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The hands on activity helped me to visualize how math problems can relate to real life. Making the model was also very fun, it gave me a pretty good image of 3 dimensional triangles.

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The hands on strategy was a bit confusing, and it seemed like too much with all the strings, straw, and it was just a little annoying. I prefer to just see it in my mind, which is a much easier way to learn for me. My understanding is at about a 3, because I know what it is, and how to use it, but I won’t always be perfect with it.

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I liked to learn the theorem both ways because to me, there really isn't a difference. I think my level is a 3 because I only know the basics of the theorem and converse and how to prove them.

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The hands-on way to learn the theorem not only allowed me to visualize how the theorem works but I was able to remember how to prove the theorem because of the unique lesson and understand how it can be applied in real life. I do believe that because of the roof activity in addition to the activity with the flat square and 4 triangles that I understand how to prove why the theorem works through these demonstrations.

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I think it really helped me visualize the concept by doing to project. I really got an in depth understanding of how and why the theorem works the way it does. It also helped to do some arithmetic problems. I liked learning the theorem visually. I think I know the theorem but sometimes get confused so I would rate myself 3.

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So what i think is it was helpfull and the stargtys all helped me and i found out there are multiple ways so but when I visualized  i got go and try different numbers for the abrbathec problem i got to try negative and positive numbers.

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1) I prefer the traditional way. It is the way I have known for some time now. The formula helped me better understand why the pythagorean theorem works. It is a better representation of the relation of square-length sides of triangles, in my opinion.
2) I believe my level of understanding the pythagorean theorem is a 4. I think I fully understand the pythagorean theorem and will be comfertable applying it and even teaching it to another person.

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1) I prefer using the traditional way because I am used to it, and because I have more experience with it. Also, I am not very comfortable with using the model, and feel that it doesn’t help as much as a textbook.
2) I think that my level of understanding is a 3 because I am pretty comfortable with the theorem, and because I have been doing the homework problems. However, I am not very comfortable with the 3D model.

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1) This activity did help me visualize the different types of right triangles in a triangular prism; however, if I got a 3D model drawing of the same thing, I could have visualized it as well. The model just was something tangible to work with and the different sizes of right triangles were clearer.
2) I would rate myself a 3 on the Pythagorean Theorem because I get how the equation works and everything, and I could apply it to real world problems. I don’t think I could teach it to someone, and the proof of the theorem doesn’t really make sense.

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This activity helped me because it was a hands on activity which helped me see, feel, and turn the model. This helped me because rather than visualizing it in my head, I could see it in a 3-d model.

Overall, I would rate myself a 4 on the Pythagorean theorem. I can calculate the squares and square roots of numbers and apply them to the formula aˆ2+bˆ2=cˆ2

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1. I liked the textbook, non-hands-on version of learning the Pythagorean Theorem. I was not here on Friday, so I can’t attest to the building of it, but when I saw the model, I did not understand what is was meant to represent. After someone told me it was right triangle, I was still confused. Then I was finally explained to by my group that the carboard represented one leg, the straw in the middle the second leg, and the yarn the hypotenuse. Simply remembering a^2 + b^2= c^2 is much easier than looking at this model and trying to measure/calculate. I took nothing away from this model.
2. I understand the Pythagorean Theroem and its converse very well. I can easily find the steps needed to calculate said theroem. I would rate myself a 4. I feel comfortable enough to, in theory, teach it to someone else although the results would be doubtful.

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This activity helped me because I could feel the model, and that helped me learn. Also, I could see the 3D picture of the shape, and no the 2d drawing in the book

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This did not really help me as I could do this in my head. I think this would just further confuse others and that they would not get the point.

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We learned about decomposing and composing integer and how to compare that to real life examples. For example, a tightrope walker walks 10 steps forward and doesn’t go backwards. This is an example of composing integers.

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1) I liked the hands on method because it helped me to see how many different types of triangles there were, and it allowed me to accurately count how many triangles there were. If I had done it without the hands on part, I would’ve not been able to visualize the model enough to do these things.
2) I think my level of understanding is a three because I understood it well enough, like how to prove it, but I don’t really think I could apply it to a 3D situation without taking a long time, which would make it hard to teach.

