




Massachusetts Comprehensive Assessment System
2014, Grade 7 Mathematics
Question 18: OpenResponse 

Reporting Category: Statistics and Probability Standard: Mathematics.7.SP.3.07  Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

Susan put blue tiles, green tiles, and yellow tiles into a bag. All the tiles are the same size and shape. Susan will select one tile from the bag without looking, record its color, and then put the tile back into the bag. She will repeat this experiment 240 times. Based on the number of tiles of each color in the bag, Susan predicted the results shown in the frequency table below. Predicted Results Color of Tile  Frequency  blue  120  green  40  yellow    Based on the table, what is the best prediction for the number of times Susan will select a yellow tile from the bag? Show or explain how you got your answer.
A total of 12 tiles are in the bag. Based on the table, determine the number of blue tiles, the number of green tiles, and the number of yellow tiles that are in Susan’s bag. Show or explain how you got each of your answers.

Scoring Guide and Sample Student Work Select a score point in the table below to view the sample student response.
Score  Description 
4 
The student response demonstrates an exemplary understanding of the Statistics and Probability concepts involved in developing a probability model and using it to find probabilities of events. When given the total number of selections and some of the data, the student completes a frequency table and predicts the number of tiles of each color in a bag. 
4 
3 
The student response demonstrates a good understanding of the Statistics and Probability concepts involved in developing a probability model and using it to find probabilities of events. Although there is significant evidence that the student was able to recognize and apply the concepts involved, some aspect of the response is flawed. As a result the response merits 3 points. 
2 
The student response demonstrates a fair understanding of the Statistics and Probability concepts involved in developing a probability model and using it to find probabilities of events. While some aspects of the task are completed correctly, others are not. The mixed evidence provided by the student merits 2 points. 
1 
The student response demonstrates a minimal understanding of the Statistics and Probability concepts involved in developing a probability model and using it to find probabilities of events. 
0 
The student response contains insufficient evidence of an understanding of the Statistics and Probability concepts involved in developing a probability model and using it to find probabilities of events to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 7 Mathematics
 Question 10: The Number System
 Question 18: Statistics and Probability
Return to the MCAS 2014 Student Work Directory
Last Updated: March 23, 2018


