Chapter 12 9-12

New Jersey Mathematics Curriculum Framework - Preliminary Version (January 1995)
© Copyright 1995 New Jersey Mathematics Coalition

STANDARD 12: MEASUREMENT

All students will develop their understanding of measurement and systems of measurement through experiences which enable them to use a variety of techniques, tools, and units of measurement to describe and analyze quantifiable phenomena.

9-12 Overview

Building upon the measurement skills and understandings developed in grades K-8, high school students move to a more routine use of measurement. They further examine measurement as a more abstract process, focussing more on measurement error and degree of precision. They spend much more time on indirect measurement techniques, expanding their repertoire to include not only the use of proportions and similarity but also the use of the Pythagorean Theorem and basic right triangle trigonometric relationships.

Students at the high school level will frequently use measurement to help develop understanding of other mathematical concepts. For example, students may use a computer program that measures angles to help them discover the relationship between the measures of two vertical angles formed by intersecting lines or the measures of inscribed and circumscribed angles intercepting the same arc of a circle. They may also develop algebraic techniques that help them to find measures, as, for example, when they develop a formula for finding the distance between two points in the coordinate plane.

High school students also use measurement frequently in connection with other subject areas. Science experiments generally require some use of measurement. Social studies activities often require students to read and interpret maps and/or scale drawings. In technology classes, woodshop, drafting, sewing, and cooking, students must also use a variety of measuring tools and techniques. Even in physical education, students frequently will measure distances (approximately or exactly) and rates.

STANDARD 12: MEASUREMENT

9-12 Expectations and Activities

The expectations for these grade levels appear below in boldface type. Each expectation is followed by activities which illustrate how the expectation can be addressed in the classroom.

Building upon K-8 expectations, experiences in grades 9-12 will be such that all students:

Q. apply their knowledge of measurement in the construction of a variety of two- and three-dimensional figures.

Students use paper fasteners and tagboard strips with a hole punched in each to investigate the rigidity of various polygon shapes. For shapes that are not rigid, they determine how they can be made so.
Students use straw and string to construct models of the five regular polyhedra: the cube, the tetrahedron, the octahedron, the icosahedron, and the dodecahedron.
Students use cardboard and tape to construct a model that demonstrates that the volume of a pyramid is one-third that of a prism with the same base and height.
Students design and carry out an experiment to see how much water is wasted by a leaky faucet in an hour, a day, a week, a month, a year.
Students build scale models of the classroom, the school, or a monument.

R. determine the degree of accuracy of a measurement, for example by understanding and using significant digits.

Students use significant digits appropriately in measuring large distances, such as the distance from one school to another.
Students explain how accurate measurements of distances on maps are by referring to the degree of accuracy of a measurement.
In making a scale drawing of their bedroom, students discuss the degree of accuracy of their measurements.

S. develop and use the concept of indirect measurement, and use techniques of algebra, geometry, and trigonometry to measure quantities indirectly.

Students use coordinate geometry techniques to determine the distance between two points.
Students use similar figures and proportions to measure the height of a tree or a flagpole.
Students use the Pythagorean Theorem to determine how long a ladder is needed to climb a wall.
Students use right-triangle trigonometry to measure the width of a canyon or the height of a waterfall.

T. use measurement appropriately in other subject areas and career-based contexts.

Students investigate how the volume of a cereal box changes with its area by finding the volume and surface area of a box of their favorite kind of cereal. They also discuss how the shape of the box affects its volume and surface area and why the volume of the box is so large for the amount of cereal it contains.
Students measure their own femurs and heights to determine the relationship between the length of the femur and the height of a person.

U. choose appropriate techniques and tools to measure quantities in order to achieve specified degrees of precision, accuracy, and error (or tolerance) of measurements.

Students use computer drawing and measuring utilities to discover geometric concepts. They also discuss the limitations of such a program. For example, a program may give 14.7 and 7.3 for the lengths of the base and the midline of a triangle because of its measurement limitations.
Students determine what kind of measuring instrument needs to be used to measure ingredients for pain-relievers, for cough syrup, for a cake, and for a stew. They discuss the accuracy and error of each measurement.