/Error The student is unable to describe how the dependent and independent variables change in relation to one another. 
Examples of Student Work at this Level The student makes a correct table and a correct graph (with only minor exceptions) but does not clearly explain how the dependent variable changes in relation to the independent variable.
Â Â Â
Â Â Â

Questions Eliciting Thinking Can you be more specific? What gets bigger each week and by how much?
Every time the number of weeks increases by one, by how much does the total savings increase?
What does your table show about the weekly changes in T? 
Instructional Implications Provide the student with some completed tables of values and guide him or her to recognize trends or patterns. Have the student determine whether the value of the dependent variable increases or decreases as the value of the independent variable increases. Then encourage the student to analyze the relationship more closely and describe the actual amount of change by referring to numerical values and operations. Consider implementing the CPALMS Unit FunctionsDay Trips (National Security Agency) (ID 4008) which is a three lesson unit that explores using patterns to analyze tables. 
Almost There 
Misconception/Error The student does not clearly explain how the relationship between the independent and dependent variables is shown in the equation. 
Examples of Student Work at this Level The student does not explain how the relationship is shown in the equation.
Â Â Â

Questions Eliciting Thinking You said that the total amount saved increases by five each week. How is this increase shown in the equation? What part of the equation increases the savings by five with each successive week?
Can you identify the dependent and independent variables in the equation? Can you identify the coefficient and constant in the equation? How does each part of the equation show the relationship between the total amount saved and the number of weeks?
What is happening to the independent variable that causes the dependent variable to change? Can you locate that in the equation? 
Instructional Implications Explain to the student how the equation T = 5wÂ + 10 shows the relationship between the dependent and independent variables. Point out that the value of the dependent variable, T, depends on the value of the independent variable, w. Explain how 5w represents five dollars for every week Latasha saves. Use associated vocabulary such as coefficient, factor, term, variable, and constant. Explain that the constant represents the initial ten dollars Latasha had in her account before putting in five dollars each week. Clarify that Latashaâ€™s account balance increases by five dollars for every week, but the initial ten dollars must be added to determine the total savings up to that point in time. Make explicit that the ten dollars is added only once to determine the total. Point out that the ten dollars is not added for each week because the ten is a constant not a factor or coefficient.
Consider implementing the CPALMS Lesson Plan The Speeding Ticket (Part 1: Solving Linear Equations with One Variable) (ID 48701) and The Speeding Ticket (Part 2: Graphing Linear Functions) (ID 48695) which addresses dependent and independent variables and makes connections between linear equations and their graphs. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student:
 Completes the table and graph correctly.Â
 Explains that the total amount saved increases five dollars every week.Â
 Can point out the parts of the equation that show the relationship between the total amount saved and the number of weeks. For example, the student says the term 5w represents five dollars times the number of weeks; the constant â€ś10â€ť represents the initial ten dollars she started with; and by adding those two terms together, 5w and 10, the result is T, the total amount saved.Â

Questions Eliciting Thinking Is the relationship between the dependent and independent variables proportional?
Is the graph linear?
What is the value of T when w is zero? What does this ordered pair tell you about the problem?
Can you interpret the ordered pair (5, 35) in the context of this problem? What do the coordinates mean? 
Instructional Implications Challenge the student to write an equation that shows a proportional relationship between the dependent and independent variables, and then describe a realworld problem which can be represented by the equation.
Consider using the MFAS task Table to Equation (6.EE.3.9), which assesses the studentâ€™s ability to write equations that represent the relationship between dependent and independent variables. 