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Museion Original · Arithmetic

developing · Ages 11–14 · upper primary to secondary

Proportional Reasoning

Keep the ratio fixed — scale without losing the rate.

Start the path 3 lessons · about 50 minutes
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Three connected investigations

  1. 01Proportional Reasoning: Unit Rate as the InvariantFind the unit rate that stays fixed inside a relationship, and use it to tell a proportional relationship from one that only looks like it.Open
  2. 02Proportional Reasoning: Scaling QuantitiesScale a recipe, mixture, or map up or down while keeping its ratio intact, and match the right quantities to each other when solving for a missing value.Open
  3. 03Proportional Reasoning: Proportional or Not?Decide whether a fresh real-world relationship — currency, speed, or density — is actually proportional before computing with it, and watch for a hidden fixed fee.Open

What this path asks you to reason about

  • Find a unit rate and recognize a proportional relationship.
  • Scale quantities up or down while holding the ratio fixed.
  • Decide whether a fresh relationship is proportional before computing.