Creativity Lesson: The Golden Rectangle

*This lesson coincides with break time from Whack on the Side of the Head by Roger von Oech.

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Lesson created by Rob Perry

Grade level range:  7-12

Length of time to teach lesson: 45 minutes

Overview of lesson:  I will draw upon students prior knowledge (proportions) where we covered the golden rule by having them create the golden rectangle  using geometric figures.  Each student will start with a square and follow a series of steps to create several figures.  They will then draw a continuous quarter circle to prove the golden rectangle.


Objective (Learning target) of this lesson:  I can prove the golden ratio by creating the golden rectangle, solving the problem and share my answer.


Resources/supplies/handouts needed to teach this lesson: Paper, rulers and compasses, rubric

Teaching instructions for the lesson: 

I will open up my lesson by activating the students prior knowledge of the golden ratio from proportions.  We will have the discussion of how a line segment can be divided into 2 line segments and the following statement will be true.  AC/AB = AB/BC = 1.618.  Today’s lesson will show how we can create the Golden rectangle by having the students draw a series of rectangles and draw a quarter circle inside every square creating a continuous arc.  I will pass out paper, rulers and compasses to each student and they will create the golden rectangle.

Step 1:  Draw a rectangle (A)

Step 2:  To its right, draw a square (B) whose sides are the same length as A’s longer side. The golden rectangle (A + B) has been created.

Step 3:  Add another square (C) whose sides are equal to the new golden rectangle’s (A + B) longer side.  You have created another golden rectangle (A + B + C ).

Step 4:  Add another square (D) whose sides are equal to the new golden rectangle (A + B + C) longer side.  You have created another golden rectangle ( A+B+C+D).

Step 5:  Take your compass and draw a quarter starting from the bottom left corner of rectangle D and ending in the upper right corner of Rectangle D.  Continue your arc until you have arrived at rectangle

       A.    What shape have you created?  

Assessment: I use the attached rubric to assess each student's project.

 

 

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