Mirror Image Symmetry from Different Viewpoints

From the YouTube description:

Erica Flapan (Pomona College) explains why it is important to determine whether a molecule has mirror image symmetry, and discusses the differences between a geometric, chemical, and topological approach to understanding mirror image symmetry.

Engaging students: Graphing and symmetry

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Dorathy Scrudder. Her topic, from Precalculus: finding symmetry when graphing a function.

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As a dancer, I love movement and I know my students would be appreciative of not sitting still the entire class period. Therefore, I would have my students get into groups of three or four and have one of them do a back bend (pictured below). The other students would then plot points of the first student’s hands, shoulders, stomach, knees, and feet. The students will have to work as a team to connect the points and find the function of the graph. Theoretically, the graph should be symmetrical if the student is flexible enough to do a back bend. As a class, we will look at the different graphs drawn and functions created and determine which graphs are symmetrical and which graphs are not. We will then discuss what makes a graph symmetrical versus asymmetrical. Picture is found at http://www.dreamstime.com/stock-photo-woman-back-bend-image18008780

 

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How can this topic be used in your students’ future courses in mathematics or science?

Finding symmetry when graphing a function will help my students in their future physics classes and math classes. Symmetry is used in physics when talking about projectile motion. When an object is thrown up into the air, it has a constant horizontal velocity and a constant vertical acceleration. This creates a symmetrical parabola when graphed. By covering symmetry when graphing a function with my students in pre-calculus, they will be better prepared to understand the concepts being introduced in their physics classes. Symmetry in functions is also used in calculus classes when discussing trigonometric functions such as sine, cosine, and tangent. Symmetry is also found in statistics classes when talking about normal bell curves. By introducing the concept of symmetry in graphing functions in pre-calculus, my students will have an easier time understanding trigonometric functions in their calculus classes and bell curves in their statistics classes as well as higher level math classes.

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How has this topic appeared in the news?

Weather has always been a touchy subject, especially for us here in Texas. We love claiming that we have the hottest summers and we “never see snow” (although we all know we have seen it multiple times over the past few years – including the recent ice-pocalypse). In an article by Ricochet Science, the extreme weather temperatures are analyzed. The article is titled “Extreme Weather: Are High Temperatures the New Normal?” It takes a look at the weather patterns over a series of years since the 1950s. In the graph below, we can see how the temperatures changed over the years and how the normal distribution from the first decade needs to be adjusted to fit the “new normal.”

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This information was found at http://ricochetscience.com/extreme-weather-are-high-temperatures-the-new-normal/ .