Rectangle Problem is Introduced

Math Content: Proportional Reasoning
Introduction to the Rectangle Problem

Ms. Bithell begins her lesson by introducing a system to help students highlight the idea that both rectangles are similar. She uses the CAHSEE release question as her model of this process. As a reminder, here is the problem:

"The actual width (w) of a rectangle is 18 centimeters (cm). Use the scale drawing of the rectangle to find the actual length (l)."

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PDROM Bar Video

In the video, you saw the problem being solved by writing a proportion in which the actual measurements are on the left hand side and the drawing's measurements are on the right hand side. You can also write an equivalent proportion in which the lengths (actual and drawing) are on one side and the two widths are on the other side. Now, why is this true? Well, each of the proportions a / b = c / d and a / c = b / d is equivalent to the cross product equation ad = bc. Therefore, each of these proportions is equivalent to the other.

Classroom Clip Reflection:

  • How does Ms. Bithell?s system work to support her student?s abilities to set up their proportion problems?
  • What other strategies could she use?
  • What are the implications of this for your work with students?