by Debi Wright

for Walden University

MATH 6682K- 2 Geometry

Connections A group of fifth grade students were given disposable cameras and asked to photograph shapes in their environment. Many of them took similar pictures. I chose one photo of each shape type. Shapes Everywhere Tessellations are a tiling of a plane using one or more shapes that do not overlap or leave gaps between shapes, typically arranged in a pattern that repeats. Tessellations I worked with a group of third grade students to do an activity with geoboards. They recreated shapes from a picture and then created their own designs. One of the aspects of the activity I focused on was the communication between partners. Geometry Activity Why do I need to learn geometry? Games that use geometry Jewelers

Car designer

Construction worker

Optical lens maker

Interior designers

Astronomers

Robotics engineer

Plumber

Landscaper

Medical researcher

Window maker

Radiographer

Computer aided designer

Artist Other careers that use geometry There are many careers in the Science, Technology, Engineering and Mathematics industries. Here are just a few that use geometry and measurement daily. Student D's Photos A group of fifth grade students were asked to look for tessellations and photograph them. Tetris: uses shape transformations Photo retrieved from http://tetrisaxis.nintendo.com/ Battleship: uses coordinate pairs Photo retrieved from http://redpandagamer.wordpress.com/ Angry Birds: uses angles and parabolas Photo retrieved from http://redpandagamer.wordpress.com/ Tessellations can be found in nature.

Photo retrieved from

http://www.strangezoo.com/content/item/150323.html Photo retrieved from http://patternizer.wordpress.com/patterns/mathematical-patterns/tessellation/ Photo retrieved from

http://www.greatschools.

org/students/academic-skills/slideshows/3713-fourth-grade-math-slides.gs?page=9 Photo taken by D.Wright Irregular tessellations are symmetric designs featuring animals, people, figures, etc, which fit together in repetitive patterns like a jigsaw puzzle.

M.C. Escher was the pioneer of this form of art. Tessellations such as these are often referred to as Escher-style tessellations. Tessellations. Retrieved from http://www.mathpuzzle.

com/Tessel.htm The students worked in pairs to recreate shapes onto the boards. One student gave the directions of where to place the rubber bands while the other student placed the rubber bands. Many of the students were able to give clear directions to their partners. One pair of students had difficulty communicating. Student C was able to describe where to place the band, but Student D preferred to look at the example sheet. When the situation was reversed, Student D was frustrated at Student C, who was not as fast, and preferred to reach over and place the band. The students were then allowed to create their own designs with the bands. Video Game

Designer Civil

Engineer Civil engineers design and construct buildings, roads, and bridges. As population grows, the demand for civil engineers will increase. They are also needed to repair roads, bridges, and other structures.Civil engineers can earn about $36.00 per hour. Science, Technology, Engineering and Math (STEM) Careers (1999-2102) Retrieved from

http://www.iseek.org/careers/stemcareers.html Video game designers plan, design and create video games. Video game designers can earn around $36.00 per hour. Fashion Designer The Art Career Project. (2012) Retrieved from

http://www.theartcareerproject.com/combine-work-and-play-information-about-video-game-design/93/ Fashion designers need geometry and measurement to make clothes. Clothing is made by taking a three dimensional shape and converting it into a two dimensional pattern. The median salary for a fashion designer is around $31.00 per hour Passy World of Mathematics (2012) Retrieved from http://passyworldofmathematics.com/jobs-with-geometry/ Chron.com (2012) Retrieved from

http://work.chron.com/much-fashion-designers-make-annually-1711.html Passy World of Mathematics (2012) Retrieved from http://passyworldofmathematics.com/jobs-with-geometry/ Van de Walle, J., Karp, K., Bay-Williams, J. (2010). Elementary and Middle School Mathematics: Teaching Developmentally (7th ed.)(p. A-8). Boston: Allyn & Bacon. Student A's Photos "I chose this picture because it had two different size circles on one thing. This picture reminded me of a pyramid with the top part cut off. Each side is a trapezoid. This is one of those balls at the Target stores. When I was little, I liked to try to roll them. This is kind of like a diamond. The sides are not the same size though, so I guess it is a rhombus." Student A. "I took this picture because it had a lot of different shapes on one thing." Student B. Student B's photo Student C's photos "I liked how this shape had many sides to it. This picture has two shapes. The outside circle is one and the arrow in the middle is another." Student C. "I knew the other kids were going to have circles and squares. I wanted to have something different like the star." Student D. Student E's Photo "This was outside of Walgreens.I liked how the roof made an angle besides having the other shapes in there." Student E. The next thing we did was to get pictures of tessellations. All five of the students took a picture of bricks. "This is a garbage can at Target."

Student A. "This is the

cover of a sewer."

Student C. "This is the fence in my back yard" Student D. "When you said tessellations were like tiles, my mom and I went to Lowes and saw alot!" Student E. Yellow diamondback snake Giants Causeway

Antrim, Northern Ireland Honeycomb Pineapple. There are three categories of tessellations.

Regular

Semi-regular

Irregular. Regular tessellations are created with regular polygons that are congruent. Semi-regular tessellations are created with two or more regular polygons that are identical at every vertex. Photos retrieved from Tessellations.org Tessellations I created using an online tessellation program. http://www.pbs.org/parents/education/math/games/first-second-grade/tessellation/ When creating the star, Student A said to "put the loop on the third peg. Now stretch it to the corner."

Student B replied with, "Which corner?"

Student A replied back with "either one, we're going to do both corners."

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# Geometry Connections

Presentation for Elementary Mathematics - Geometry and Measurement (MATH - 6682K - 2)

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