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Cross Multiplying When Comparing Fractions? What We Should Do Instead!

Why does cross multiplying work when comparing fractions? Where did it come from? Should we be teaching this technique to our students? Is there a better way?

These are the questions we should ask ourselves about every procedure we teach to our students.

We want to fuel sense making in our students. We want them to know how the strategies we use regularly connects to key understandings we’ve used in the past.

Helping students understand why and how strategies connect will limit that dreaded question, “Why do we have to learn this?”

In this video we’ll:

  • show you how to compare fractions using digital manipulatives from Mathigon;
  • help you so you can help your students use visual models to compare fractions;
  • explain why cross multiplication can work sometimes; and,
  • discuss a strategy that builds off of prior knowledge so students don’t think they are using a new technique.

 

Resources Related To The Video

 

 

 

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!

DOWNLOAD THE 3-PART FRAMEWORK GUIDEBOOK

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!

LESSONS TO MAKE MATH MOMENTS

Each lesson consists of:

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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

SNACK TIME!

Partitive Division Resulting in a Fraction

Shot Put Multi Day Problem Based Unit - Algebraic Substitution

SHOT PUT

Equivalence and Algebraic Substitution

Wooly Worm Race - Representing and Adding Fractions

WOOLY WORM RACE

Fractions and Metric Units

 

Scavenger Hunt - Data Management and Finding The Mean

Scavenger Hunt

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!