Jerrica Crosby and Emma Donharl
We chose the concept of stacking fruit to demonstrate mathematical modeling. We learned how to find an equation that models data, after creating a table of data based on patterns we observed. In the display we created a pyramid by stacking a total of 84 pieces of fruit. We used the number of layers and amount of fruit on each layer to calculate the total number of fruit. Using this data, we found an equation to predict the next layer of the pyramid. In addition to the pattern for the number of fruit on each layer, there is also a pattern with the total number of fruit in the pyramid or the sum of all the layers of fruit.
Referring to the table of data, if you add the number of fruit in layer one to the number of the second layer, you get the number of fruit in the second layer, and so on. The other pattern is when you add the number fruit on each layer; you get the next value representing the total number of fruit for all layers.
Using our TI-84 calculator, we entered the data into lists and created a scatterplot. The scatterplot showed us that the data might be either exponential or quadratic. After calculating an exponential regression equation and a quadratic regression equation, we determined that the quadratics equation is a better fit for this data. We call this the best fit curve: Y=2.5x2-6.5x+6
If we have 3 layers in our fruit pyramid then let x equal 3: Y(3)=2.5(3)2-6.5(3)+6 = 10 The result of 10 is the total number of fruit in the pyramid.
If we have 7 layers in our fruit pyramid then let x equal 7: Y(7)=2.5(7)2-6.5(7)+6 = 84 fruit create a pyramid of 7 layers.
In conclusion, this project will help us read graphs and draw conclusions.
Our personal connection to this project involves critical thinking and real life experiences. For critical thinking we had to create a table, graph, equation, and a model to diagram this concept. Math is important for life to recognize patterns, identify and interpret data, and model raw data in a readable form. This project helped us hone our skills with recognizing patterns and being able to correctly interpret data. The real life experience is if we ever work at a place for stacking things, we will know how to stack anything.
The piece of work I am the most proud of was logarithms. I have never encountered logarithms before, and it was challenging. Learning new math concepts is never easy, but I feel like I really got the hang of it. I put a fair amount of effort into this concept, and I am glad that I understand it now.
The topic I enjoyed learning the most was solving linear equations. My previous math teacher, Mrs. Miller, did a really good job at teaching this concept. If I ever had to go into a math field, dealing with linear equations would have to be a part of it. It’s so simple; all you have to do is calculate. Its literally 1, 2, 3.
The concept I really struggled with but mastered (hopefully) is matrices. I’ve studied them for two years and I still struggle with the turning and aligning and the size dimensions. Thankfully we learned this earlier in the year, so I was eager to finally get this conundrum down. Mrs. Eagen helped me a lot, but I really hope that I don’t have to deal with these later on in life.
