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I can show my work in many ways!

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9/6/14

i loved the bubble model but it was not always smooth sailing & don't think this would be trivial to prove

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9/6/14

I found modeling the problem through using various ways was great.  From the pictorial to the 3-D bubbles.

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We modeled in mathematics by demonstrating our solutions pictorially,

graphically, tabularly, and symbolically.

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The bubble and pipe cleaers show how nature come up with the optimal path. Instead of working and answer on the board. You showed how nature shows the most optimal path. It demonstates their is a relationship between the two.

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We were able to draw multiple pictures of possible answers,

to validate and support our thinking skills.

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Drawing pictures really helped in the understanding of the concepts

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9/6/14

We were able to model mathematics by having

the 3-D model of least surface tension represented by

the bubbles. We are able to understand optimization

by using the concept of "Fermat Point"

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9/6/14

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9/6/14

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9/6/14

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MP#4

Groups modeled their solutions to a similar problem

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9/6/14

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The use of the pipe cleaners allowed us to visually see what was required to join all 4 locations.

Also the drawing of the phone company locations helped us to "see" the problem

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When given a problem many of us created a diagram or picture to help visualize the situation. when we were figuring out the points for the shortest path we orginally started 2D representations which was finalized with 3D path created with soap bubbles!!!

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I tend to teach real-life problems that apply to the lesson, but I rarely give them one of these problems out of the blue and ask them to solve it using whatever they know. I need to start stretching their brains a little bit...