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MTED 5318 - Meeting 4 (September 16)

by: Mitzelle Escobar

MTED 5318 - Meeting 4 (September 16) MTED 5318, Teaching and Learning with Techonology in the Mathematics Classroom

Mitzelle Escobar
GPA 4.0

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About this Document

This week we covered the subject of Symmetry and did an activity with an equilateral triangle. Enjoy!
Teaching and Learning with Techonologh
Dr. David Carrejo
Class Notes
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This 3 page Class Notes was uploaded by Mitzelle Escobar on Thursday October 1, 2015. The Class Notes belongs to MTED 5318, Teaching and Learning with Techonology in the Mathematics Classroom at University of Texas at El Paso taught by Dr. David Carrejo in Fall 2015. Since its upload, it has received 17 views. For similar materials see Teaching and Learning with Techonologh in Education and Teacher Studies at University of Texas at El Paso.

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Date Created: 10/01/15
MTED 5318 September 16, 2015 Week 4 Homework 1 Due 9/23 ­ Will be hard copy and turned in next class ­ Can find it tomorrow on black board by late tomorrow (9/17) Symmetry PowerPoint Today we will/Agenda ­ Cover more topics on Geogebra ­ Last week we looked at  ­ Today we will talk about symmetry (something he finds very important) o want to have some discussion on the conceptual level  o when in high school: they take it for granted and then realize that students are not  visualizing certain things symmetrically, they have a confused look.  o Want to connect symmetry and algebra (there is a key connection between the  two) – especially important for people teaching higher level mathematics Symmetry  ­ Can by applied at pedagogical perspective ­ This is something that is normally pushed through as a pedagogical framework when  looking at science.  ­ Regardless at what level they are working at, we want something that will have them  involved and engaged  The Five E’s (Polygon Math – 2D symmetry) 1. Engage  a. What is symmetry? What is “symmetrical”? i. Not so difficult, it can be as simple as showing something on the  computer and you start asking questions. ii. With relation to symmetry, sometimes just asking a question to  students is:  1. “what are the things that are naturally occurring” 2. “what are things in the natural world that have symmetry” iii. Therefore, it is not too difficult to get them active b. How can we tell if an object has symmetry? i. What is symmetry? What are we talking about? 1. Reflection is a type of symmetry, but what kind of symmetry a. We have reflection, translation, rotation, and dilation   2. Symmetry is related to motion in the plane a. The way we visualize it is that it is actually a motion,  which means  b. When looking at the symmetrical work, students and  young children always see reflection vertically; because that’s the way they see life.  c. Mathematically, we teach symmetry as a flip (within  the middle of the object) d. ** Patty paper can be helpful in the classroom (sell by  the bulks) and you can have hands on activity and is  literally like students picking up symmetry.  e. Can turn the page 180 degrees and 360 degrees (360  degrees is called the do nothing rotation because you  see no difference – you are back to where you started) 2. Explore ( the hands on part) a. Objects/Materials: i. Square and triangle templates ii. Construction paper iii. Journals iv. WORK TOGETHER!!! b. Directions: i. Cut out the paper triangle and the paper square and label corners  (vertices) on both sides where the letters are the same on each side ii. Determine the lines of symmetry and the rotational symmetries for  each  ** what is an angle? ­ teaching an angle can be represented through a turn (if students can visualize it through a  turn, then connect it to the circle (creation of 360 degrees) ­ tie it to geometry and show it as a sense of motion  ­ how many rotation symmetries does it have?  infinite  Transformations in the plane ­ begins to involve a number of things:  o what happens when you reflect something along the origin  For the time being, think of algebra ­ what happens when you start combing symmetries  ­ what happens when you combine L1 with R1 becomes L2 Key for Symmetry with a Triangle Flipping by Symmetry (Vertices) Rotation Symmetry L1:  AA,   BC,   CB R1 (120 degrees): AC,   BA,  CB L2:  AC,   BB,   CA R2 (240 degrees): AB,   BC,   CA L3:  AB,   BA,   CC R3 (360 degrees): AA,   BB,   CC *Multipl R1 R2  R3 L1 L2 L3 y R1 R2 R3 R1 L3 L1 L2 R2 R3 R1 R2 L2 L3 L1 R3 R1 R2 R6 L1 L2 L3 L1 L3 L2 L1 R3 R1 R2 L2 L1 L3 L2 R2 R3 R1 L3 L2 L1 L3 R1 R2 R3 Through many activities, such as the one above (along with area and volume) ­ Students can begin to see proofs through a different perspective.  Algebra ­ a really general term ­ algebra of the real numbers ­ – a great link for a refresher and to help students  **if it weren’t for geometry, we would not be able to have algebra Computer Time with Geogebra ­ Packet on Symmetries (only covered the first two pages) ­ The rest of the packet can be homework, you can complete/review the packet at home  (make sure to download Geogebra on your computer)


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