Fencing Your Dog

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003 - Group 3 - Fencing Your Dog

Neena

The coding activities are excellent for allowing students to place different values into the length and width portions to see how that affects the overall area while the perimeter remains the same. Or allow students to alter perimeter to see how that affects the area. It allows students to see a graphed representation of which set of dimensions will include the largest amount of area (a square) and allows them to calculate these dimensions based off the perimeter being constant. I think this could be a useful activity for the students to do through coding because it allows them to determine the largest amount of area with parabola representation. Students can see if their calculations work or if they need to be adjusted. Many students are more likely to be engaged if given the chance to work on a computer or an interactive activity.

Another great thing about these perimeter and area activities is that they allow students to see and visualize patterns. On my practicum I observed and taught students identifying growing and shrinking patterns with the use of tables and number lines. When the students were able to use charts to see the differences in the pattern and figure out what the patterns were increasing or decreasing by, they felt a sense of achievement and truly enjoyed trying to figure out the next pattern rule. I think the In a Story activity would be an amazing way for students to identify the relationships between area and perimeter, see patterns, and understand the concept of dimensions.

I also really liked the use of manipulative and resources in this module. The story relate math to real life situations and are engaging so students don't feel they are doing math standard math problems. As well the large graph paper is a great way for students to visually enlarge and see the problem laid out in from of them. I also liked that it allows students a chance to try out different variations while easily comparing them.

I think the constant area and constant perimeter activities are useful for relating real world applications to math. In the video on constant perimeter in classrooms the teacher described these activities (like the 16 chairs 16 tables) engaging and exciting for the students. They were able to use various manipulatives like bingo dabbers and grid paper to come up with solutions to the problems. I found this insightful to me because I remember being a young student and disliking math for the reason of not making those real-world connections. Rarely did my teachers make the math we learned applicable to every day situations. The use of manipulatives to solve these area and perimeter problems is also very insightful. During my practicum my teacher used pegboards and 2-D block shapes for some of her math activities and the students always loved doing math far more with manipulatives vs. simply with pencils and paper. I understand the importance of using just pencils and paper, but to me I think its proven to be successful when you can engage the kids in multiple ways that they find interesting and entertaining. The students can make more real world and concrete observations about math instead of always abstract.

Adriana

With regards to the coding activity I found the activity a little confusing, mainly because my parabola didn't come out correctly. However I did find that this activity would be a great way for students to easily manipulate the numbers to determine the largest area with a graphical representation. I think I would need a little more practice with this activity however I would definitely use it in my future class as another option for students to work with this concept.

I also found the coding a bit confusing! I think students who have experience with Scratch would catch on very quickly. I agree that having students practice beforehand (maybe using paper graphs or manipulatives would be beneficial to all. I think this would be a good way to consolidate their knowledge of perimeter and area and not a way to introduce the basic concepts. - Erin

I am a very visual and tactile learner and I found the use of the large graph paper and bingo dabbers was a great way for students to visually try out the area problems. It also allowed students a chance to map out variations side by side which made it very convenient to visually compare and figure out which arrangement was the best option.

I really liked the use of story books in both the constant area and perimeter modules. It give the students a real life and relatable example to work with as well students are more engaged when it doesn't seem like a regular math problem. Although I am not a fan of singing I also found the song creation part a great way for students to apply and remember the work they just did. My associate teacher had a few songs for helping students remember some of their multiplication tables and I found students would sing them to themselves when they were stuck on one.

Main topic

Leeanne

I also believe that stories and scripts are great ways to start lessons and engage children to start thinking about the math while keeping it fun. I think the scratch activities are pretty useful when trying to see the relationships between the the change in dimensions and the parabolas. Like you said when you made the perimeter increasingly smaller the parabola also decreased in size. I think this is a great visual tool for students and also an opportunity for them to play around with code to see the different outcomes of selected dimensions. It can also help students to visually and spatially understand real dimensions and base measurements and allow them to apply these in the future. - Neena D.

It was interesting to complete the code for "Fabulous Fence." To help me better understand the code I completed the table to see what the largest area possible was. I then went into the code and was able to see all the possible areas that the fence could be. It was a nice visual and helpful as the highest point on the parabola was the answer (5x5). I then went and changed the code to see what would happen if the perimeter was 24 meters. I discovered that this changed the parabola and the results (6x6).I changed the perimeter again to 12 meters and was able to see the big difference in the graph. This parabola was a lot smaller with maximum height reaching 3x3. I liked how simple it was to change the code and how easy it would be for students to discover if there answers made sense.

