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A headline reads, “Two out of three Americans owned a smartphone in 2015.” Does that mean two out of every group of three Americans? Is it possible to have a group of Americans who all own smartphones?  Adults encounter ratios and proportions all the time in news or media statistics, estimates of risk, shopping for the best deal, creating mixtures and recipes, and countless other daily activities. The ability to reason about these numerical relationships develops over a long period of time and through deliberate exploration of the mathematics involved. Language teachers can provide opportunities for students to encounter and expand their ability to reason with ratios in real life contexts.

Mathematizing ESOL III: Integrating Ratio Reasoning is a course for English language teachers who want to deepen their own conceptual understanding of ratios and proportions and to learn strategies for helping students build ratio reasoning skills. This course is for participants who have successfully completed Mathematizing ESOL I and Mathematizing ESOL II


This professional development activity/course is designed for:

  • Any ESOL instructor interested in integrating math into his or her language acquisition classroom. No prior math background is needed; however, instructors must have successfully completed Mathematizing ESOL I and Mathematizing ESOL II.

The online course is divided into five core lessons. Each lesson contains math practice activities, discussion forums, and lesson ideas for adult ESOL classes. Participants are required to read course content, complete activities and related documents, respond to discussion prompts and read the responses of other participants. Massachusetts participants who wish to earn Professional Development Points (PDPs) are asked to design a lesson for ESOL students that that integrates conceptual understanding and application of proportional reasoning, and incorporates the key elements of each lesson covered in this course as a final project. 

Lessons must be completed according to the course schedule listed below. The estimated time to complete the course is 18 to 20 hours. Upon completion of the course, including all related activities, final reflection, and evaluation, participants will receive a Certificate of Completion. 

For more information, please contact Mollie Behan at

Learning Objectives: 

Upon completion of this professional development activity/course, you will be able to:

  • Identify contexts that involve ratios and proportions that would make sense in an ESOL classroom and use in creating activities/lessons.
  • Explain what a ratio is and is not, and whether ratio reasoning is appropriate in a situation.
  • Connect different types of mathematical comparisons to language structures.
  • Explore the different multiplicative relationships in a proportion.
  • Use concrete strategies to help students reason about ratios.
  • Identify different ways of expressing ratios and how these can be used to persuade.
  • Differentiate activities with open-ended math questions for ESOL learners.

Mathematizing ESOL I and Mathematizing ESOL II

03/19/2018 - 9:00am
End Date: 
04/23/2018 - 11:45pm
PD Center: 
Topic Area: 
ABE/Adult Education
ESOL/English Language Learner
Mathematics and Adult Numeracy
PDP Eligible: 
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