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National Standards for Grade 8 - Mathematics (page 3)

Measurement

In this NAEP Mathematics Framework, attributes such as capacity, weight/mass, time, and temperature are included, as well as the geometric attributes of length, area, and volume. Although many of these attributes are included in the grade 4 framework, the emphasis is on length, including perimeter, distance, and height. More emphasis is placed on area and angle in grade 8.

Units involved in items on the NAEP assessment include non-standard, customary, and metric units. At grade 4, common customary units such as inch, quart, pound, and hour and the common metric units such as centimeter, liter, and gram are emphasized. Grades 8 and 12 include the use of both square and cubic units for measuring area, surface area, and volume; degrees for measuring angles; and constructed units such as miles per hour. Converting from one unit in a system to another (such as from minutes to hours) is an important aspect of measurement included in problem situations. Understanding and using the many conversions available is an important skill. There are a limited number of common, everyday equivalencies that students are expected to know.

Items classified in this content area depend on some knowledge of measurement. For example, an item that asks the difference between a 3-inch and a 1¾-inch line segment is a number item, while an item comparing a 2-foot segment with an 8-inch line segment is a measurement item. In many secondary schools, measurement becomes an integral part of geometry; this is reflected in the proportion of items recommended for these two areas.

 GRADE 8 1) Measuring physical attributes a) Compare objects with respect to length, area, volume, angle measurement, weight, or mass. b) Estimate the size of an object with respect to a given measurement attribute (e.g., area). c) Select or use appropriate measurement instrument to determine or create a given length, area, volume, angle, weight, or mass. d) Solve mathematical or real-world problems involving perimeter or area of plane figures such as or composite figures. e) Solve problems involving volume or surface area of rectangular solids, cylinders, prisms, or composite shapes. f) Solve problems involving indirect measurement such as finding the height of a building by comparing its shadow with the height and shadow of a known object. g) Solve problems involving rates such as speed or population density. 2) System of measurement a) Select or use appropriate type of unit for the attribute being measured such as length, area, angle, time, or volume. b) Solve problems involving conversions within the same measurement system such as conversions involving square inches and square feet. c) Estimate the measure of an object in one system given the measure of that object in another system and the approximate conversion factor. For example: • Distance conversion: 1 kilometer is approximately e of a mile. • Money conversion: U.S. dollar is approximately 1.5 Canadian dollars. • Temperature conversion: Fahrenheit to Celsius d) Determine appropriate size of unit of measurement in problem situation involving such attributes as length, area, or volume. e) Determine appropriate accuracy of measurement in problem sit­uations (e.g., the accuracy of each of several lengths needed to obtain a specified accuracy of a total length) and find the measure to that degree of accuracy. f) Construct or solve problems (e.g., floor area of a room) involving scale drawings.

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