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March 6, 2018
Using Visual Models to Build Proportional Strategies with Understanding

Interacting with visual models is a key strategy for developing students' understanding and fluency with fractions. Moving to efficient and effective proportional strategies relies on understandings that are built through opportunities for students to construct their own models as well as interact with given visual models. 
Initially, models should be used to build an understanding of a concept. In the following rate problem, notice how the Double Number Line can be used to help students make sense of the meaning of the rate and the meaning of the mathematical language "miles per hour." Sometimes students think miles per hour is one word -"milesperhour", but this model helps to clarify the meaning of the expression, that every 55 miles in distance is equivalent to 1 hour in time. 
Visual models can also help support the development of more efficient and generalizable proportional strategies. Below is the information from the same problem shown in a Ratio Table. Note how the ratio table can be used to highlight the multiplicative relationship between the equivalent ratios that is so important for understanding and developing proportional strategies. 
Note that the numbers in this problem are easy to model, and these transitional strategies are an essential step for building procedural fluency with understanding.
Action Item

  • Use a double number line and a ratio table to solve OGAP Item RC28:
Paul's dog eat's 20 pounds of food in 30 days. How long will it take Paul's dog to eat a 45 pound bag of dog food?    Click here for sample solutions.
  • Where do you see double number lines and ratio tables in your curriculum materials? If you don't see them, where can you introduce them?
  • Identify some OGAP items that have quantities that are easy to model (see the Rate sections). Select one to administer to your students. Analyze the evidence in their work and decide where on the OGAP Proportional Progression the solutions are and your next instructional step.  How can you use visual models to help build and extend their understanding? 
Did you know?

You can access the OGAP Item Banks online in two ways: find our new searchable OGAP item bank  here ( bookmark it! ) or view the PDFs at  www.ogapmath.com/item-bank .

Also, you can access past issues of OGAP Teacher Tips by visiting  www.ogapmath.com/ogap-teacher-tips-archive.