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