Grade 6, Chapter 9 Investigation Organizer:

**1. Plan It**

**A. Measure the front panel of several cereal boxes.** Find the length-to-width ratio of each front panel by dividing the length of the rectangle by the width. Record the length-to-width ratio for each front panel. Which panel had a ratio closest to the Golden Ratio?

**Our planning completed**

**2. Put It Together**

**A. Draw Golden Rectangles.** The pattern on page 341 of the *Math Central * textbook is made of squares of different sizes. You'll find a similar pattern here. Your group will find the hidden Golden Ratio in this pattern. Remember that the square labeled **1** measures 1 unit by 1 unit. Find the dimensions of each square in the pattern. Remember that proportions remain the same in drawings to scale, if you wish to use a measurement other than inches for your drawing.

Find all the rectangles in the pattern. Determine their measurements. Calculate and record their length-to-width ratios first as fractions and then as ratios. What did you notice? Rectangles with a length-to-width ratio the same as the Golden Ratio are called Golden Rectangles.

**Our drawings and calculations completed**

**3. Wrap It Up**

**Design a cereal box. **On the other side of your rectangle pattern, design a front panel for a box of your favorite cereal. Try to use Golden Rectangles in your design. Can you use the Golden Ratio to determine side lengths of rectangles in your design?

**Our designs completed**

**4. Discuss Your Results**

- How did you figure out the length of the sides of squares in the pattern?
- Are your calculations accurate?
- How well did you keep track of the rectangles and the ratios of the lengths of their sides?
- Did you notice any patterns with the rectangles in the figure you copied?
- How well did you incorporate Golden Rectangles in your cereal box design?
- How well did you use ratio in the investigation?

**Review completed**

Return to Investigation Page.

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