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The National Council of Teachers of Mathematics (NCTM, 2000) has identified measurement as a strand in its Principles and Standards for School Mathematics. In grades pre-K-12, instructional programs should enable all students to do the following:
• | Understand measurable attributes of objects and the units, systems, and processes of measurement |
• | Apply appropriate techniques, tools, and formulas to determine measurements |
In grades 3-5 classrooms, students are expected to do the following:
• | Understand such attributes as length, area, weight, volume, and size of angle, and select the appropriate type of unit for measuring each attribute |
• | Understand the need for measuring with standard units and become familiar with standard units in the customary and metric systems |
• | Carry out simple unit conversions, such as from centimeters to meters, within a system of measurement |
• | Understand that measurements are approximations and understand how differences in units affect precision |
• | Explore what happens to measurements of a two-dimensional shape such as its perimeter and area when the shape is changed in some way |
• | Develop strategies for estimating the perimeters, areas, and volumes of irregular shapes |
• | Select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles |
• | Select and use benchmarks to estimate measurements |
• | Develop, understand, and use formulas to find the area of rectangles and related triangles and parallelograms |
• | Develop strategies to determine the surface areas and volumes of rectangular solids |
The NCTM (2000) Measurement Standards suggest that "students in grades 3-5 should explore how measurements are affected when one attribute to be measured is held constant and the other is changed. For example, consider the area of four tiles joined together along adjacent sides. The area of each tile is a square unit. When joined, the area of the resulting polygon is always four square units, but the perimeter varies from eight to ten units, depending on how the tiles are arranged. ... This activity provides an opportunity to discuss the relationship of area to perimeter. It also highlights the importance of organizing solutions systematically" (NCTM, 2000, p. 173).
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