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Course, Subject

Chemistry, Math, Science & Technology, Mathematics (NYS P-12 Common Core)

Virtual Manipulative

Click here for this interactive resource.

Description

This manipulative is intended to help students understand the conversion from one set of units of measurement to another.

The five sets of units are Time, Length, Weight (we do not distinguish between weight and mass), Area, and Volume. The choices within each category are limited, but working within these limited options can nevertheless give students the understanding necessary to make other conversions they may encounter.

The fundamental principle at work here is "cancellation of units." This is accomplished by multiplying by an expression equal to unity that accomplishes a cancellation. As our students learn, "Multiplying by 1 doesn't change the value." Each equivalence, such as "12 inches equals 1 foot," can be written as two fractions each representing 1: (12 in / 1 ft) and (1 ft / 12 in). Given an expression involving feet, multiplication by only one of the fractions will allow cancellation of feet, yielding an expression in terms of inches.

Multiplying by the inappropriate fraction produces an error message, "No cancellation available. Undo and try again." Students should recognize that multiplication by that particular choice is not in any way "wrong;" rather, it just does not allow a cancellation of the type that moves us toward our goal. In this regard, it should be noted that there is not a single correct sequence of steps to be followed to a particular unit conversion. As long as a cancellation occurs, the step is shown and the student can continue. The computer indicates "Correct" when the desired units are achieved, and there may be many different paths to that end.

All cancellations are shown in the workspace with colored hash marks. At the end of a sequence of steps, the whole operation is still visible, with all cancellations and the result of all computations.

This manipulative has no provision for multiplying length units to get area or volume units. At some point, students need to learn that a square yard contains 9 square feet. While such a conversion cannot be done directly with this Convert Units manipulative, students who have worked with the manipulative should be able to recognize that 1 square yard represents the product (1 yd x 1 yd) so that conversion to square feet (1 ft x 1 ft) can be accomplished in two steps by multiplying twice by the unit fraction (3 ft / 1 yd).

Content Provider

The National Library of Virtual Manipulatives is a three-year NSF supported project to develop a library of uniquely interactive, web-based virtual manipulatives or concept tutorials, mostly in the form of Java applets, for mathematics instruction (K-8 emphasis). The project includes dissemination and extensive internal and external evaluation. For more information, please visit http://nlvm.usu.edu/en/nav/vlibrary.html.

Credits

Principal Investigators
Larry Cannon
Jim Dorward
Bob Heal
Leo Edwards

Java Applet Programming
Ethy Cannon
Joel Duffin
David Stowell
Zeke Susman
Richard Wellman
Jennifer Youngberg

Web Site Programming
Joel Duffin

Related Academic Standards

New York State

5.MD.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

6.RP.3.d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2 / 1/4 miles per hour, equivalently 2 miles per hour.

7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

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