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1) I liked the hands on method because it ambled me to look and feel the model. This made me think more, and visually see it. (I’m a visual learner). This made it easier to find the relationship than just imagine it, which is much harder for me. This also gave me something to remember it by; I can remember this in the future ,(this activity will help me), because I involved my senses into doing the project.. (Touch, hear.) This helps me remember he project and therefore remember the relationship as well.
2) I think I consider myself to be a 3 in this aspect. I understand it, but am not very comfortable and familiar with it. I hope, as time goes on, I will do more problems, and my 3 can become a 4.

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1. I like the hands on method of doing the Pythagorean theorem, because it allows me to actually touch something, and feel it. I can also  look right at it, and it is there, instead of me having to use my imagination to solve the problems, which is harder than just having it in front of us. I feel that when having it in front of us, and it being something that we have made, it will help us better remember it for the future. Even if I know the theorem, I still like this visual method better
2. I would rate myself as a 4 in the Pythagorean theorem. I think that if someone needed help, I could help them, and even teach them. I understand the equation. This project helped me to understand why it works, why it is what it is. For this reason, I think I can teach them.

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1) I personally prefer the non hands on better than the hands on activities because I think I understood the non hands on better, since there is also a visual aspect to it. The squares with triangles made more sense to me. I think I am at a 3 since I feel like I have fully understood it, but I dont think I am a 4 since I still sometimes get confused when I have to apply the theorem to real world problems.

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I felt like that the hands on really helped me feel how the theorem worked. I would prefer the hands on version because it really helped me thoroughly understand. I would be a 4 because I really understood the theorem and how it works in real life situations like the antenna.

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I liked the non hands on theory. I could understand the equation better I understood it well that way and the model could get a bit confusing. The measurements could be decimals and not exact, and they could be irrational which made it harder to calculate and measure. It was still fun to make, but making so many triangles made it confusing on which triangle we were trying to analyze for some models. Using paper squares was easier and I had no problem seeing it, whereas the model was tedious and hard to understand. “Should we count this part or not?” was a common question we had. It was fun to do, but I prefer non hands on and simply drawing it or cutting out shape made it easier for me. I am at a 4, because I understood the equation well and why it works in different ways. I am also pretty sure I could teach it.

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1)   I like the hands-on activity because it made it easier to look at the model and  see the pythagorean theorem in a 3d view. It also helped me enjoy math more. It was more easier for me to imagine the angles on the model rather than looking at a paper.

2)I think that I am at a 4 for the pythagorean theorem because I can understand it well and I know how to calculate square roots which is and important thing when using the pythagorean theorem.

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1. I prefer the non- hands-on method, for I think I understood drawing triangles in a square better. The visual on paper from Problem 9-146 was easier for me to understand, because it was also hands-on. At home, my dad and I cut out the triangles in the square and rearranged them manually to create a square with an area of c². So, in the end, we got c² square from an a2  square and b² square combined. It showed me the proof of the Pythagorean Theorem in a simple, yet fun, way.
2.  I would rate myself a 3 on the Pythagorean Theorem. This is because I understand the formula and that it does work. The proofs showed that it does work. What I still don’t know is why the Theorem works in the sense of how people came up with it.

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I liked the hands on method because it helped me visualize the theorem better and I like using visuals. I also thought that the hands on method was fun and it helped me understand better

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1) I liked the hands-on way to do it because with I could actually see the model of what we were doing. It was 3-D and I didn’t have to imagine the pyramid’s height, whereas with writing/drawing it on paper, it would’ve been harder to see the heights since paper only allows 2-D objects (length and width without height). The hands-on way also required me to think and engage more in the subject, so I’ll remember it better.

2) My level of understanding of the theorem is about a 3. I know how to prove it and I can apply it to real-world problems, but I am only able to do this slowly and am not comfortable with teaching it to somebody else, one of the conditions to reach level 4.

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1. I liked the non hands on activity because making the model was a little annoying since it was hard to get done well. Besides, I would have been able to do the question perfectly fine, model or not, so I don’t think I would have lost anything by skipping the model altogether.
2. I understand the Pythagorean Theorem and would rate myself a 3. I understand why it works and how it works, but I’m not a 4. Yet.

