Proportional reasoning

Use proportional reasoning to determine mole ratios from a balanced chemical equation. 

Beland, A. Mislevy, R. J. (1991). Probability-based inference in a domain of proportional reasoning tasks (Tech. Rep. ONR Contract N00014-91-J-4101). Princeton Educational Testing Service. 

Different representations in text may affect students problem solving, and the application of intuitive rules to proportional reasoning may be enhanced when the problems are presented in different representations (Liu Shen, 2011). Take Liu and Shen s study as an example they adopted two kinds of representation of the same problem (Fig. 17). One is the iconic form and the other is the symbolic form. 

This is the first time in this book that you have considered proportional reasoning. This thinking skill has its basis in the mathematics of ratio and proportion. If a variable, y, is directly proportional to another variable, x, we express this mathematically as... 

Conversions between metric units are an example of proportional reasoning. Let s examine the 1000-units-per-kilounit relationship more closely. In any measured quantity, the number of units is directly proportional to the number of kilounits ( of units) ( of kUounits). In the form of Equation 3.2, ( of units) = m X ( of kilounits). Solving for the proportionality constant, m, gives... 

Dimensional analysis Directly proportional Given quantity (Given) Inversely proportional Per expression (Per) Proportional reasoning Proportionality constant The symbol =... 

The reasoning approach discussed here is the essence of thinking about your thinking on the subject of proportional reasoning. When all other variables are held constant, cooling a gas reduces the volume, so the temperature fraction by which the initial volume will be multiplied will be less than 1. Heating a gas increases the volume, which means that the ratio of temperatures must be greater than 1. 

The number of eggs in a dozen and the number of particles in a mole are both examples of direct proportionalities nsed in proportional reasoning. 

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