Module Eleven

Pentomino Activities

Being that I want to teach kindergarten, I am not really sure that I would have these types of activities within my classroom, but I did find some interesting websites that students can go to and play with pentominoes on their own. 

https://teachbesideme.com/pentomino-blocks-math-game/

http://www.mathsphere.co.uk/fun/pents/pents.html

http://www.transum.org/Maths/Activity/Jigsaw/Pentominoes.asp

http://pbskids.org/cyberchase/math-games/cant-wait-tessellate/

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

https://www.mathsisfun.com/geometry/tessellation-artist.html

During the PowerPoint, I did just fine with learning objectives that were given. But I don't struggle with finding area or perimeter. I didn't have any frustrations until it came to creating the Pentominoes with spatial sense, last week I said I thought I had good spatial sense, this activity makes me rethink my words. How about you Aubrey, did you have any problems?

Pentomino Narrow Passage

I was not all that successful with this activity, the longest I was able to get was 17. I will keep trying though!

Tessellating T-Shirts 

While I have not done tessellating t-shirts before I have worked with students while they were doing tessellations. This article brings to light the fun that can be had while also teaching students of many grade levels important aspects of geometry and the vocabulary associated with the learning. This article points out how preservice teachers can take the learning that they are doing and creates a fun learning for the students they will one day teach. The idea of working with a larger tessellation before bringing the tessellation to the shirt is helpful to the students so they can see how the creation works before doing it. Tessellating is creating an image that can repeat itself without any gapping or overlapping of the image. 

Tangram Discoveries

• Which polygon has the greatest perimeter? …the least perimeter? How do you know?
• The triangle, parallelogram, and trapezoid all have a perimeter of 14 while the square and the rectangle have a perimeter of 12. When you take the larger triangle piece, you can stack the two smaller triangles on it to create the larger triangle. I gave each side a number to represent it and then calculated the outside totals. The larger triangle had sides of 3 and a base of 4 while the smaller triangles had sides of 2 and a base of 3. 
•  Which polygon has the greatest area? …the least area? How do you know? 
• The area for each of these shapes should be the same, as they are each created with the same number of triangles. 

Aubrey, did you get the same results? Do you agree with me, or did I think through this wrong?

Ordering Rectangles 

1. 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. 

As I moved the pieces around I decided that D and E are the smallest, A and B are next, followed by F and G, and finally, C having the largest perimeter.

2. 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. 

I think C has the smallest area, then D, B, F, E, A, and G with the largest area.

3. 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 decided to use color tiles to check my estimations from the previous questions. I found that E and D have the same perimeter with 14, then A, B, and G have the same perimeter of 16 and C and F have the same perimeter of 18.  In my previous assumptions, I thought that C had the largest perimeter but was wrong. I was correct that D and E had the smallest perimeter. 

4. 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? 

I found that C had the smallest area of 8, which I had assumed in the previous question, D had an area of 10, B and E an area of 12,  F and area of 14, A an area of 15 and G an area of 16. I had also guessed that the largest area was with G. Using the color tiles was rather simple and helped to see the difference between the sizes. 

5. 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? 

These activities helped me see that my visual thinking of the differences in the sizes of the rectangles was pretty accurate. However, using the color tiles is what really set the activity apart for me. I have done a lot of area and perimeter with my oldest daughter recently in helping her learn the area of rectangular prisms and pyramids and triangular prisms and pyramids, so I have a hand up on this learning. :) 

Aubrey, what about you, did you have any difficulty putting them in the correct order? 

For Further Discussion

I decided to look up Native American rugs first and came across a site called indians.org. Here it talks about the symmetrical balance that the rug has when it is viewed, an interesting piece of information is that not only is the rug symmetrical from left to right but also top to bottom. Many of the art forms in jewelry and pottery are repeating shapes, these shapes can include triangles, rectangles, and squares just to name a few. Introducing these artifacts and showing the geometric shapes and patterns could allowing students to create their own "works of art".