~~~~Symmetry~~~~

Annenberg Symmetry Module

As humans, we are attracted to symmetry.  If some one has a symmetrical face, they are considered more attractive.

This series was easy for me in the beginning.  As we moved on to rotation symmetry Session 7, B, I realized how important it is to have the right tools required to solve the math problem you are working on.  Our math kits should have come with a protractor and compass. I eventually worked out the problem in my head but to be able to work out the proper angels using the proper tools would have been beneficial and a real time saver.

What do you think Em?  Did you have the right tools?

Pentomino Activities

This was a fun and easy activity.  It brought back memories of my son bringing home a picture similar to the one I made seen below.

Tessellations

Spatial Sense

Use the pentomino pieces to make different size rectangles (Amount of pieces used varies from puzzle to puzzle.)

3 x 10 rectangle

5 x 5 rectangle

5 x 8 rectangle

I was unable to figure out the last two rectangles. Em how many did you find? Was this hard for you?

•4 x 10 rectangle

•6 x 10 rectangle (there are 1339 different ways to do this and it requires using all the pieces)

Pentomino Narrow Passage

My Pentomino Narrow Passage is a whopping 33 in length. This took me a while to figure out. I kept coming up 22 in length. I hope I did it right. Did you have a hard time as well? Do you think this would be an activity you would use in your classroom?

Tessellating T-shirts Article

How has this article furthered your understanding of transformational geometry? 

 I learned that when you tessellate a shape the area does not change but it is clear to see that the perimeter does.  The article also talks about how some pre-service teachers thought that transformational geometry is taught in high school, my son learned this, this year, in third grade.  

What does it mean to tessellate?  To tessellate in two dimensions is the branch of mathematics that studies how shapes, known as tiles, can be arranged to fill a plane without any gaps, according to a given set of rules. 

Look online for different examples of tessellations and share what you’ve found. 

http://illuminations.nctm.org/Activity.aspx?id=3533

http://www.shodor.org/interactivate/activities/Tessellate/

Tangram Discoveries

Take the two small triangles and the one medium triangle.  Using just threes three pieces (but all three), make five different (that is, non-congruent) polygons: 

Triangle

Square 

Rectangle

Parallelogram

Trapezoid

Which polygon has the greatest perimeter?…the least perimeter?  How do you know? 

This was hard to see so I started by listing the shapes by how many sides were showing. I assigned estimated lengths to the sides of the triangles.

Then I added up the sides.  

Which polygon has the greatest area?  

All the polygons have the same area.  We have not changed the size of the shapes we are using; we are just flipping them around.

I love that this moduel was so hands on! Was it easier for you to figure things out as well givin could work with shapes to figure thigs out? 

Ordering Rectangles Activity

Take the seven rectangles and lay them out in front of you.  Look at their perimeters. Do not do any measuring; just look.  What are your first hunches?  Which rectangle do you think has the smallest perimeter?  The largest perimeter?  Move the rectangles around until you have ordered them from the one with the smallest perimeter to the one with the largest perimeter.  Record your order.

D, E, C, A, B, G, F

Now look at the rectangles and consider their areas.  What are your first hunches? Which rectangle has the smallest area?  The largest area?  Again, without doing any measuring, order the rectangles from the one with the smallest area to the one with the largest area.  Record your order.

C, D, B, E, F, A, G

Now, by comparing directly or using any available materials (color tiles are always useful), order the rectangles by perimeter.  How did your estimated order compare with the actual order?  What strategy did you use to compare perimeters? 

 I used the color tiles to compare the perimeters and then just did the math.

D, E, C, A, B, G, F (first numbers)

E, D, C, B, G, A, F   I did not do as bad as I thought

By comparing directly or using any available materials (again…color tiles), order the rectangles by area. How did your estimated order compare with the actual order? What strategy did you use to compare areas?

C, D, B, E, F, A, G (first numbers)

C, D, E, B, F, A, G  WOW I only mixed up two of the numbers

What ideas about perimeter, about area, or about measuring did these activities help you to see?  What questions arose as you did this work?  What have you figured out?  What are you still wondering about?   

 I was worried that with out a ruler I would be unable to figure out the perimeter or area.  I learned to be resourceful and that I could use anything as my tool to measure as long as I stayed consistent. 

For Further Discussion

Multicultural mathematics offer rich opportunities for studying geometry.  Research the art forms of Native Americans and various ethnic groups such as Mexican or African Americans.  What kinds of symmetry or geometric designs are used in their rugs, baskets, pottery, or jewelry?

Discuss ways you might use your discoveries to create multicultural learning experiences.

I looked up all three groups and what wonderful pictures I saw.  I loved the bright color and use of shapes. Many artistes used symmetry in their work. I looked at both folk art and new art.  I could see the influence of the old in the new.  This tells me how influential art is in there culture, how they see and determine what is art. This tie may be able to help me one day bridge a math barer.  I could introduce any of these pictures while talking about geometry.  

Em, I am interested how you see geometry. Dis you learn geometry in your home land or in the States?

Native American

African American

Native American

African American

Mexican American

Mexican American