Math 246 Introduction to Symmetry: Focus on Line Symmetry

Math 246 Introduction to Symmetry: Name: ______

(5 pts.) Lab Focus on Line Symmetry

Complete the Following and upload your results to your dropbox on line symmetry by 8 am Tues. Oct. 16th. Enter your text in a deep yet different color so easy to distinguish your results on this lab from the questions.

1. Read pages 612 -615 in section 9.4 of your textbook on reflection symmetry.

2. View the interactive video and do all the activities within the video (will give you feedback) at the Links Learning for Kids: Math: Illustrated Lessons on Line Symmetry at: (sound and video work well in Firefox). This includes 3 activities and a final activity for children.

http://www.linkslearning.k12.wa.us/Kids/1_Math/2_Illustrated_Lessons/4_Line_Symmetry/index.html

3. How does this site define line symmetry?

4. One of the activities relates to finding lines of symmetry for capital letters of the alphabet. Let the universe be the set of capital letters (in Times New Roman text font, no italics.)

The universal set is {A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z}

Let's describe when diagonal line symmetry occurs. If a design may be folded on a line that is not horizontal, nor vertical, on the original design and the 2 halves formed match each other exactly, then the design has diagonal line symmetry.

Use these set names: H = {capital letters that have horizontal line symmetry}, V = {capital letters that have vertical line symmetry}, D = {capital letters that have diagonal lines of symmetry}, N = {capital letters that have no lines of symmetry}.

a) List all the members of H using set notation: {B, }

b) List all the members of V using set notation: { }

c) List all the members of D using set notation: { }

d) List all the members of N using set notation: { }

For parts e – h, list the members after the set operation takes place.

e) List all the members of V U H using set notation: { }

f) List all the members of V Ç H using set notation: { }

g) List all the members of H - V using set notation: { }

h) List all the members of V - H using set notation: { }

i) Describe in words how set V relates to set H. Do they overlap somewhat, are they disjoint or is one a subset of the other (if so, which is the subset).

5. Create a Venn Diagram showing this relationship. (Only need to include set V along with set H in the Universe.) Place one example letter in each region of your Venn diagram below (no need to include all the letters). Be sure to label V as well as H. This diagram should show if the 2 sets overlap, if they are disjoint, or if one set is a subset of the other set.

One free Venn diagram creator on the web is at read write think.

http://www.readwritethink.org/files/resources/interactives/venn/

The first template asks for the name of the topic, student name, and the name of each set. Here is an example of the initial setup for the diagram:

In this applet you enter one example at a time as a Concept (no description is required for each example). Then you drag the example onto the area of the Venn where it would be placed.

The example is moved as a rectangular textbox. See the letter A as an example below.

If you found a nice Venn diagram applet that you used instead, include the link to the website below:

Now copy and paste your Venn diagram that you created below. Do NOT turn this in as a hand drawn diagram. Use an applet or software to create this. Kidspiration found on computers in the WEB may also be used to create this.

6. How many total lines of symmetry (horizontal, vertical, diagonal) do each of these capital letters have? The first one is done for you (this one also shows the line(s) of symmetry.)

a) A __1__ b) B ____ c) Z ____ d) H ____

e) J ____ f) W ____

g) O ____ (careful this is an oval not a circle)

7. What traffic sign shown in the video (item 2 above) had the greatest number of lines of symmetry? Also, what is the name of the shape of this sign?

Sign ______Shape ______

How many lines of symmetry does this sign have? ______

Note: Line symmetry is also referred to as folding symmetry, flip symmetry, mirror symmetry, or reflection symmetry. Line symmetry is only 1 type of symmetry. We will also focus on the math teacher content pedagogy for teaching turn (rotation) symmetry in this unit. We will focus on the symmetry of 2-d shapes (designs that lay in a plane).