School Improvement in Maryland
Public Release Item Scoring Information Return

Goal 3 Data Analysis And Probability

Expectation 3.2 The student will apply the basic concepts of statistics and probability to predict possible outcomes of real-world situations.

Indicator 3.2.3 The student will communicate the use and misuse of statistics.

Assessment Limits:

  • Examples of “misuse of statistics” include the following:
    • misuse of scaling on a graph
    • misuse of measures of central tendency and variability to represent data,
    • using three-dimensional figures inappropriately
    • using data to sway interpretation to a predetermined conclusion
    • using incorrect sampling techniques
    • using data from simulations incorrectly
    • predicting well beyond the data set.

Extended Constructed Response (ECR) Item - Released in 2007

The table below shows the age and the value of a computer.

Complete the following in the Answer Book:

  • Write an equation for a line of best fit. (If you choose to draw a graph to help you write the equation, use the grid provided in the Answer Book.)
  • What is the slope of your equation? What does the slope represent in the context of this problem?
  • What is the age of the computer when its value is $300? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
  • Will your equation remain a good model to predict the value of a computer when it is 6 years old? Use mathematics to justify your answer.

The following 4 Sample Student Responses represent a range of score points.

Sample Student Response #1

image of student response

Score for Sample Student Response #1: Rubric Score 3

Annotation: This response demonstrates application of a reasonable strategy that leads to some correct solutions within the context of the problem. The representation in the form of an equation is correct (y= -201x+809). A slope is not given but the contextual meaning is complete (the slope is how much the value decreases by yearly). The age of a computer valued at $300 is correct (2.5 years old). The explanation supports the solution (I got this by solving the equation for x when y was 300). The student states that the equation would not be a good prediction model and the justification supports the solution (A computer can be worth negative dollars). This response demonstrates a clear understanding and analysis of the problem.


Sample Student Response #2

image of student response

Score for Sample Student Response #2: Rubric Score 2

Annotation: This response demonstrates an incomplete application of a reasonable strategy. An equation is not provided. The slope is correct (-210) and the contextual meaning is complete (the value will go down about $210.00 each year). The age of a computer valued at $300 is correct (around 2½ years old) and the explanation supports the solution (when its 2 years old, it costs $410 and when its 3 years old it costs $200 and $300 is right about in the middle of them). The student states that the equation would not be a good prediction model and the justification supports the solution (it would be a negative number according to the equation). This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.)


Sample Student Response #3

image of student response

Score for Sample Student Response #3: Rubric Score 4

Annotation: This response demonstrates application of a reasonable strategy that leads to correct solutions within the context of the problem. The representation in the form of an equation is correct (y= -201x+809). The slope of the equation is correct (-201) and the contextual meaning is complete (which represents the amount of money that the value of the computer decreases each year). The age of a computer valued at $300 is correct (2.5 years old) and the explanation is fully developed (To determine the value I input $300 for y and solved for x which gave me 2.532338308≈2.5 years). The student states that the equation would not be a good prediction model and the justification is fully developed (the value of the computer will be a negative number). This response demonstrates a complete understanding and analysis of the problem.


Sample Student Response #4

image of student response

Score for Sample Student Response #4: Rubric Score 1

Annotation: This response demonstrates little application of a reasonable strategy. The representation in the form of an equation is correct (y= -201x+809). The student has not responded to the second, third or fourth parts of the question. This response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.)


Additional Resources

Anchor Papers used in scoring

Extended Constructed Response (ECR) Rubric
Print: Scoring Rubric (pdf)
Score 4

The response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The representations are correct. The explanation and/or justification is logically sound, clearly presented, fully developed, supports the solution, and does not contain significant mathematical errors. The response demonstrates a complete understanding and analysis of the problem.

Score 3

The response indicates application of a reasonable strategy that may or may not lead to a correct solution. The representations are essentially correct. The explanation and/or justification is generally well developed, feasible, and supports the solution. The response demonstrates a clear understanding and analysis of the problem.

Score 2

The response indicates an incomplete application of a reasonable strategy that may or may not lead to a correct solution. The representations are fundamentally correct. The explanation and/or justification supports the solution and is plausible, although it may not be well developed or complete. The response demonstrates a conceptual understanding and analysis of the problem.

Score 1

The response indicates little or no application of a reasonable strategy. It may or may not have the correct answer. The representations are incomplete or missing. The explanation and/or justification reveals serious flaws in reasoning. The explanation and/or justification may be incomplete or missing. The response demonstrates a minimal understanding and analysis of the problem.

Score 0

The response is completely incorrect or irrelevant. There may be no response, or the response may state, “I don't know.”

Explanation refers to the student using the language of mathematics to communicate how the student arrived at the solution.

Justification refers to the student using mathematical principles to support the reasoning used to solve the problem or to demonstrate that the solution is correct. This could include the appropriate definitions, postulates and theorems.

Essentially correct representations may contain a few minor errors such as missing labels, reversed axes, or scales that are not uniform.

Fundamentally correct representations may contain several minor errors such as missing labels, reversed axes, or scales that are not uniform.

Last Revised 8/16/00
/share/clg/xml/public_release/mathematics/2007_323_alg12.xml
Resources for 3.2.3:
Skill Statements | PUBLIC RELEASE ITEMS |