Maryland Math 6.AT.D.11

6.AT.D.11 is a cluster heading. These are the individual standards under it.

• 6.AT.D.11.a

  Write an equation (one-step) to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variab...

• 6.AT.D.11.b

  Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation (e.g., in a problem involving...

01

What Students Need to Do

Students choose a letter for each changing quantity and decide which one depends on the other. They write a one-step equation, make a table of pairs, and graph the pairs on labeled axes.

02

What Mastery Looks Like

Given tickets that cost $3 each, a student writes c = 3t, with t for tickets and c for total cost. They make matching table values and plot (0, 0), (1, 3), and (2, 6). They put tickets on the horizontal axis.

03

Common Misconceptions

Students may write t = 3c even though cost depends on the number of tickets. They may reverse the ordered pairs or leave the axes unlabeled. Some write c = t + 3 instead of c = 3t.

04

How to Assess It

Exit ticket: A printer makes 5 pages per minute, with m for minutes and p for pages. Name the dependent quantity, write an equation, complete a table for 0, 1, and 3 minutes, and plot those pairs on labeled axes.

1. 01

   Put three counters in each cup, then record cup and counter counts in a table, graph the pairs, and write an equation.

2. 02

   Ask students to explain why time goes on the horizontal axis for a bike traveling 6 miles each hour.

3. 03

   Give pairs cards with tables, graphs, and equations for 3 or 5 stickers per sheet, and have them sort matching sets.

4. 04

   Use a posted $2 per bus ride fare to graph total cost for zero to five rides and write C = 2r.

• 7.AT.C.9

  Use variables to represent quantities and write and solve inequalities to model and reason about constraints and conditions in context.

• 7.AT.C.8

  Use variables to represent quantities and write and solve equations to model and reason about relationships in context.

• 8.AT.D.10

  Construct and interpret a linear function to model a relationship between two quantities.

• 6.AT.C.8.a

  Explain that a variable can represent an unknown number and use substitution to determine whether a given number makes an equation true.