Module 11
Hey Jess! I hope you had a great Easter weekend!
Pentomino Activities
The activities in this PowerPoint did not really cause me any frustration, I found them interesting and enjoyed them! It was a great review of symmetry and the different types of symmetry. I found a site titled Super Teacher Worksheets (superteacherworksheets.com) that offered a wide variety of activities, worksheets, and lessons for working with pentominoes and tessellation! Most of what I found was for an 8th grade curriculum, so it would not really apply to the 5th grade class I am teaching in, but some of it can be simplified to fit younger grades. For younger grades just starting out, I found a ton of worksheets and activities similar to the one below. The students have to play around with the shapes to make it fit into the animal or puzzle provided. This is a great and fun way to introduce these topics and I would definitely use this in my classroom!
Would you use an activity like this? Does it seem like a good introduction? It looks a bit simple at first but may be harder than we think to make them all fit.
Pentomino Narrow Passage
After playing around for what felt like a very long time and making passage after passage, I got one that was 22 spaces. I admittedly got frustrated and googled ideas, so I can't take credit for this one. I kept finding ones that were around 17 until finally getting this one. I think I took this a bit too seriously and got let myself get a little too frustrated. Was this challenging for you too?
Tessellating T-Shirts
I have not done this myself before but I have seen things similar. This article showed me new ways that geometry can be used in the classroom in an educational way using fun and exciting activities. To tessellate means to move shapes around to fit them together to create a new shape. This article showed me how to use this information in a classroom setting. I was able to see how the students were involved in the lesson and to view how the students changed their thinking about tessellations. They were able to create t-shirts that displayed designs that were created from their tessellations. It was important to show the students how their designs were created from their own tessellations with shapes. Below are some intricate examples that I found interesting!
Tangram Discoveries
The triangle, parallelogram, and trapezoid have the same perimeters, making them the largest, because they use the largest sides of each triangle for the perimeters.. I drew these out to figure it out and to check my work. I made each of those by rearranging the large triangle with the two smaller triangles, which may make you think that every shape would have the same perimeter, but some shapes use the longer sides of the triangles while other use the shorter sides. The square and rectangle will have the smallest perimeters because they use the smaller sides of the triangles on the exterior. As for the area, they would all be the same because they use the exact same shapes to make them up.
Ordering Rectangles
1. My prediction in order from smallest to largest would be D, E, A, B, F, G, and C.
2. My smallest to largest area prediction would be C, D, B, F, E, A, and G.
3. I found that E and D have a perimeter of 14. A, B, and G have a perimeter of 16. Finally, C and F have a perimeter of 18. I thought that C would have a larger perimeter than the rest of them, but I was off by a little.
4. C had an area of 8, D had an area of 10, E & B had an area of 12, F had an area of 14, A an area of 15, and G had an area of 16. My prediction was slightly off with E, but the rest were correct.
5. This activity helped me to see that while the visuals can give you a good idea, they are not completely accurate. Were your visual predictions more accurate than mine?
For Further Discussion…
Using things like this is a great way to integrate culture and social studies into mathematics. I know my 5th graders would love studying geometry in this way. Below are some Native American rug designs I found while researching. They use patterns of repeating triangles/diamonds.
Pentomino Activities
The activities in this PowerPoint did not really cause me any frustration, I found them interesting and enjoyed them! It was a great review of symmetry and the different types of symmetry. I found a site titled Super Teacher Worksheets (superteacherworksheets.com) that offered a wide variety of activities, worksheets, and lessons for working with pentominoes and tessellation! Most of what I found was for an 8th grade curriculum, so it would not really apply to the 5th grade class I am teaching in, but some of it can be simplified to fit younger grades. For younger grades just starting out, I found a ton of worksheets and activities similar to the one below. The students have to play around with the shapes to make it fit into the animal or puzzle provided. This is a great and fun way to introduce these topics and I would definitely use this in my classroom!
Pentomino Narrow Passage
After playing around for what felt like a very long time and making passage after passage, I got one that was 22 spaces. I admittedly got frustrated and googled ideas, so I can't take credit for this one. I kept finding ones that were around 17 until finally getting this one. I think I took this a bit too seriously and got let myself get a little too frustrated. Was this challenging for you too?
Tessellating T-Shirts
I have not done this myself before but I have seen things similar. This article showed me new ways that geometry can be used in the classroom in an educational way using fun and exciting activities. To tessellate means to move shapes around to fit them together to create a new shape. This article showed me how to use this information in a classroom setting. I was able to see how the students were involved in the lesson and to view how the students changed their thinking about tessellations. They were able to create t-shirts that displayed designs that were created from their tessellations. It was important to show the students how their designs were created from their own tessellations with shapes. Below are some intricate examples that I found interesting!
Tangram Discoveries
The triangle, parallelogram, and trapezoid have the same perimeters, making them the largest, because they use the largest sides of each triangle for the perimeters.. I drew these out to figure it out and to check my work. I made each of those by rearranging the large triangle with the two smaller triangles, which may make you think that every shape would have the same perimeter, but some shapes use the longer sides of the triangles while other use the shorter sides. The square and rectangle will have the smallest perimeters because they use the smaller sides of the triangles on the exterior. As for the area, they would all be the same because they use the exact same shapes to make them up.
Ordering Rectangles
1. My prediction in order from smallest to largest would be D, E, A, B, F, G, and C.
2. My smallest to largest area prediction would be C, D, B, F, E, A, and G.
3. I found that E and D have a perimeter of 14. A, B, and G have a perimeter of 16. Finally, C and F have a perimeter of 18. I thought that C would have a larger perimeter than the rest of them, but I was off by a little.
4. C had an area of 8, D had an area of 10, E & B had an area of 12, F had an area of 14, A an area of 15, and G had an area of 16. My prediction was slightly off with E, but the rest were correct.
5. This activity helped me to see that while the visuals can give you a good idea, they are not completely accurate. Were your visual predictions more accurate than mine?
For Further Discussion…
Using things like this is a great way to integrate culture and social studies into mathematics. I know my 5th graders would love studying geometry in this way. Below are some Native American rug designs I found while researching. They use patterns of repeating triangles/diamonds.
Hey Megan! I I agree that the pentomino activity could definitely be modified for multiple grade levels. I think there is always a way to introduce topics to younger students to familiarize them, without overwhelming them. The narrow passage activity was also challenging for me. I also allowed myself to get ahead and frustrated when I didn't need to be. I thought the ordering rectangles activity was interesting and really got me thinking of ways to incorporate something like this into the classroom. My predictions were also slightly off, once I found the actual measurements I saw where it was easy to get mixed up with my estimates. I think something like this is important to keep in mind to allow students to play around with concepts before just telling them what is right and wrong. I also love the rugs you found, I didn't think to look for rugs! I went straight to pottery and other visual art pieces. This is just another example that geometry really is all around us and we can always be on the lookout for ways to use it in fun ways in the classroom!!
ReplyDeleteAwesome post :)