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1. I liked the hands on activity because you can learn and understand how it works in a more visual way. I understood this concept more because you could see the model which made it easier compared to the textbook because you can only see the view that CPM has printed in the textbook. 2. I understand the Theorem because of all the lessons we have been doing in class that relate to the theorem. The real-life problems made it way easier for me to understand the theorem because it helps me to relate to the theorem and I can see how the theorem works in real life.

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I prefer the hands on method because we had the opportunity to apply the Pythagorean theorem into real world situations, which not only makes it more enjoyable, but it also makes us more engaged in the subject because we know that this rule (a2+b2+c2) is not only just an equation created by a math geek who drew up a bunch of right triangles and square.

I understand the theorem well because not only do I know the equation, I can apply them to problems such as finding the area of a square if I only know the length of a line between two points diagonal to each other, or using it to find the volume or surface are of three -dimensional shapes.

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1. When it came to which process I preferred for the Pythagorean Theorem it was a confusing situation when we did the hands on activity. Although I usually prefer visual concepts to understand the problem better, this activity was more confusing than most with the strings and the straws, if it was a simpler situation I might have preferred it but for now I prefer the traditional system.
2. My level of the theorem is around a level three. I learned it before and now I discovered more parts of the concept so my understanding was improved. But I’m not all the way to an outstanding level four but I do have a good level of understanding of the theorem.

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1. I liked learned how to do the Pythagorean Theorem non-hands on, or with the equation. It was easier to understand this way because I'm better with numbers rather than messily tied strings to a straw with no center point of balance. It wasn't a very accurate representation of the actual measurements in the problem, and we got the measurements in the next problem.
2. According to the Learning Mastery Target, I would assess myself as a 3. I can calculate the hypotenuse or either leg, but I sometimes forget the ² on some of the numbers when writing the equation.

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1. I liked the hands on activity that we did on this better than the traditional way because I am an interactive learner. However, I find the traditional way useful too. Sometimes it got a little confusing on what to do because it wasn't always possible to look at it properly by yourself. I enjoyed learning the Pythagorean theorem because I find this an interesting concept that can be used in real life.
2. I think that my level of understanding for the theorem is a three. I understood it much better because I learned about this concept before. I understand this concept and how and why it works.

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1. I preferred the non-hands on way of learning the Pythagorean Theorem because not only was I still able to learn the Thoerem visually by drawing, but I felt I was able to understand the idea or concept better without having to create a 3D model. Though making the 3D model was designed to help me learn the Pythagorean Theorem, I feel as though it didn’t help me at all and instead it kind of confused me on how the model was supposed to help us learn the theorem.
2. I would say that I know the Pythagorean theorem pretty well because I know why the theorem works and how to use it to solve problems.

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Pythogorean
Thr hands on way helped me because it helped visualize the theorem and get a better idea.

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I liked learning the non hands on because I don’t really enjoy creating things, and bringing boxes to school

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1) I

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I like the hands on better, because it is more fun, and involves teamwork. The model helped me visualize the questions and I feel that I understood better with the model.

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1.) I liked the hands on activity because It was easier to understand and you can see what is happening. Sometimes when I just read a bunch of words it’s confusing so to see the shapes helped me.

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I think that it was easier learning about the Pythagorean theorem with the traditional way, because the hands-on activity was slightly confusing with all those strings and and straws. Learning the Pythagorean theorem the traditional way was more straight forward. I think that I understand the Pythagorean theorem pretty well, and am pretty certain I am at a 4.

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Jacqueline
I think the hands on project was better because you can visualize the model. It was easier to see how the figure worked. Visualizing things helps me learn better.

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I liked it to be traditional, because it is an easy formula and it’s easy to remember. Even though I liked this way, I liked the 3D one too because it was hands on and showed the different triangles, even though ours was kind of lopsided.

I understood it really well, it was easy to follow. The hands on helped kind of replenish the understanding.

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1.)  I think that the hands on reflection helped me understand the Pythagorean Theorem better since it helped me visualize how to calculate all of the hypotonueses/lengths.
2.) My level of understanding of the theorem is probably a level four. In other words, I feel I have mastered it. This is because I understand the theorem itself, and how to apply the theorem to real life situations, such as the problems we did in 9.2.

