# Performance Assessment Task Gym Grade 6. Common Core State Standards Math - Content Standards

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2 flowcharts, and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Assessment Results This task was developed by the Mathematics Assessment Resource Service and administered as part of a national, normed math assessment. For comparison purposes, teachers may be interested in the results of the national assessment, including the total points possible for the task, the number of core points, and the percent of students that scored at standard on the task. Related materials, including the scoring rubric, student work, and discussions of student understandings and misconceptions on the task, are included in the task packet. Grade Level Year Total Points Core Points % At Standard % 2012 Noyce Foundation

3 Sixth Grade 2003 pg. 15

4 Sixth Grade 2003 pg. 16

5 Sixth Grade 2003 pg. 17

6 Looking at Student Work Gym Students seem to have a difficult time analyzing the effects of operations on units (dimensional analysis) and making comparisons. Student A does a good job of tracking the units as he works through different parts of the task. The work is organized in a manner that makes the logic very is easy to follow. Part 3 starts with the cost of visits per month to visits per year, then monthly fee to yearly fee, and finally total cost. Student A Sixth Grade 2003 pg. 18

7 Student A Sixth Grade 2003 pg. 19

8 Student B makes the most common error in part 3. The student finds the yearly cost of gym visits and yearly total for monthly fees, but forgets to add in the cost of joining the gym. Student B Sixth Grade 2003 pg. 20

9 Student C finds the cost per month of visits and fees and compares them to the cost per month of the Regular deal gym. This would have worked if the student had additionally found the monthly cost of the initiation fee (\$25) and added that to the Superfit total. The student would still have needed to multiply the difference by 12 to find the yearly difference. Student C Sixth Grade 2003 pg. 21

10 Student D makes two common errors. In part 2 of the task the student confuses the increase in number of visits with the total number of visits. In part 2 the student finds the cost of 20 visits per month, but forgets to multiply that number by 12 to find the cost for visits per year. Student D Sixth Grade 2003 pg. 22

11 Student E forgets the monthly cost for regular deal and finds the number of visits that will equal all-in-one price. Students have difficulty keeping track of the different constraints or features involved in the different pricing schemes. Student E Teacher Notes: Sixth Grade 2003 pg. 23

12 Grade 6 Gym Gym Mean: 3.30, S.D.: Frequency Frequency Score Score: % < = 23.3% 33.0% 39.7% 55.6% 61.8% 80.0% 86.7% 89.8% 100.0% % > = 100.0% 76.7% 67.0% 60.3% 44.4% 38.2% 20.0% 13.3% 10.2% The maximum score available for this task is 8 points. The cut score for a level 3 response is 3 points. Most students (about 80%) could find the cost of the Pay as you go plan and the Allin-one plan. A little more than half of the students (about 67%) could correctly calculate the costs of all three options and compare to find the better deal. Almost 44% could compare the 3 options and find the number of visits that would make Allin-one and regular deal the same. About 10% of the students could meet all the demands of the task, including comparing the yearly costs and savings of two different gym plans. Almost 20% of the students scored no points on this task. 90% of those students attempted the task. Sixth Grade 2003 pg. 24

15 Instructional Implications: Students need more experiences making comparisons. They need to calculate the full costs of both options before making a decision. It is not enough to just calculate the cost for the favored choice. Students might consider different choices about family entertainment options or cell phone plans to determine the best price. Students lack experience analyzing the effects of operations on units or systems for keeping track of units as they work through steps in a problem. Dimensional analysis is a topic that many teachers need to deal with more explicitly. Students also have trouble identifying the various constraints of within each option and seeing how they interconnect. Students need to work with more problems in context instead of working isolated number calculation skill sets. Sixth Grade 2003 pg. 27

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When 95% Accurate Isn t Written by: Todd CadwalladerOlsker California State University, Fullerton tcadwall@fullerton.edu Overview of Lesson In this activity, students will investigate Bayes theorem using