Friday was a continuation of Thursdayâs lesson about patterns. At the beginning of class, students played a card game called SET and then discussed how it relates to patterns. Then, we looked at a few patterns of numbers including an arithmetic series, a geometric series, and the Fibonacci numbers. Students found the first 20 Fibonacci numbers on paper and then found the ratios of the Fibonacci numbers, which are the Golden Ratio.
The students then worked on an activity with a partner dealing with the Golden Ratio. Hanley told them that many artists have used the Golden Ratio in their artwork and that many rectangles are close to the golden ratio. They measured and recorded several rectangles they found in the classroom and in artwork. They were given a worksheet with a table to record their measurements and with a diagram of the Parthenon, Chartres cathedral, and the Mona Lisa. They found the ratios of all of these rectangles and averaged the ratios to see how close they were to the Golden Ratio.
Then, Pascalâs triangle was introduced. Two blank Pascalâs Triangles were projected onto the whiteboard, and Hanley filled in the first four lines. Then, in two teams, the students figured out the pattern or âruleâ and filled out the rest of the triangle. Afterwards, they were given worksheets of completed Pascalâs Triangles and asked to find patterns within the triangle. The students found quite a few patterns; they really liked Pascalâs Triangle.
At the end of class, each student was to make a very short slideshow of 3 slides about patterns. One slide had to be a pattern found in nature, one found in art or architecture, and one found in math or science. Hanley was able to put some of the slideshows together with one she had made previously and presented it to the class as a conclusion to the lesson on patterns. It made the point very well that patterns are all around us in the world.