I have discovered a substantial amount of information upon working with the tangram pieces. I have discovered that several shapes can be made from three simple tangram pieces. I also discovered that the big triangles smaller sides are equal to the small triangles large side. With this being said simply by looking and counting the sides of each shape I could determine which shape had the larger perimeter. I found that the square had the smallest perimeter and the triangle shape has the largest perimeter. I also realized after a moment of thought, that the shapes will all have the same area because they were constructed with the same smaller shapes.
Pentomino Narrow Passage:
The passageway below is 17 spaces long. There are no branches, and it is closed. The area of my passage is 17 cubic units.
I will full admit that I was very frustrated when playing the STACKS scholastic game. I did not understand hope I was supposed to possibly make a rectangle with so many different shaped pieces. I found that my first issue was that I was attempting to created a rectangle that was white in it’s center because of the graph behind it. I then realized that I needed to make a rectangle that was filled in. Once I made that connection, I had a better understanding of what I was supposed to do. This would be a great activity to explore with students, and allow them to do these puzzles as a “finished early” activity.
** I stumbled across this website as I looked for more puzzles. It give several other shapes that can be made from pentominoes!
Upon reading Tessellating T-shirts, I learned a variety of ideas about tessellation. I realized that tessellations are a concept that dates back in history and involved the use of geometry in everyday life. This covers art work, potteries and over styles. To tessellate means creating a pattern with a geometrical shape that fits within the same shape over and over across a plane. I also learned how tessellates can be introduced through items all around us such as tile floors, ceiling tiles, and brick walls. The article demonstrated how T-shirts could be made with the students to express how a tessellate can be used. Here are a few examples that I found of different types of tessellates.
1. Mexican Ancient Art: This rug offers an opportunity to observe Mexican art history as well as investigate geometry. When we look closely, shapes such as hexagons, pentagons, quadrilaterals and squares can be found. We could use this to determine the types of shapes we see as well as finding area using the “bead like” stitching as a unit of measure.
2. Native American Ancient Art: This bowl is a great example of how geometry was used as a form of art. Students could use the repeating of this pattern to determine where or not it is a tessellate or not. The students could also study how this bowl could be changed to meet tessellate features.
3. African American Ancient Art: This beaded jar has the opportunity for great study within the classroom. Students could use this to determine surface area using nonstandard measurement and visualizing tessellates in real objects. I think this would be an easy way for students to examine patterns as well.
Shockey, T. & Snyder, K. (2007). Engaging pre-service teachers and elementary-age children in transformational geometry: Tessellating t-shirts , Teaching Children Mathematics, 14(2), 82-87.
*****Can you see any other ways this art could be used?