BL0G #2

WOAH, look a pretty box!

In my opinion, the applicability of measurement, in terms of area and volume, is unique to the observer. Let’s see what I mean by this. Hopefully the image above got you thinking or questioning what possible relationships the topics of “swimming pools and hot tubs” and “fueling up” have. Or, how they connect at all to “bottoms up” and “water conservation”.

Time to put on your mathematical lens’. The first thing to notice is that these objects and tasks (and many more) are things you encounter and experience on a daily basis. Secondly, you should observe that these objects are made up of combinations of cylinders, prisms, spheres and other geometric figures. Can you visualize them?! Now, think about tasks like filling up your car’s gas tank, or measuring how much chlorine you need to put in your pool to ensure its sanitary and safe. As you fill up a gas tank remember that you need to be aware of how much gas your tank can hold, how much is already inside, how much you can put in, and how much it costs etc. Similarly, when you have a pool you must be attentive to the volume of water in it. Making sure it has the appropriate water level so that the jets and filters can operate successfully. Since the typical person conducts tasks like these so routinely, they easily overlook the mathematics involved. No worries though, it’s still there! In fact, these situations (and many more) surround us daily and are real life examples that implement the key concepts of measurement; measuring area, surface area, and volume.

WHERE AM I WITH MY TOPIC?

             The beauty of mathematics can be seen through its connectivity, which permits the concepts of area and volume to form a linkage with basic geometry, algebra, trigonometry, probability, and even calculus (Here!). Although this gives us a nice open canvas to work with, I will be focusing on area and volume of different solid figures throughout my next couple blog posts. I plan to explore aspects of measurement, through interesting applications. Currently my idea to implement this in a classroom is to use a solid figure to model the shape of a real world object. For example, using a cylinder to model the shape of a shark. In this case, the volume formula being used follows from the typical one students learn early on in middle school: V=bh. [aka. the area of the base times the height: V= (area of the base) x (height)] Since the base is a circle, and we know the area of a circle is: A=(pi)(radius squared) , the formula for the volume of the cylinder will be V=(pi)(radius squared)(h) when you substitute in the appropriate area formula. Looking deeper into this formula for the volume of a cylinder, it can be evaluated (and estimated) if only given the radius and height. I want to focus on three dimensional figures, because we live in a three dimensional world! This leaves the possibilities open (hopefully) for good literacy and texts that can help deepen my content knowledge on the topic. If you are more interested in other solid figures or are interested in more explicit information on volume of three dimensional figures, I would recommend viewing either of the print-based books below.

WHERE DO I WANT TO GO?

I want to know more about using different technology and programs to find the area, and volume of different dimensional shapes and objects. I want to further explore the options that teachers have when introducing problems that involve irregular shapes and figures that aren’t simple solids. As a future teacher, I also want to dig deeper and explore texts, activities, and tasks that will guide me and help my students learn volumes. Specifically focusing on finding good strategies or approaches for students to use when finding the volume for various solids. Specifically, for them to understand where it is derived from and how the volume formulas connect to other formulas for area that they already know. I would also be interested in interactive programs or games that students could do involving this as well.

RESOURCES

. . . Interested in digging deeper with mathematics and what it has to offer? Or, are you searching for intriguing, yet meaningful classroom-friendly texts? ME TOO! Let’s follow our curiosity and explore! The following resources further investigate the beauty of mathematics:

Print-Based:

Sultan & Artzt, The Mathematics that Every Secondary School Math Teacher Needs to Know.

Berlinghoff & Gouvea, Math Through the Ages. A Gentle History for Teachers and Others. (Either 1^st or 2^nd edition.)

Media-Based:

http://www.cut-the-knot.org/geometry.shtml (Cut-The-Knot)

http://schools.amsi.org.au/times-modules/ (AMSI Schools)

As always, I encourage you to share any and all interests, discoveries, comments or questions!

"May Your Life Be Like Arithmetic:

Joys Added -
Sorrows Subtracted -
Friends Multiplied -
Love Un-Divided "