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Unit 2: Key Mathematical Modellings in Real-Life Word Problems

From KNILT

Learning Objectives

At the end of this unit, learners will be able to:

  • Identify key mathematical models that students will use in middle school
  • Identify at least two models that their students can benefit from in the current grades
  • Explain how mathematical models support students’ logical thinking and deeper understanding of new concepts
  • Analyze examples of how mathematical models can be used in their respective grade level

Do Now

Do:

Reflect:

  • What models were used in the exemplar work?
  • Which models have you used or not used in your classroom?
  • Which models are relevant to your grade content standards?

Key Mathematical Models in Middle School

Place Value Chart

Take a look at the Place Value Chart song by Teach and Glow

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Ratio Table

Take a look at the ratio table that represents the relationship between two quantities

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Here is another video of the ratio table representing the constant multiplicative relationship of ratio

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Number Line

Take a look at how number line can be used to add integers. Here is another video of how

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This video also show how number line can be used to solve a ratio and proportional relationship problem.

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Reflect & Record

  • How are these three models similar and/or different?
  • Why does understanding multiple functions of a model important to students' conceptual understanding?
  • How do these models support your students and/or differentiation for your students?
  • Record your thoughts on the Jamboard here and read at least 3 peers' comments

Mini-Stamp
 A mathematical model is a process of using the model in mathematics to visualize or solve a problem. There are different levels of math models and different types of models in K-12. Students who use the math model can understand the problems better, which supports them in solving the problem.

How Does Mathematical Model Fit into My Curriculum?

Explore:
The Common Core Math Standards, a national standard that the majority of the United States abide by, include two different types: Content Standards and Practice Standards. Explore the Practice Standards and one of your grade-level Content Standards. As you explore, think about where modeling lies within the given standards.

Reflect & Record:

  • How do mathematical models fit into your curriculum?
  • Record your thoughts on the Jamboard here and read at least 3 peers' comments

Self-Reflection

Reflect: Set a timer for four minutes and write down some key takeaways from today's unit. As you reflect, use the following guiding questions:

  • What stood out to you about this unit?
  • How did this unit align/contract your practice and/or belief?
  • Identify the reasons why mathematical models are essential to students' learning.

Unit Takeaways

STAMP

  • Mathematical models allow students to visualize the problems and understand mathematical contexts more deeply
  • Mathematical models directly align with the Common Core Content and Practice standards as they support conceptual understanding and mathematical precision
  • Research has shown that students who use accurate visual representations are “six times more likely to correctly solve math problems than are students who do not use them” (Boonen, van Wesel, Jolles, & van der Schoot, 2014)
  • Research has also shown that math models support students who have learning disabilities or lower-performing students (Krawec, 2014)
  • Modeling presents problem-solving as a creative, iterative process as they support many possible justifiable answers

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