Getting Started 
Misconception/Error The student is unable to correctly determine the numbers of bricks remaining from either the graph or the verbal description of the functions. 
Examples of Student Work at this Level The student attempts to determine the number of bricks each person has after 20 minutes but is unable to do so correctly.
Rather than determining the number of bricks each person has after 20 minutes, the student makes a decision based on:
 The rates of change of the two functions and/or the scale used in the graph.
 The initial values of the two functions.

Questions Eliciting Thinking Can you explain what the graph shows? Can you use the graph to determine how many bricks Francis will have after 20 minutes?
Can you determine how many bricks Frank will have after 20 minutes? 
Instructional Implications Review linear functions and the various ways that they can be described (with equations, tables, graphs, and verbal descriptions). Focus on the rate of change and initial value in a linear function, and relate these components of the equation to the slope and yintercept of the graph. Review how to calculate a value of one variable given a value of the other. Provide additional examples of linear functions that model the relationship between realworld quantities and ask the student to identify and compare properties of functions represented in different ways. 
Making Progress 
Misconception/Error The student is able to correctly determine the number of remaining bricks from the graph but not from the verbal description. 
Examples of Student Work at this Level The student determines that Francis will have 320 bricks left after 20 minutes by identifying the appropriate point (20, 320) on the graph. But, to determine the number of bricks that Frank will have left, the student:
 Multiplies 15 by 20 to get 300 (the number of blocks Frank places in 20 minutes).
 Divides 630 by 15.
The student determines that Frank will have 330 bricks left after 20 minutes but is unable to use the graph to correctly determine the number of bricks that Francis will have left.

Questions Eliciting Thinking How many bricks did Frank start with?
What did you actually calculate? Will that tell you how many bricks Frank has left?
Can you explain what the graph shows? How did you use the graph to determine the number of bricks that Francis will have left after 20 minutes? 
Instructional Implications Review the important properties of linear functions (e.g., rate of change and initial value) and how to identify and interpret them. Provide sample graphs, tables, equations, and verbal descriptions of functions, and ask the student to identify the xintercept, yintercept, rate of change, an xvalue when a yvalue is given, and a yvalue when an xvalue is given. Ask the student to describe in general terms the significance of each of these properties of a function (e.g., slope is the increase in a yvalue when an xvalue increases by one, yintercept is the yvalue when the xvalue is zero).
Provide the student with a linear function represented by a verbal description. Have the student represent the same function with an equation and a graph. Help the student to identify the rate of change and the initial value in the equation and graph. Then provide the student with two different functions (e.g., one represented by an equation and the other represented by a graph). Challenge the student to find and compare values of y (given values of x), the rates of change, and the initial values. 
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 correctly determines the number of bricks that each will have left after 20 minutes. For example, the student determines that Francis will have 320 bricks left after 20 minutes by identifying and interpreting the appropriate point, (20, 320), on the graph. To determine the number of bricks that Frank will have left, the student subtracts the product of 15 and 20 from 630 getting 330.
The student concludes that Francis will have fewer bricks left after 20 minutes. 
Questions Eliciting Thinking What would Frank’s graph look like compared to Francis’s graph?
How many more bricks will Frank have left after 20 minutes? 
Instructional Implications Have the student write an equation that represents the number of bricks that Frank has left over time. Then have the student graph the equation on the same set of axes as Francis’s graph. Challenge the student to determine the significance of the point of intersection of the two graphs and explain it in the context of the problem. 