




Massachusetts Comprehensive Assessment System
2013, Grade 10 Mathematics
Question 20: OpenResponse 

Reporting Category: Number and Quantity Standard: 10.N.4  Use estimation to judge the reasonableness of results of computations and of solutions to problems involving real numbers. (AI.N.4)
Standard: Mathematics.7.EE.2.03  Solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

The table below shows the numbers of tickets sold for three professional baseball games at a stadium. Baseball Game Ticket Sales Day  Number of Tickets Sold  Friday  31,937  Saturday  28,359  Sunday  38,031   Estimate the difference in the number of tickets sold for Friday’s game and the number of tickets sold for Sunday’s game. Show or explain how you got your estimate.
For Saturday’s game, the stadium ticket office sold 71.6% of the total number of tickets available. Estimate the total number of tickets that were available for Saturday’s game. Show or explain how you got your estimate.
The table below shows the prices of tickets that the stadium ticket office sells.Prices of Tickets Type of Ticket  Price  bleacher  $11.25  pavilion  $24.75  grandstand  $53.75  An equal number of bleacher, pavilion, and grandstand tickets are available for each game. Estimate the average price, in dollars, of a ticket at the stadium. Show or explain how you got your estimate.
 Use your answer from part (c) to estimate the total amount of money, in dollars, the stadium ticket office received in ticket sales for the games on Friday, Saturday, and Sunday. Show or explain how you got your estimate.

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 Number and Quantity concepts involved in solving multistep reallife problems and assessing the reasonableness of answers using estimation strategies. The student makes estimates based on ticket sales and prices. 
4 
3 
The student response demonstrates a good understanding of the Number and Quantity concepts involved in solving multistep reallife problems and assessing the reasonableness of answers using estimation strategies. 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 Number and Quantity concepts involved in solving multistep reallife problems and assessing the reasonableness of answers using estimation strategies. 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 only minimal understanding of the Number and Quantity concepts involved in solving multistep reallife problems and assessing the reasonableness of answers using estimation strategies. 
0 
The student response contains insufficient evidence of an understanding of the Number and Quantity concepts involved in solving multistep reallife problems and assessing the reasonableness of answers using estimation strategies to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 10 Mathematics
 Question 17: Statistics and Probability
 Question 20: Number and Quantity
 Question 21: Algebra and Functions
 Question 31: Algebra and Functions
 Question 41: Geometry
 Question 42: Geometry
Return to the MCAS 2013 Student Work Directory
Last Updated: October 4, 2016


