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Apply proportionality to measurement in multiple contexts, including scale drawings and constant speed.
Remarks
The student might convert among different units of measurement to solve problems involving rates.Example 1: On a floor plan of your school, your classroom is 9 inches long and 6 inches wide. If the scale is 1 inch = 3 ft., what is the width of your classroom in feet? Explain your answer.
Example 2: You have a 4 in. by 5 in. photograph and you want to enlarge it to an 8 in. by 10 in. photograph. Roberto thinks that the new picture is four times as big as the old one. Dora thinks that the new picture is twice as big as the old one. Explain their thinking.
General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 7
Body of Knowledge: Algebra
Idea: Level 2: Basic Application of Skills & Concepts
Big Idea: BIG IDEA 1 - Develop an understanding of and apply proportionality, including similarity.
Date Adopted or Revised: 09/07
Content Complexity Rating:
Level 2: Basic Application of Skills & Concepts
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More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications
-
Item Type(s):
This benchmark may be assessed using:
MC
,
GR
item(s)
- Clarification :
Students will solve problems by applying proportionality to measurement contexts.
Students will determine the scale factor for a given situation or use a scale to determine a measurement. - Content Limits :
Measurements may be in either metric or customary units, but measurements from both systems may not be used in the same item.
Items may include the concepts of average speed or constant speed.
Items may include fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 24, 25, 32, or 50.
Items may include decimals through the hundredths place.Items will NOT include circumference, perimeter, area, or volume.
Items will NOT include percents of increase or decrease.
Items will NOT include converting units between two derived units (e.g., converting miles per hour to feet per second).
- Stimulus Attributes :
Items should be set in a real-world context or a mathematical context.
Graphics should be used in some of these items, as appropriate.
Sample Test Items (2)
- Test Item #: Sample Item 1
- Question: Dale and his family are planning to fly from Seattle to Miami. The direct flight is 5322 kilometers. Dale drew a line segment on a U.S. map from Seattle to Miami to show his younger sister the flight distance between the two cities. If the scale on the map shows that 2 centimeters represents 600 kilometers, what is the length of the line segment Dale drew on the map from one city to the next?
- Difficulty: N/A
- Type: MC: Multiple Choice
- Test Item #: Sample Item 2
- Question: Dominic drove 324 miles from Salt Lake City, Utah, to Bryce Canyon National Park in 6 hours and 45 minutes. What was his average speed, in miles per hour?
- Difficulty: N/A
- Type: GR: Gridded-Response
Related Access Points
Alternate version of this benchmark for students with significant cognitive disabilities.
Related Resources
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Lesson Plan
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Student Resources
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