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## Math 7-9 Math 7-9 > Factors > Proportional Reasoning

# Proportional Reasoning

## Factor Connections

Hover to see how factors connect to Proportional Reasoning. Then click connected factors to explore strategies related to multiple factors.

How Proportional Reasoning connects to...

Proportional Reasoning involves an understanding of ratio and the relationships between ratios. Ratios express a part-to-whole relationship that can be represented in the form of fractions, percentages, or rates. Proportional Reasoning is an essential component of arithmetic proficiency in elementary school and provides entry to higher math skills including algebra, geometry, and probability and statistics.

### Main Ideas

Students begin with an informal understanding of proportional relationships (e.g., partitioning or fair sharing, or relating proportions in shaded areas of shapes). This informal knowledge develops over several years into a more formal conceptual understanding as they connect different aspects of Proportional Reasoning including:

• Learning to make comparisons based on multiplication rather than addition;
• Learning which aspects of a proportion can be changed (i.e., the specific values) and which must be constant (i.e., the multiplicative relationship between the values); and
• Learning to make composite units -- that is, learning to reconceptualize a proportion as a single entity.