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I think it was easier learning the Pythagorean Theoram the traditional way because the hands-on one was really confusing, while the traditional way is a bunch of eqautions and other things to prove it.
I understood the theoram pretty well

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I think it is easier to understand the Pythagorean Theorem by doing the hands on project because I understood it easier when I actually saw it. The model helped me figure out how it worked and it helped me to see how the theorem actually works. It helped me understand that the hypotenuse, or the string, is a squared plus b squared, or the base squared plus the length of the straw/“antenna” squared. It is easier to understand doing the hands on project than the non hands on because when you just write it down on paper, you don’t understand it as much as when you can actually visualize it.

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The problem was fun because we got to do the hands on thing with the model. I like learning the hands on version because it is more fun and challenging. My understanding of these types of problems is pretty strong I know what I am doing when I solve them. So I guess I know what I am doing in this problem. The a2 + b2 =c2 is pretty basic and easy to understand.

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1) I liked doing the hands on project because it made me look at the problem a different way and it made it easier for me to figure out for example how long the guy wire is. The model was like a big picture that helped me find the lengths of the triangle such as the hypothenuse
2) My level of understanding is a 3 because I understand it but it would be hard for me to teach other people and also I am not a full master in Pythagorean Theorem yet. I understand how to find any lengths of the triangle if there is a problem like that.

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I liked using the Pythagorean Theorem because it made more sense for me to use an equation rather than having the model. The model was kind of confusing, since it’s not always 100% accurate, and it was hard to tell if it was a right triangle or not.
I think I understand it pretty well.

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I think it was easier to learn the Pythagorean theorem in the traditional way because it is easier to understand and takes less time to set up the equation. The hands method was also very hard to explain to the people in my group who didn’t understand how to do it. However, the traditional method was very simple and easy to solve because you just need to solve the equation to find the hypothenuse.
-Kevin

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I liked hands on because the visual representation helped me model and understand the problems easier
I think I understand is pretty good.

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Shravani Venkatesh
I thought that the hands on problems were easier to understand, because you can actually visualize and see how the Pythagorean theorem works. The hands on problems make it easier to prove the Pythagorean theroem, and how a^2 + b^2= c^2. I understood that the hands on and non-hands on work well, when trying to understand the Pythagorean Theorem. I think that my understanding of the Pythagorean theorem is a 3, because I have understood the equation well, and what is required to make a right triangle. I am not a 4, because I won’t be able to easily explain the proof and equation of the Pythagorean Theorem.

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1) I learned the Pythagorean Theorem better the non-hands on way. I thought the hands-on way was pretty confusing, but the other way was easier to understand. I didn’t understand the model because it was very messiah and confusing to look at it.
2) I think my level of understanding for the Pythagorean Theorem is a 3 because I understand the concept, but I would not be able to teach someone about the Pythagorean Theorem.

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I liked doing the hands on project because it helped me understand the problem better. This made it easier for me to answer the questions. Also it’s easier to work as a table group when we had the model. I understood the Pythagorean Theorem the non hands-on and the hands-on way. I think my understanding is at a 3. I understand how to find the hypotenuse and the legs of a right triangle. But, I don’t think I would be able to teach someone how to do it.

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I did not like the hands on but I I liked the non hands on. I do better without diagrams in the long run. They take a long time to use and are sometimes not useful. The hands on project also took a whole period and it didn’t give out satisfactory results. But, my understanding of the Pythagorean theorem is a 3. I do know the what it is and how to use it in problems. I don’t feel comfortable teaching someone because I don’t have much experience teaching this sort of thing. So if two sides were 7 and 9, I could find the hypothenuse. So 49 plus 81 which is 130. 130 square root is about 11.4.
-Justin W

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The hands on way helped me understand the problem better. It is easier to learn visually than from reading the concept in my opinion.
-Heather

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Today

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Today we learned is decompose and compose numbers. So for axample 20 +-5=15 it means subtract

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Composing and decomposing integers, Suhaan 

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Composing and decomposing integers, Suhaan 

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So the th

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1. I liked the hands on method more. This is because seeing a visual representation helps me connect the numbers and measurements onto a proper model. I can see what the result of the theorem would look like in real life. The fact that we did a hands on activity, I can understand why the concept would make sense to use in real life.
2. The Pythagorean theorem has been pretty much drilled in my head. I understand that a2+b2=c2, where a and b are the perpendicular side lengths, and that the hypotenuse is c. I can solve missing side length problems and apply concepts in some real life situations.