A Progression Toward Mastery Assessment Task Item STEP 1 Missing or incorrect answer and little evidence of reasoning or application of mathematics to solve the problem STEP 2 Missing or incorrect answer but evidence of some reasoning or application of mathematics to solve the problem STEP 3 A correct answer with some evidence of reasoning or application of mathematics to solve the problem, or an incorrect answer with substantial evidence of solid reasoning or application of mathematics to solve the problem STEP 4 A correct answer supported by substantial evidence of solid reasoning or application of mathematics to solve the problem 1 a S-ID.A.2 Student to address the tendency for lower scores. Student picks Quiz 2 because of the low outlier at points, rather than focusing on the overall distribution. Student chooses Quiz 3 but does not give a full explanation for the choice. Student uses an appropriate measure of center (e.g., mean or median) to explain the choice of Quiz 3. b S-ID.A.3 Student fails to address the idea of spread, variability, or clustering. Student Quiz 1 because the heights of the stacks are most irregular. Student picks Quiz 3 but does not give a full explanation for the choice. OR Student chooses Quiz 3 and uses an appropriate justification such as stating that the data ranges from to .
Student picks Quiz 2 based on one score (the low outlier), as opposed to the overall tendency. c S-ID.A.2 Student does not make a choice between SD and IQR. Student does not justify choice based on shape of distribution or on presence of outlier. Student considers the distribution symmetric and chooses the standard deviation. Student chooses the IQR in an attempt to reduce the impact of the one extreme observation. d S-ID.A.2 Student does not clearly explain how dot will be moved. Student adds a dot near the center of the distribution (e.g., –). OR Student moves a dot toward the center of the distribution. Student’s dot is moved to change the heights of the stacks of the dots. Student’s dot is moved to be further from the mean of the distribution (without much change in the mean of the distribution). e S-ID.A.2 Student’s placement of dots does not appear to focus on spreading the values as far apart as possible. Student focuses on having as many different values as possible or focuses on having as much change in the heights to the stacks as possible. Student spreads the dots out as far as possible without using repeat values (with justification) or does not split the dots into two equal pieces at the two extremes. Student places half the dots at zero and half the dots at ten. f S-ID.A.2 Student selects measure of spread with a weaker explanation. Student selects measure of spread because of the use of the max and min values. Student selects measure of center but does not fully explain reasoning. Student selects measure of center and discusses how the value will correspond to a “middle” number. g S-ID.A.2 Student selects measure of spread with a weaker explanation. Student selects measure of spread because of the use of the quartile values. Student selects measure of center but does not fully explain reasoning. Student selects measure of center and discusses how the value will correspond to a “middle” number. h S-ID.A.2 Student fails to address the question. Student selects midrange. Student selects midrange but does not give a clear explanation. Student selects midrange and discusses lack of impact on calculation of extreme values.
2 a S-ID.A.1 Student selects A or C. N/A Student selects B, thinking that the longer boxplot indicates more observations. Student selects D and states that the quartiles tell us percentages, not about counts. b S-ID.A.1 Student selects A, C, or D. N/A Student selects B but justifies based on the steel coasters having a longer box to the right of . Student selects B and compares the median of steel ( above) to upper quartile of wooden (only above). c S-ID.A.1 Student selects A or D. N/A Student selects B and justifies based on the steel coasters having a longer box to the right of . Student selects C and cites the similarity of the two lower quartiles. d S-ID.A.1 Student selects A or C. N/A Student selects B, focusing on the length of the whisker. Student selects D, does not clearly correspond to one of the quartiles. e S-ID.A.1 Student does not address which type of coaster goes faster. Student makes a weak comparison without clear justification or context. OR Student focuses on the one coaster at mph. Student describes shape, center, and spread, but does not focus in on center or fails to give some numerical justification with the description of center. Student describes the center of the distribution and gives some numerical evidence (e.g., median, Q3). Name Date The scores of three quizzes are shown in the following data plot for a class of students. Each quiz has a maximum possible score of . Possible dot plots of the data are shown below. On which quiz did students tend to score the lowest? Justify your choice.