Group Model for Proportional Relationships and Slope Application

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In my experience, many students struggle with translating word problems modeled by a proportional relationship or a linear function into a algebraic expression or equation. (Image below.)

Here is a link to a Jamboard that can be used to introduce the algebraic expression to model the unit rate. (See image below on how to copy and edit.)

Here is how you can use this to introduce modeling the word problem.

  • Start with the unit rate concept. In this case there is $45 “in” every hour. This is modeled in slide 1 (top 2 photos).
  • The next 2 photos show slide 2 in which the student duplicates the $45 image and fills 2 hours, with $45 “in” each. They complete the multiplication expression by multiplying by 2.
  • This is followed by the same steps for 3 hours (photo bottom left) and sequentially to 6 hours.
  • In the last slide there are no hours shown because the # of hours is unknown. This leads to using “X” to represent the unknown NUMBER of hours (I don’t let students get away with x=hours) and finally the algebraic expression (bottom photo).

You can make a copy and edit it.

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