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Massachusetts Comprehensive Assessment System

2014, Grade 7 Mathematics

  Question 10: Open-Response no calculator allowed
Ethan plotted points E, F, G, H, and I on a number line, as shown below.
A number line measuring from negative 10 to 10, increasing by intervals of 1, with every 5th interval labeled. Point E is located to the right of negative 10; Point F is located to the left of negative 5; Point G is located two points to the left of 0; Point H is located to the right of 5; Point I is located two points to the right of Point H.
  1. Which two points that Ethan plotted represent numbers that have a sum of 0? Show or explain how you got your answer.
  2. Write an equation using subtraction that could be used to find d, the distance, in units, between point E and point I.
  3. Solve the equation that you wrote in part (b). Show or explain how you got your answer.
Ethan wrote the expression below to represent the distance between point G and point H.
The absolute value of negative two plus the absolute value of six.
  1. What is the value of Ethan’s expression?
  2. Explain how you know Ethan’s expression is equivalent to the distance between point G and point H.

Scoring Guide and Sample Student Work
Select a score point in the table below to view the sample student response.

ScoreDescription
4 The student response demonstrates an exemplary understanding of the Number System concepts involved in applying and extending previous understandings of addition and subtraction to add and subtract rational numbers and representing addition and subtraction on a horizontal number line diagram. The student identifies two numbers on a number line that have a sum of zero, and writes and solves an equation that could be used to find the distance between two points on the number line.
4
3 The student response demonstrates a good understanding of the Number System concepts involved applying and extending previous understandings of addition and subtraction to add and subtract rational numbers and representing addition and subtraction on a horizontal number line diagram. 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 System concepts involved in applying and extending previous understandings of addition and subtraction to add and subtract rational numbers and representing addition and subtraction on a horizontal number line diagram. 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 Number System concepts involved in applying and extending previous understandings of addition and subtraction to add and subtract rational numbers and representing addition and subtraction on a horizontal number line diagram.
0 The student response contains insufficient evidence of an understanding of the Number System concepts involved in applying and extending previous understandings of addition and subtraction to add and subtract rational numbers and representing addition and subtraction on a horizontal number line diagram 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: June 26, 2017
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