## Creativity Lesson: The Golden Rectangle

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

Suggested Books (paid link)

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.

 Help Wanted onMont VernonThis book combines historyand mathematics withadorable characters to teachkids about the many talentsof the first U.S. President. The UnderAchievers:Woven into a fun story, this book provides excellentmath lessons for kids. Writing Across the Curriculum:The NumberFix Project Wacky We-Search Reports:A popular book on writingacross the curriculum.