How To Solve Proportions Without Cross Multiplication

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:

  1. How to avoid rushing to the algorithm with ratios and rates;
  2. Why strategies and models are more helpful to promote student reasoning than rushing to set up and solve proportions with cross multiplication;
  3. How to use context to emerge the proportional reasoning strategy of scaling in tandem;
  4. Which models are helpful to leverage as students use ratio reasoning; and,
  5. Where you can go to use Day 1 and the remainder of this problem based math unit.

Resources Related To The Video

  1. Learn about the Curiosity Path by reading our 3-Part Framework
  2. Check out the Stacking Paper [Ratios, Rates and Proportions] Problem Based Math Unit
  3. Visit Make Math Moments Problem Based Math Lessons page for other useful problem based units
  4. Learn more about ratios, rates and proportionality in our Proportional Relationships Course
  5. Up your pedagogical and content knowledge game by joining our Make Math Moments Teacher Academy!

Want to Run Problem Based Lessons Without a Hitch In Your Classroom?

Head over to the Make Math Moments 3-Part Framework page to dive right in or click below to download the guidebook to take with you!


Why not bring the 3-Part Framework Guidebook with you?

Download the PDF so you can share with your professional learning network via print or email!


Each lesson consists of:

Each Make Math Moments Problem Based Lesson consists of a Teacher Guide to lead you step-by-step through the planning process to ensure your lesson runs without a hitch!

Each Teacher Guide consists of:

  • Intentionality of the lesson;
  • A step-by-step walk through of each phase of the lesson;
  • Visuals, animations, and videos unpacking big ideas, strategies, and models we intend to emerge during the lesson;
  • Sample student approaches to assist in anticipating what your students might do;
  • Resources and downloads including Keynote, Powerpoint, Media Files, and Teacher Guide printable PDF; and,
  • Much more!

Each Make Math Moments Problem Based Lesson begins with a story, visual, video, or other method to Spark Curiosity through context.

Students will often Notice and Wonder before making an estimate to draw them in and invest in the problem.

After student voice has been heard and acknowledged, we will set students off on a Productive Struggle via a prompt related to the Spark context.

These prompts are given each lesson with the following conditions:

  • No calculators are to be used; and,
  • Students are to focus on how they can convince their math community that their solution is valid.

Students are left to engage in a productive struggle as the facilitator circulates to observe and engage in conversation as a means of assessing formatively.

The facilitator is instructed through the Teacher Guide on what specific strategies and models could be used to make connections and consolidate the learning from the lesson.

Often times, animations and walk through videos are provided in the Teacher Guide to assist with planning and delivering the consolidation.

A review image, video, or animation is provided as a conclusion to the task from the lesson.

While this might feel like a natural ending to the context students have been exploring, it is just the beginning as we look to leverage this context via extensions and additional lessons to dig deeper.

At the end of each lesson, consolidation prompts and/or extensions are crafted for students to purposefully practice and demonstrate their current understanding. 

Facilitators are encouraged to collect these consolidation prompts as a means to engage in the assessment process and inform next moves for instruction.

In multi-day units of study, Math Talks are crafted to help build on the thinking from the previous day and build towards the next step in the developmental progression of the concept(s) we are exploring.

Each Math Talk is constructed as a string of related problems that build with intentionality to emerge specific big ideas, strategies, and mathematical models. 

Make Math Moments Problem Based Lessons and Day 1 Teacher Guides are openly available for you to leverage and use with your students without becoming a Make Math Moments Academy Member.

Use our OPEN ACCESS multi-day problem based units!

Make Math Moments Problem Based Lessons and Day 1 Teacher Guides are openly available for you to leverage and use with your students without becoming a Make Math Moments Academy Member.

MMM Unit - Snack Time Fractions Unit


Partitive Division Resulting in a Fraction

Shot Put Multi Day Problem Based Unit - Algebraic Substitution


Equivalence and Algebraic Substitution

Wooly Worm Race - Representing and Adding Fractions


Fractions and Metric Units


Scavenger Hunt - Data Management and Finding The Mean


Represent Categorical Data & Explore Mean

Downloadable resources including blackline mastershandouts, printable Tips Sheetsslide shows, and media files do require a Make Math Moments Academy Membership.

Use our OPEN ACCESS multi-day problem based units!