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Write your ideas about the role that proportional thinking plays in algebra. Cite a specific example of an algebra task that requires proportional thinking for completion. Make sure your selected task is from real sources, such as an algebra curriculum, an algebra textbook, or your classroom experiences. Explain the ways in which you see the use of proportional thinking as part of the problem-solving process.
Proportional reasoning has been identified as a benchmark for the critical foundation of algebra. One central idea in the algebra curriculum is the study of change. All graphs are a representation of a mathematical relationship showing change. In fact, the graph of an equivalent ratio is a straight line that passes through the origin.
Read the following list of characteristics that describe “proportional thinkers”:
Proportional thinkers have a sense of covariation. That is, they understand relationships in which two quantities vary together and are able to see how the variation in one coincides with the variation in another.
Proportional thinkers recognize proportional relationships as distinct from nonproportional relationships in real-world contexts.
Proportional thinkers develop a wide variety of strategies for solving proportions or comparing ratios, most of which are based on informal strategies rather than prescribed algorithms.
Proportional thinkers understand ratios as distinct entities representing a relationship different from the quantities they compare.
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