I am someone who is a visual learner in math. I really liked the video where the grade 4 students were looking at the shapes of their bar graphs and learning about hyperbolas and parabolas. I think that graphing this information is very visual and that it can make it easier to understand the results. It wasn't until high school that I learned graphing these types of results were very helpful as I could visually see what shape the graph made and fully understand what it meant. -Dan's comment: I never saw a parabola until I was in high school. It's interesting children are doing this at a grade four level! If it is explained properly and thoroughly, as in the video presentations I watched, it makes a lot of sense and it's good to get them familiar with this concept.

I really like the idea of using books or stories in your math lessons. I think that it is a great way to introduce a math problem to your class and then have them use different kinds of ways to solve the problem. In my practicum, I used the book, The Mitten, by Jan Brett, after we finished reading the story the students had to code an animal from the book to the mitten. I think it was a great activity and worked really well as students were being introduced to coding.

Comment by Leah: I really like this idea of connecting a book to coding, we talk about using books and stories in math all the time but not specifically coding. Im interested in what you mean by "code an animal from the book to the mitten", Im not 100% sure what this entails. But I think this would be a very good activity that I would like to try with my students, thanks for sharing!

Dan

The Scratch activity actually didn't help me understand this idea very much. Only until I drew it out myself, as shown above, did I understand.

I also had a hard time understanding the Scratch activity. It wasn't until I made a table and figured out the results manually could I fully understand the significance of the code. Honestly, I am not sure I would use this activity in my classroom, but can see how other teachers might use it to let their students figure out the code-Leeanne

Constant perimeter

Constant area

If the perimeter remains constant and the area is adjusted, it will form a parabola. The highest point in this parabola will be a square. The opposite is true of a constant area and changing perimeter. The two lowest points will be squares and the perimeter that is highest will be most rectangular.

Subtopic

Insight: I never really thought about area and perimeter in this way (i.e. as chairs and tables). It makes a lot of sense. This is a good way of relating it to children. I mean, we have been sitting at desks and in chairs our whole lives! How have I never considered this before? I also liked in the video how the teacher tried to get the students to think about what else in their lives followed the shape of a parabola. As they move on and learn more and more about math and science, this concept will continually come up.

I agree! It is interesting to think that you can find ways of teaching math even in things such as table and chairs. I liked how the teacher relates the concepts to everyday items because this allows students to make connections to their own lives and makes it more relatable. - Erin

Erin

I found the coding activity on Scratch very confusing. I haven’t completely gotten a hang of Scratch yet and this activity seemed especially difficult to follow and complete. I think for students who are comfortable using the program, it would be a very good opportunity for them to control the graph and parabola using different dimensions and they can immediately see where their calculations went right or wrong. Using coding seems to be happening more and more in the classroom and this would be a great activity for students to use.

When I took math classes growing up, I always understood the concepts best when they were introduced in a visual way. In the different videos, the kids graph it out on a big paper and use bingo dabbers to represent the chairs around the table and it is something I could see myself doing with my future students. The use of manipulatives is also a great way to engage kinaesthetic math learners who struggle with the abstract, and using the song would be great for the aural learners. It was surprising to me that elementary kids were learning about parabolas but it was introduced in a way that was level-appropriate and visually, which as mentioned before, is a great way to take something that is abstract and turn it into something tangible. It also allows them to conceptualize the relationship between perimeter and area in a way that is easy to see.

I also really liked how it gave many examples of perimeter and area using books. I believe that this helps kids who don’t really love math to get into it and see it as something that has real-life representation, through a fun story. The concepts of perimeter and area will most likely come up many times throughout the students lives, whether they are building something or planning a party, it is useful to know how these concepts affect one another.

Leah

When you look at the code of F. Model it with scratch you can see the formula that the code uses to determine the different areas with the same perimeter... as the length goes up by one the width is (p/2)-l ... if you were to change this you would no longer have a rectangle anymore and it would not make a parabola... it would be interesting to see if the students could find this formula by looking at the code and understand what the significance of it is

Constant area can have different perimeters

Min perimeter is always a square

Constant perimeter can have different areas

Max area is always a square

I really like this activity with seeing the plots of areas or perimeters on a graph as a parabola because it gives me a real life example of a parabola... when I was learning about parabolas in school I found it very difficult to wrap my head around because I did not understand the relation of them to real life... therefor seeing constant area or constant perimeter as a parabola really helped me understand them and could really help one of my students understand it better