Getting Started 
Misconception/Error The student is unable to describe the relationship between the two variables given a scatterplot and line of best fit. 
Examples of Student Work at this Level The student:
 Attempts a general description of the graph.
 Attempts to interpret the slope of the line of best fit.
 Describes the location of a cluster of points on the graph.

Questions Eliciting Thinking What two variables are related by this graph?
What does the line of best fit indicate about their relationship?
Does the equation that models the data tell you anything about the relationship between foot length and height? 
Instructional Implications Review as needed:
 Independent and dependent variables and how functions that describe the relationship between them are represented by equations, tables, graphs, and verbal descriptions.
 The concept of a linear function and its graph.
 The slopeintercept form of a linear equation, y = mx + b.
 Solutions of equations in twovariables as ordered pairs of numbers.
Explain that the line of best fit models the relationship between the two variables, height and foot length. A line is used since the data points form a generally linear pattern. The line is placed so that it is as close to as many points as possible (e.g., the sum of the squares of the vertical distances between the points and the line is minimized). It is not expected that every point will fall on the line. Guide the student to observe that the line is increasing which indicates that as height is increasing, foot length is also increasing. Since the relationship is modeled by a line, this increase occurs at a constant rate.
Provide other graphs in context and ask the student to describe the relationship between the variables represented by the graph. 
Making Progress 
Misconception/Error The student is unable to explain the meaning of the slope or yintercept. 
Examples of Student Work at this Level The student can identify the relationship between foot length and height (e.g., by saying that the taller the student, the greater his foot length) but cannot explain the meaning of the slope or yintercept in the context of the data. The student may identify the slope and the yintercept from the equation but cannot interpret their meanings in the context of the linear model.

Questions Eliciting Thinking What is the slope? What are the units of the slope? What does this slope tell you about the relationship between height and foot length?
What is the yintercept? If you graphed it, where would it be located? Can you explain the meaning of its coordinates? 
Instructional Implications Review the concepts of linear function, slope, and yintercept. Focus on the slopeintercept form of the equation of a linear function. Review how to identify the slope graphically and from an equation written in slopeintercept form. Describe slope as a quality of a line but also describe it as a unit rate. Guide the student to explain the meaning of slope as an amount of change in the dependent variable (e.g., foot length) associated with a oneunit change in the independent variable (e.g., height). Have the student initially describe the slope as a unit rate including the units of measure (e.g., as 1.52 mm/1 cm). Then guide the student to interpret the slope in terms of the independent and dependent variables. Model explaining, “For every one cm increase in height, foot length increases 1.52 mm.”
Review the concept of a yintercept. Discuss how it is represented on a graph (as a point on the yaxis) and in an equation written in slopeintercept form. Explain that the yintercept is the yvalue (foot length) that corresponds to an xvalue (height) of zero. Have the student write the yintercept as an ordered pair including units of measure, as (0 cm of height, 4.35 mm of foot length). Guide the student to first interpret the yintercept as an associated pair of values (e.g., A male student who is 0 cm in height has a foot length of 4.35 mm). Then have the student consider whether this statement makes sense in the context of the model. Use this as an opportunity to discuss what constitutes a reasonable domain for this model, considering both the lower limit and upper limit on height.
Provide additional opportunities for the student to identify and interpret the slope and yintercept in linear models. 
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 writes:
 As height increases, foot length also increases.
 The slope of 1.5 means that foot length increases 1.5 mm for every one cm increase in height.
 The yintercept of 4.3 indicates that a male student who is zero cm in height has a foot length of 4.3 mm. This does not make sense since foot length cannot be negative.

Questions Eliciting Thinking Can you describe the increase in foot length in more detail? Is the rate of change constant?
What do you think the domain of this function is?
Would there be any change in the graph if both variables were in cm? Or in mm? 
Instructional Implications Ask the student to use the linear model to predict the foot length of a male student whose height is 130 cm and the height of a student whose foot length is 250 mm.
Consider implementing MFAS task Tuition (8.SP.1.3) to use the equation of a linear model to solve problems. 