In this assignment, I was able to demonstrate communication as we had to work together as group and agree on what to write about. I was able to contribute to the assignment by putting forth ideas while also listening to the ideas of other group members in order to collaborate and develop a good paper. We were also able to split our roles and choose one person to write without any problems or conflicts. Everyone was able to work together in a positive way and create a good environment where we were able to complete the assignment to our best efforts and we were able to get a good mark as a result.
In parabolas, a, h, and k, have a significant effect on the way she shape looks and where it appears on the graph. This is evident on my graph in all of my parabolas. For example, In my second parabola, (the blue one), the a value is positive and is a fraction which makes the parabola open up and wider than the parent function. There is no h and k in this equation therefore this makes the vertex (0,0) as the parabola does not shift up, down, left or right. In the third parabola (green), the vertex is also (0,0) for the same reason as there is no h or k in the equation and the parabola does not shift. However, there is an a value in this equation which makes the parabola open down and be narrow as it is a negative whole number. In the fourth parabola (purple), the vertex is (15,12). This means the h is 15 which causes the parabola to shift to the right and the k is 12 which makes the parabola start up higher as it’s minimum value is 12. This parabola has an a value of 1/5 which is a positive fraction and makes the parabola open up and wide. My last parabola (black) has no h value and therefore does not shift on the x-axis. However, it does have a k value of -6 causing the parabola to start opening from below 0 and shifts the parabola down the y-axis. This parabola is also effected by its a value which is -1/2. This value is negative which makes the parabola open down. It is also a fraction which makes the parabola open wide. In conclusion, the values a, h, and k, drastically effect the shape of the parabola and can also help us predict a parabolas shape just from the equation. This also makes it easier to check your work when solving and plotting points on a graph.
In this assignment, I represented the same mathematical idea in multiple ways as I showed how the different letters effect multiple equations by changing their values and adding more changes to the equations. For example, in the last equation, I made it be shifted down from the parent function and then I added a value for a which made the parabola open up as well.
To demonstrate my understanding, I used lots of vocabulary and terms that relate to the mathematical concepts. Some of these terms include parabola, shape, shift, y-axis, x-axis, opening up/down, values, equation, points, fraction, minimum value, etc.
I was able to use formatting to share my information in a clear and organized way as I adjusted the settings in desmos, like changing the steps, thickness, labelling, and choosing colours. I also took pictures of my equations so they would be clear and easy to see.
Collaboration: For this lab, me and my partner had to collaborate when finding different parts to label them correctly. We had to work well with each other and communicate our thoughts and ideas about how we would complete the lab well. We also had to make sure we divided the work evenly and each got a chance to work on dissecting and labeling the pig. Me and my partner were able to collaborate well with each other and we were able to complete the lab fully and were even able to unravel the intestines of the pig and measure them.
Thinking: This lab required lots of critical and creative thinking. We showed this when we found the parts of the pig to label with the correct label. This took lots of thinking back to lessons and things we had learned in class. We needed to interpret 2D diagrams we had seen and find those parts on a 3D pig. This took thinking and connecting skills.
When creating our Rube Goldberg Machine, there were many examples of our collaboration and communication. Firstly, we had to work together to think of what features we would decide to include. This was shown when we all brainstormed ideas and agreed on some or got inspiration from each others’ ideas to make them better. This demonstrates how we can conspire and communicate as a group. In addition, we helped each other get through obstacles. We displayed this when we failed an attempt or something wouldn’t work how it should’ve and we helped each other find a solution or a different option to achieve our goal. This illustrates good cooperation and persistence within the group. Finally, we all participated equally to make the machine work in the best way. We showed our participation when we had to come up with strategies to make steps work more seamlessly, for example, changing the way something is arranged or adding mass to weigh something down. This makes it evident that we can all split the work equally in a group. Because of the examples mentioned, it is clear that we are able to work fairly in a team setting and contribute to group discussions.
