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Goal 3 Data Analysis And Probability |
Expectation 3.1 The student will collect, organize, analyze, and present data. |
Indicator 3.1.1 The student will design and/or conduct an investigation that uses statistical methods to analyze data and communicate results. |
Assessment Limits:
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Brief Constructed Response (BCR) Item - Released in 2006 |
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A cereal company awards a prize to anyone who collects all 5 different game pieces. Each game piece has an equal chance of being placed in a box of cereal. Each box of cereal contains only 1 game piece. Complete the following in the Answer Book:
The following 12 Sample Student Responses represent a range of score points. |
| Sample Student Response #1 |
Score for Sample Student Response #1: Rubric Score 1 Annotation: This response indicates little attempt to apply a reasonable strategy. The student designs a simulation using a spinner with five equal parts, each representing a different game piece. However, the student only describes conducting one trial instead of thirty (spin it 30 times or until your spinner lands on every space at least once). No interpretation of the data is provided. The response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.) |
| Sample Student Response #2 |
Score for Sample Student Response #2: Rubric Score 3 Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. A simulation is designed using a spinner with five equal sections numbered 1-5. The student understands that each trial should last (until every number has been spun) and that thirty trials should be performed. The student correctly describes how to interpret the data so you have confidence in the estimation (Add up the amount of times it took to get all the numbers on the spinner on all 30 trials. Then divide that total by 30). The response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 3 anchor paper.) |
| Sample Student Response #3 |
Score for Sample Student Response #3: Rubric Score 2 Annotation: This response indicates an incomplete application of a reasonable strategy. The student designs a simulation using a five section spinner, with each section representing a different game piece. The student understands that each trial lasts (until you get every game peice) and that thirty trials should be conducted. However, the interpretation of the data is not complete (count how many times it took you to get all of them). The response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.) |
| Sample Student Response #4 |
Score for Sample Student Response #4: Rubric Score 2 Annotation: This response indicates an incomplete application of a reasonable strategy. The student designs a simulation using a random number generator and the numbers 1-5. The student understands that each trial lasts (until all 5 numbers appear) and that thirty trials should be conducted. The interpretation of the data is not complete (however many times it takes for all five numbers to appear during a trial would be how many boxes it may take to buy to get all of the prizes). The response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.) |
| Sample Student Response #5 |
Score for Sample Student Response #5: Rubric Score 1 Annotation: This response indicates little attempt to apply a reasonable strategy. The student designs a simulation using a random number generator with the numbers 1-5 each representing a game piece. The student gives an example of thirty integers generated but this does not show understanding of a trial or that thirty trials should be conducted. The response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.) |
| Sample Student Response #6 |
Score for Sample Student Response #6: Rubric Score 2 Annotation: This response indicates an incomplete application of a reasonable strategy. The student designs a simulation using five colored or numbered pieces of paper in a bag, each representing a different game piece. The student understands that one trial lasts until each game piece is selected (draw out of the bag until I have one of every color) and that thirty trials need to be conducted. The student begins the interpretation of the data but it is not complete (count how many times it took you to get all 5). The response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.) |
| Sample Student Response #7 |
Score for Sample Student Response #7: Rubric Score 2 Annotation: This response indicates an incomplete application of a reasonable strategy. The student designs a simulation using a random number table, with two numbers representing each game piece. The student understands that each trial should last (untill you have all 5 prizes) and that 30 trials should be conducted. However, the interpretation of the data is incomplete (record how many numbers were used when all 5 prizes were found). The response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.) |
| Sample Student Response #8 |
Score for Sample Student Response #8: Rubric Score 1 Annotation: This response indicates little attempt to apply a reasonable strategy. The student gives a partial simulation design by assigning each game piece a number and then randomly selecting the numbers. However, there is no description of how to randomly select the numbers. The student understands that each trial should last until (you have recieved all five numbers) and that 30 trials should be performed. There is no indication of how to interpret the data so that you have confidence in the estimation. The response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.) |
| Sample Student Response #9 |
Score for Sample Student Response #9: Rubric Score 3 Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. A simulation is designed using a random number generator and the numbers 1-5, with each number representing a different game piece. The student understands that each trial should last until you (get numbers 1 through 5) and that thirty trials should be conducted. The student correctly describes how to interpret the data by finding the mean of the thirty trials. The response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 3 anchor paper.) |
| Sample Student Response #10 |
Score for Sample Student Response #10: Rubric Score 2 Annotation: This response indicates an incomplete application of a reasonable strategy. The student designs a simulation using (50 cards equaly marked with numbers 1-5 on them to simulate the 5 different game pieces) in a bowl. The student understands how long each trial should last (until you get all five game pieces) and that 30 trials should be conducted, but the student does not include replacing the card after each time a card is picked out of the bowl. The student interprets the data by using (the measures of central tendency to find the average number of boxes to get all five game pieces). The response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.) |
| Sample Student Response #11 |
Score for Sample Student Response #11: Rubric Score 1 Annotation: This response indicates little attempt to apply a reasonable strategy. The student designs a simulation using a spinner with 5 equal sections (which each represent a different game peice). It is unclear whether the student understands that each trial lasts until each section is landed on at least once, and that thirty trials should be conducted. There is no indication of how to interpret the data so that you have confidence in the estimation. The response demonstrates a minimal understanding and analysis of the problem. |
| Sample Student Response #12 |
Score for Sample Student Response #12: Rubric Score 2 Annotation: This response indicates an incomplete application of a reasonable strategy. The student designs a simulation using random integers 1 through 5, with each integer representing a different game piece, but does not specifically state how the numbers are randomly selected. The student understands that each trial lasts (until you finally recieve all five numbers) and that thirty trials should be conducted. The interpretation of the data is not complete (record how many times it took you to get all of them). The response demonstrates a conceptual understanding and analysis of the problem. |
Additional Resources |
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Brief Constructed Response (BCR) Rubric |
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| Print: Scoring Rubric (pdf) | ||||||
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Resources for 3.1.1: Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans | |