How To Solve Proportions Without Cross Multiplication

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What do most educators think of when it comes to teaching ratios, rates and proportional relationships in math class?

Setting up and solving proportions!

How do most handle solving proportions for an unknown quantity?

You got it: cross multiplication!

While setting up and solving proportions with cross multiplication (or any other set of steps) may work to ensure we come up with the correct answer, the problem is that often times these methods are taught as tricks that lead to less reasoning by students.

Of course, Math Moment Makers certainly are after more thinking in their math classrooms, so the question becomes: "what do we do instead?"

In today's video, we'll be diving into Day 1 from the Stacking Paper problem based math unit to leverage a context involving a composed unit ratio to emerge the proportional reasoning multiplicative strategy of scaling in tandem and mathematical models including tape diagrams, double number lines and ratio tables!

In particular, you'll learn:

How to avoid rushing to the algorithm with ratios and rates;

Why strategies and models are more helpful to promote student reasoning than rushing to set up and solve proportions with cross multiplication;

How to use context to emerge the proportional reasoning strategy of scaling in tandem;

Which models are helpful to leverage as students use ratio reasoning; and,

Where you can go to use Day 1 and the remainder of this problem based math unit.

Resources:
Learn about the Curiosity Path by reading our 3-Part Framework:

Check out the Stacking Paper [Ratios, Rates and Proportions] Problem Based Math Unit:

Visit Make Math Moments Problem Based Math Lessons page for other useful problem based units:

Learn more about ratios, rates and proportionality in our Proportional Relationships Course:

Up your pedagogical and content knowledge game by joining our Make Math Moments Teacher Academy!