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4.  Digital Pan Balance:
Applying proportional reasoning using an online manipulative

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	SREB Readiness Indicator Write and use ratios, rates and proportions to describe situations and solve problems. > Additional indicators
	Skills Write and use ratios, rates, and proportions to describe situations Solve problems using concepts of ratio and proportion
	Figure 1: Unequal shape representations (Click to test this tool) NCTM disclaimer

Overview

Using the NCTM Illuminations' Pan Balance (Figure 1), students apply ratio concepts as they determine unknown values for balance weights. Shapes, which represent weights, are dragged onto pans which rise or fall, simulating a physical pan balance. When the weights are equal, the pans balance, the shape combinations are automatically recorded in a table, and students can go on to experiment with other combinations. Working with the pan balance helps students move from concrete to abstract thinking by using the shapes to represent variables and providing the table to bridge from the balance to mathematical sentences.

The Value of This Technology

This technology-enhanced version of the familiar math classroom activity allows each student to engage in hands-on explorations and use properties of equality, ratio, and proportion to solve for unknowns. The stand-alone applet also provides a nearly unlimited set of weights and generates new sets of weights for each exploration, enabling students to conduct many more pan balance investigations than would ever be possible with physical balances and a static sets of weights.

Look in the Classroom

Ms. Daken knows that her students have a good conceptual understanding of equivalent fractions that express part-to-whole relationships but that they need more work with ratios that express part-to-part relationships.
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