#derivingformulas

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Inspired by Duckworth’s “The having of wonderful ideas” I encountered a mathematical experience…. One of the greatest qualities of a great teacher is learning from your students as much if not more than they learn from you. Over the past week I’ve discovered many new innovative uses for my tools. Actually my honors geometry class discovered the many uses. We started Pythagorean theorem and special right triangle’s sometime last week. Most of the shapes I printed included right triangles within them. The main objective for my tools as previously posted was to derive area formulas. Yet, as I sat back and watched my kids play with my tools one of them exclaimed, This is just like the ramp question Ms. B, it would have been so much easier to understand if I saw this.

Eureka… Something dawned on me

As explained by McLuhan in “The medium is the message” it becomes less about the tool and more about how kids interact with the tool. What do YOU see when you look at the tool. What experience are you having with the tool. How does it inspire you. As a project I’m having my kids think of other ways this tool may have helped strengthen their knowledge in past units. How could it be applied if at all. By doing this I believe they will enlighten me to new creative ideas I would otherwise never have thought of.

[mathbymaking-blog]

Finally got my kite and rhombus. It took a while with the difficulties of getting to campus to pick it up and the 3d printers going on a fritz but there they are. I didn’t expect them to be so tall so I’ve decided to reprint them and change the dimensions. I took it for a spin today. The kids loved it. Especially after they heard I created it. I think I’m going to modify my project a bit. I like the idea of the stencil but I believe my initial idea of printing out pieces that would be attached together with some form of adhesive may be better for the visual learners. I re designed my pieces and sent them to print. Hopefully I can get them sometime this week.

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A piece of pie

I’m still trying to create my stenciled pieces for my “deriving area project.” You would think cutting a circle into 36 congruent sector would be a “piece of pie” (pun intended) but it’s proving rather difficult. I currently have my regular polygons, rectangles and parallelograms all set and ready to go, but the circle has me stumped. Just as I am finding cutting up this circle into pieces difficult, I imagine the students might as well. I will send the first version of my completed stencils to print and see if any modifications need to be made. After all, there is about less than 2 weeks till I test out my project. I imagine my honors students may catch on rather quickly. Since they move a lot faster then my regular geometry and low level class, I shall consider them my beta group. This will give me enough time to modify the project if necessary to reduce limitations previously overlooked. Since I will be teaching, I believe recording the lesson and evaluating it’s effectiveness would be the best method for reflection. Often as teachers we do not see everything going on in the class. Recording the beta group will allow me to analyze the results of my experiment.

As time draws near I find myself excited and confused. As mentioned in an earlier post, I as a mathematically inclined individual may see the connection, yet I question the clarity of the objective for those who may be mathematically challenged. Is it challenging enough to evoke thought, yet appropriate enough to yield desired results? Well I guess we will find out soon enough…

[mathbymaking-blog]

Discovering Geometry

I’ve always considered myself a creative person but “creating” certainly has me stumped. I’ve just started “tinkering” and I must say it is alot of fun. The hardest part of it all is not the designing but rather the thought of what to design.

Idea 1: Composition of solids used to device a formula or a method in which to accurately calculate the volume of an irregular solid.

Creating a prism or cone in which a letter has been removed and students must calculate either the removed volume or the remaining volume.

Idea 2: A spin on the composition of solids but with polygons rather than prisms. Using a polygon or a composition of connectible polygons to derive an accurate formula for calculating the area of the shape. Using manipulative(s) to see the relationships between every polygon and a rectangle and being able to accurately devise a strategy to turn these polygons into rectangles.