- MathArt in Ancient Cultures
- MathArt in the Arts & Sciences
- Math Connections with the Real World
- MathArt: Patterns in Nature
Math Connections with the Real World
For our review, we picked the Math Connections with the Real World study. This class focuses on Fibonacci numbers and the golden ratio. There are six lessons:
- #1: Introduction & History of the Golden Ratio and the Fibonacci Numbers
- #2: The Golden Number & Fibonacci in Art, Architecture & Nature
- #3: The Fibonacci Numbers in Nature
- #4: The History & the Golden Ratio of the Great Pyramid
- #5: Phi & Quasicrystals
- #6: The Mathematics of Music
Each lesson has the main lesson video (we watched the pre-recorded version), different activities, and a quizlet (a quiz that is interactive and embedded on the website). The lessons also have web resources, links to other videos, and suggested projects.
If you aren’t familiar with Fibonacci numbers (I didn’t remember learning about them in school), they are a series of numbers, starting with either 0 or 1 (depending on different sources). Each successive number is the sum of the previous two numbers. So starting with 0 and 1, the next number would be 1, and then 2, then 3, then, 5, etc. (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc.). It was named for an Italian mathematician, Leonardo of Pisa or Leonardo Fibonacci who described the sequence in his book, Liber Abaci. You’ll have to watch the supplemental video explaining how he thought of this number using rabbits.
These numbers lead into a discussion of the golden ratio. This ratio, which goes by other names like golden mean, divine proportion, and mean ratio, is explained in the first video. It’s a little too involved to try to explain in this post. It is an irrational number, approximated to be 1.618.
The Golden Ratio
The class then shows how the golden ratio and Fibonacci numbers can be found throughout art, architecture, and nature. For example, many paintings, including the Mona Lisa, are painted in proportions equal to the golden ratio. The Parthenon, Notre Dame, and other architectural elements were built according to the golden ratio. Also, you can find Fibonacci numbers throughout nature, whether it’s in the seeds of a sunflower, spiral of a nautilus, or the number of petals of most flowers. Even the musical scale can be linked to the golden ratio.
Fibonacci numbers and the golden ratio are everywhere. This class gives a lot of examples and links to different websites to be able to learn more. Ther are also links to videos describing the concepts, including Donald in Mathmagic Land, a 1959 Walt Disney cartoon.
There are also links to different activities, including plans to make your own Fibonacci ruler that gives the golden ratio proportions. The embedded quizlets have different activities including a matching game (which can become a competitive game to see who gets the best time), a learning section offering questions of the items studied in that lesson, test mode (where students have to type in answers that are automatically graded), flashcards (giving main points from the lesson), and spell (where you type vocabulary words from the lesson).
There was a lot of great content. We learned about Fibonacci numbers and the Golden Ratio. The boys liked all of the examples and how these concepts can be used in everyday contexts.
There were links to different videos that went into more detail. Also, there were links to different projects that can be done, including lapbooks.
I liked being able to download the class slides so we could review the material again. There was also a study guide that had questions with an answer sheet at the back.
We weren’t able to watch the classes live, so we missed out on some interaction. Watching the videos after the fact was difficult. The boys thought it would have been helpful to have a little more information provided in the video besides just the slideshow. I think that watching them live would have allowed for more interaction and questions.
The quizlets were more for younger-aged children. The one downside to having to fill in questions is spelling. We spelled one of the answers with a capital letter since Fibonacci was a person, but the answer was counted wrong because it was supposed to be a lowercase letter. That is just one example. We had this happen in a few different cases.
Also, the boys mentioned that there was a lot of repetition and that the classes seemed to be aimed at younger children, not high schoolers.
I think there is a lot of good content included in the Math Connections with the Real World class. It just didn’t work for us, since it seemed to be geared more towards younger children. I believe the suggested age group was listed as 10-18, but I would probably say 10-13.
I glanced at the other classes as well. There appeared to be more great content, but once again, I don’t think it would work well for teenage children. However, I think it would be a great option for those with kids around 10-13 years old, maybe even a little younger if they are an advanced learner. And definitely, pick the live version if at all possible.