So this unit in Geometry we are studying Similarity. On the first day of the unit I started my classes off with a quick video of the Washington Monument and said how tourists who like visit such sites like to take home a souvenir of their trip in the form of a scale model. I brought in a mini-Eiffel Tower I bought for my daughter on our trip to Paris and asked my students how it was made. I asked them what would they need to know and what math would be needed to create one. I got a lot of interesting responses including "a 3-D printer" (which of course my school does not have yet but is a new interest I have and hope to one day incorporate into Geometry-How cool would that be when I teach volume, similarity, dilations and symmetry, just to name a few concepts I could incorporate into 3-D printing!) Most of my students agreed to they would need to know the measurements of the the real Washington Monument and many of them came up with the idea that they would need to scale it down "in the same way". I introduced the word "proportional" and the basic idea that "similar" meant "same shape but different sizes". From that point we spent a couple days on graph paper learning dilations and the Common Core definition of Similarity of "2 figures are similar if there is a sequence of similarity transformations that can map one figure on to the next". By the end of the week I gave them the Washington Monument dimensions and told them they had 15 minutes to work in their groups to come up with a scaling factor to make a scale model small enough to fit in our classroom. All I told them was that the ceiling in our classroom was 9 feet tall and they could make their scale model any size they wanted. Below are some of the group whiteboard presentations. I was impressed with the variety of methods groups came up with to arrive at their scaling factors. Some groups chose the easy and obvious 1/100 which would make the model by 5.55 feet tall. Still not small enough to fit into a tourist's backpack but for sure small enough to fit in our classroom. Some groups used a guess and check method and just kept dividing the original height until they got a size small enough to fit in the classroom. Some groups used fractions and some used decimals. One confusion some groups had was understanding that a scale factor is what you multiply by and they were unsure of the concept of using the reciprocal of what they were dividing by to create a scale factor fraction. None the less, all the groups were able to create a scale model and did all of this with out any formal/traditional definition of "Similar figures have corresponding sides proportional and corresponding angles congruent". All they knew was dilations and similarity transformations. I was impressed how applying the new common core definition of similarity and teaching it first really allowed my students to understand what it means for two figures to be similar.
School is barely out and I am getting ready for Summer Regional ILC conference as well as Summer Session Professional Development at my own District office. The life of a teacher never ends and for me summer is a time to rejuvenate my body and reenergize my curriculum. Call me a nerd but I love curriculum development and spend hours of my summer creating lessons that I hope will excite and engage my students in the fall. I hope all attendees at both the TVUSD and ILC conferences find the tech resources I provide both inspirational and innovative tools they can apply in their own classroom next fall. Leave me a comment and let me know what you are planning for your classroom next year. |
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