Module Eleven

Pentomino Activities

Before going on the website to do this activities I thought they were going to be super easy. Boy was I wrong. It took me multiple tries to figure out 1 way to get them to work on the easy level. I tried multiple times for a good 10 minutes on the medium level. I even asked my boyfriend to come try and he also had a hard time and ending up giving up after a couple tries. This made me feel a little better about not being able to figure it out. haha One thing I did notice doing this activity was that if i was able to use certain pentominos more then once it would be a lot easier to do. But that isn't the case. I tried the hard one once just to see what it looked like and as you can guess I was unable to figure it out. I became very frustrated with the petomino spatial activities as I tried several times and just couldn't figure it out. I feel like if it is hard for me how can I expect my elementary students to be able to do it. If I had them do activities like this I would allow them to work in partners that way they could use two heads instead of one to figure it out. 

Did you have a difficult time with these activities? Do you think these activities would be easy enough for elementary students to do? If doing them with elementary students would you 

Pentomino Narrow Passage

Im not entirely sure I did this right. I don't know what Dr. Higgins meant by it couldn't have branches. Mine mine have 1 branch but I tried so many times and could nto figure it out another way. So this is my narrow passage. It is 21 tiles long. 

Did you think this activity was hard? 

Tesselling T-Shirts

This article talks about how before working with students preservice teachers need to learn the task them self. They need to do and understand the activity before they can try to help students understand it. It then talks about how to make math fun for the students by doing activities using tessellating to create their own t-shirts. This is something that I think I would like to do with my future students, it sounds fun and they will learn more when doing an activity they actually like. 

Tessellate means to do things like rotate, flip, slide, ect. to a shape. 

Here are some examples I found on google of tessellations:

Tangram Discoveries

I assigned numbers to each length that you see in the shapes we created. I had the base of the big triangle be 4, the base of the small triangles be 3 along with the sides of the big triangle. I then had the sides of the little triangles be 2. I got the perimeter for the triangle and square to be 12. The perimeter of the trapezoid to be 13, and the perimeter of the triangle and the parallelogram to be 14. For area I got the trapezoid, rectangle, and parallelogram to be 8. While the area for the triangle and square to be 9. I don't think this can be right since all the same pieces were used and took up the same amount of space. 

What did you get when doing this activity?

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.

I think that rectangle E has the smallest perimeter. I think rectangle E has the largest perimeter. The way I have them is (biggest to smallest) G, F, A, B, C, D, E

 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. 

Smallest area I have is C. Biggest area I have is G. The order I have them is (biggest to smallest) G, A, F, E, B, D, C

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? The actual order is (smallest to biggest) D & E at 14,

 A, B, & G at 16, and then C & F at 18. In my guesses I had E having the smallest perimeter which is partly true as it is tied with D for the smallest. I also had D right in front of E. I had G being the greatest which now after measuring I see isn't the case. 

I used the color tiles and filled them in each rectangle then counted the number of tiles for the across each side to figure out the perimeter. I found this way to be super easy. 

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? 

The actual order of the area of these rectangles are (smallest to biggest) C at 8 , D at 10, B&E both at 12, F at 14, A at 15, and G at 16. 

In my guesses I had C having the smallest area so I got that correct. I also had G having the largest area. 

I again used the colored tiles to figure out the areas of these rectangles. I found it was very quick and easy to do it this way. 

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? Share your responses to all the questions in 1-5 in your small groups on the discussion board. 

I knew this before the activity but it reminded me that even though shapes have the same perimeter doesn't mean they will have the same area and vice versa. I think this is something that needs to be highly stressed to students when first learning about area and perimeter. 

Did you have a hard or easy time with this activity? I thought this activity was one of the easier ones we have done this semester. 

For Further Discussion  

Many Native American Arts have tons of geometric designs that repeat them self.  As you can see in the pottery, bracelets and rug I posted they all have multiple shapes that are repeating. They use triangles, rectangles, squares, and many more. They make it fun by using all the different colors. The patterns are also fun because of the way they mix up the different shapes in their patterns. 

Do you live this kind of art? Would you wear bracelets like the ones posted? Would you have rugs or pottery like this in your house?