In Your Classroom: "The Grapes of Math"

by Brian McCombs     Department: In Your Classroom

"The Grapes of Math" segment brought forward a couple of wonderful math ideas.  The first one that I thought of was the use of modeling data.  The use of yeast in the fermentation process of making wine is an example of a substance being used to speed something up.  How does yeast work?  How fast does it work?  It has been shown that yeast, if left alone in a warm solution containing sugars, will multiply quickly.  My question to my students would be, "How quickly?"  As a class, we could get several containers of a solution of water and sugar.  We could run the experiment two different ways.  First, we have equal amounts of water in several containers.  We could add varying amounts of sugar to each container, thus making sure the ratios of water to sugar in each solution were different.  In the second set of trials, we could have equal amounts of water in each container and add varying amounts of sugar to each.  In both cases, we'd add similar amounts of yeast to the solutions.  We could determine the length of time it took to increase by 50%, 75% or 100%.  The students could plot these data sets for each set of trials.

Upon seeing the data sets, they could estimate what type of regression equation would fit the data best.  Would it be a power function?  Exponential?  Logarithmic?  Linear?  It would be up to them to decipher the information in front of them.  When they have come to the conclusion of which equation is "best," they would demonstrate how to use this equation to predict amounts of yeast, water, and sugar required to double the size of a solution/mixture.  They could experiment with their predictions to see how accurate they were.  Finally, I would expect a short paper explaining how they got their data, the graphs that ensued, the hypothesis/equations they got because of the data, their predictions, and the follow-up experiment and conclusions.

A second idea to use in an Algebra 1 or Pre-Algebra class would be the analysis of slopes.  In the video segment, they spoke of how the first winemaker analyzed the slopes of the hillsides of his land and tried to find the area that was the most similar to the hillsides in France.  This is a great practical example of the use of "slope" in the real world.  In a classroom, we could have several photos of mountains, hills, or inclines from photos or the internet.  Using a program, such as Geometer's Sketchpad, we could label certain points on each hillside.  Using the formula for slope, the students could determine which sections of each hill had identical slopes.  Or it could be used as an introductory lesson by having students determine visually which ones looked the same, and then come up with a method for testing their prediction.

The segment also made me think of a wonderful children's book, The Grapes of Math, by Gregg Tang.  My own children enjoy reading this book (designed for children in grades 3 through 5), and they like solving the picture and word riddles.  A review by the School Library Journal said:

Picture puzzles accompanied by clues in verse encourage readers to embark on some inspired problem solving.  Each riddle and an illustration are set on a two-page spread.  The goofy rhymes set a humorous tone.  Through patterns, grouping, and creative thinking, the problems to be solved will have children adding, subtracting, and multiplying.  Throughout, Tang sneaks in useful visual strategies that can be used in solving other computation problems.  Bright, appealing computer images add to the playful nature of the title.  The solutions provided at the back of the volume include a miniature color reproduction of each picture and a clearly diagrammed answer along with text outlining the process employed to arrive at that answer.  A fun addition to classroom and library shelves.
-- Lucinda Snyder Whitehurst, St. Christopher's School, Richmond, VA

There were a plethora of websites teaching slope analysis and projects.  One is part of the Hotchalk's Lesson Plans Page website.  It is a lesson written by Mikel Whiting.  His lesson has students exploring real world situations as it relates to slopes, such as stairways and inclines.  He details a 6-part lesson, where students are actively engaged in determining the conceptual basis of what slope is, how to find it on a graph, and finally how to derive the equation.  It is complete with assessment references and suggestions as well.

A second website I found to be useful in my statistics and Pre-Calculus class is the USA Today's education website.  The lesson, "Heat Watch," gives two more hyperlinks.  One is for the student information, handouts, questions, graphs, etc.  The other is for teacher resources, follow-up ideas, web site information, graphs, etc.  It is very thorough, informative, colorful, and pertinent to the student's daily lives.

See below for a really cool video on the fermentation process (for beer, not wine) which shows the several weeks-long fermentation process in just a few minutes.

If you have any suggestions regarding the segment, "The Grapes of Math," and its use in a mathematics classroom, please send them in and post a comment.  I'd love to discuss them.

Additional WIRED Science Video Segments
Don't forget to check out our Video Section for other segments from WIRED Science that you can use in your classroom.

Tags:

+ Add Comment

Post your comment

Name
Email Address
URL

Remember personal info?

Captcha:

Type the characters you see in the picture above.