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Learning goals:

Describe the essential features of a ratio

Contrast proportional and non proportional situations using addition and multiplication examples

Illustrate different ways to solve proportional problems and describe a progression of these ways

Compare traditional methods to teaching proportional reasoning to research-based methods

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Definition: a ratio is a multiplicative comparison of two quantities or measures.

They involve multiplicative rather than additive comparisons, so equal ratios from multiplication or division, not addition and subtraction

Rate is a way to represent a ratio

Proportional thinking is developed through activities involving comparing and determining the equivalence of rations

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“Forming a ratio is a cognitive task- not a writing task” a ratio is a relationship, no matter if it's written as ⅖ or 2:5 or 2 divided by 5

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Students need to:

Have opportunities to compare situation and discuss whether the comparison is due to an additive, multiplicative or constant relationship

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1. If You Hopped Like a Frog by David Schwartz: the book compares features of various creatures with those of humans. It provides factual data on which the proportions are based.

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2. Animal Farm by George Orwell: interdisciplinary opportunity with language arts. The book includes examples of telling animals to increase their “foodstuff” by 200% or 500%. This provides the opportunity to use bar diagrams to explore present increase connected to proportions

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3. Wilma Unlimited: How Wilma Became the World’s Fastest Women by Krull: can launch lessons where students measure their hopping, walking, and running rates to use proportional reasoning to determine how quickly they would travel various distances.

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Dynamic geometry software like GeoGebra or Desmos offers an effective method for exploring the idea of ratio.

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Free online apps bundle from GeoGebra: get graphing, geometry, algebra, 3D, statistics, probability, all in one tool!

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Google Earth can be used for authentic scaling activities

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Aw snap! Google Earth isn't supported on your browser. You may need to update your browser or use a different browser. Please see our system requirements for more information. Chrome is a great choice and you can download it here.

Or if you're feeling adventurous, you can try Earth anyway by choosing an option below.

Learn more about Google Earth.

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Aw snap! Google Earth isn't supported on your browser. You may need to update your browser or use a different browser. Please see our system requirements for more information. Chrome is a great choice and you can download it here. Or if you're feeling adventurous, you can try Earth anyway by choosing an option below.

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Practice addition, multiplication, fractions and algebraic reasoning with our popular math games. Discover fun learning games kids love to play.

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4. Holes by Louis Sachar: A popular book and movie, this novel tells the story of boys in a “camp” who are digging holes every day, which provides an opportunity to look at daily rates of dirt removal.

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The Meadows Center for Preventing Educational Risk

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MSTAR | Mathematics and Science Institute for Students With Special Needs

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Include visual representations as part of instruction; link to abstract and symbolic representations to help students make connections. For example, number lines help students visualize concepts (e.g., equivalent fractions, multiplication facts).