Getting Started 
Misconception/Error The student is unable to correctly identify the Lintercept. 
Examples of Student Work at this Level The student:
 Says that the Lintercept is 0.89, 0.89, or about 90 (using the coefficient of A in the model).
 Describes the variable associated with the Lintercept but not its value.
 Identifies the Acoordinate of the leftmost point.
 Uses the graph to identify the Lintercept but does so incorrectly.
 Identifies the Lcoordinates of each of the data points.

Questions Eliciting Thinking How did you determine the Lintercept?
On which axis will you find the Lintercept?
What do you know about equations written in the form y = mx + b or y = b + mx? What is m? What is b? 
Instructional Implications Review the concepts of linear model, rate of change or slope, and constant term or yintercept. Remind the student that the yintercept is given by the constant term in the linear model and also corresponds to the point where the graph intersects the yaxis. Provide examples of linear models and ask the student to identify both the slope and the yintercept of the graph of the model from the equation.
Guide the student to carefully consider the context of the linear model given in this task, the specific variables that the model relates, and their units of measure. Then guide the student to explain the meaning of the Lintercept in the context of the data. Have the student use the model to identify the Lintercept and write it as an ordered pair including the units of measure (e.g., current age of zero years, life expectancy of 77 years). Guide the student to interpret the Lintercept by saying, â€śThe life expectancy for a newborn female is 77 years old.â€ť
Provide additional examples of linear functions that have been fitted to data. Ask the student to identify the coordinates of the yintercept along with their units of measure. Encourage the student to describe the coordinates of the yintercept by associating the two values in a statement that explicitly includes what they represent along with their units of measure. Then remind the student to review the context of the data and to interpret the constant term in context. 
Moving Forward 
Misconception/Error The student is unable to clearly interpret the Lintercept in the context of the model. 
Examples of Student Work at this Level The student identifies the Lintercept as 77 but is unable to correctly interpret this value in the context of the problem. For example, the student:
 Provides an incorrect interpretation (e.g., says the life expectancy of a 77 year old woman is 0 years).
 Describes where to find the Lintercept on the graph or in the model.
 Makes an observation about the model (e.g., the older a women, the shorter her life expectancy) rather than interpret the Lintercept.

Questions Eliciting Thinking How did you find the Lintercept?
What is the value of A when L = 77?
What do A and L represent in this model? 
Instructional Implications Guide the student to carefully consider the context of the linear model given in this task, the specific variables that the model relates, and their units of measure. Then guide the student to explain the meaning of the Lintercept in the context of the data. Have the student use the model to identify the Lintercept and write it as an ordered pair including the units of measure (e.g., current age of zero years, life expectancy of 77 years). Guide the student to interpret the Lintercept by saying, â€śThe life expectancy for a newborn female is 77 years.â€ť
Provide additional examples of linear functions that have been fitted to data. Ask the student to identify the coordinates of the yintercept along with their units of measure. Encourage the student to describe the coordinates of the yintercept by associating the two values in a statement that explicitly includes what they represent along with their units of measure. Then remind the student to review the context of the data and to interpret the constant term in context. 
Almost There 
Misconception/Error The student is unable to identify the issue related to an interpretation of the Lintercept of this model. 
Examples of Student Work at this Level The student correctly identifies and interprets the Lintercept but does not recognize that A = 0 is well outside the range of ages in the data and in the model. The student provides no response or an incorrect response.
Note: The student may neglect to make explicit that the model applies only to females but upon questioning immediately revises his or her interpretation.

Questions Eliciting Thinking Does your result apply to both males and females?
Is the life expectancy you indicated at birth based on actual data?
Does the line of best fit extend to A = 0? 
Instructional Implications Explain the distinction between interpolation and extrapolation in the context of a linear model. Remind the student that the linear model is based on data collected on 20 to 70 year old females. Consequently, it is not clear to what extent the predictions made by the model apply to other populations. Challenge the student to identify other populations to whom the model may not apply or have predictive value (e.g., males of any age, females under the age of 20 or over the age of 70, or females of any age from previous centuries).
Provide additional opportunities for the student to consider whether it is appropriate to extrapolate from the data upon which a linear model is based. 
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 identifies and interprets the Lintercept by saying the Lintercept is 77 years which would mean that the life expectancy for a newborn female is 77 years old. However, the graph (or model) only applies to females age 20 to 70, so extrapolation to age zero might not be justified.

Questions Eliciting Thinking According to this model, what is the life expectancy of a 20 year old female? How many years in total is the average 20 year old female expected to live?
Why might the fit not be valid at some ages younger than 20 years old? Older than 70 years?
How do you think the graph would differ if one used data from 100 years ago? 
Instructional Implications Ask the student to determine and interpret the value of the Aintercept.
Ask the student to determine the life expectancy and the total number of years both a 20 year old and a 70 year old female are expected to live. Then challenge the student to use the model to write an equation that indicates the total number of years that a female is expected to live given her current age. 