Analysis
This page contains the data for the test trials of our final product, as well as the mean, median, and mode for the times it took for people to solve my cube. The conclusion questions are answered on this page as well.
Data
Scatter Plot
The relationship between the two variables is a negative correlation, as times go down as trials go up. The function for the line of best fit is: f(x) = -267.35x + 775.73, where x is the trial number. The y-intercept, 775.73, represents the time it takes for someone to solve the cube during trial 0, which is unreasonable in the context of the problem. The slope, -267.35, is negative, meaning the line slants down. The fifth attempt, according to the equation, will take -561.02 seconds, because if 5 is substituted in for x, -267.35(5) + 775.73 = -561.02 seconds. Again, this is unreasonable in the context of the problem because you cannot have a negative number of seconds. This number can also be reached by continuing the line and putting it into a computer. If a person solved a puzzle in 23 seconds, if we solve for x when f(x) = 23, the attempt number is 2.81, which can be rounded to 3. |
Mean, Median, Mode, etc.
Conclusion Questions
1. It is important to model an idea before making a final prototype because a model allows for you to critique your work and make sure it is perfect before making a final prototype so you can avoid wasting time and resources on a project that doesn't work.
2. To constrain the parts of the puzzle in Inventor, I used the "Joint" and "Constraint" options. When "Joint" is applied, the pieces lock together and can no longer be moved. When "Constraint" is used, the pieces line up edge-to-edge, but can still be moved. I used mostly "Constraint" multiple times to make sure that all my sides of all my pieces matched up and were flush to each other.
3. When someone says, “I used a design process to solve the problem at hand” it means that they went through each step of the design process to solve their problem. For example, for my puzzle design challenge, I first graphically modeled it, then made prototypes and tested them before making my final cube. In the end, I evaluated what I did. This is the design process, and when someone uses it, they follow steps similar to this.
4. I found that female solvers were able to solve my cube faster than male solvers. The average time for male solvers for attempt 1 was about 10 minutes and 30 seconds, while the average for female solvers was about 8 minutes.
5. How does the age of the puzzle solver affect solution time?
a. I found that the rate of increase in solving time for attempt 1 was about 30 seconds higher for every year that the solver is older than 14. For example, a 14 year-old solved my cube in 8:32, while a 16-year-old solved it in 10:23.
b. An equation using function notation that represents puzzle solution time in terms of age where x represents age in years is f(x) = 46.7x - 81.7.
c. The solution time of a three year old, according to this equation is: f(x) = 46.7(3)-81.7 = 58.4 seconds.
d. The solution time of a 95 year old, according to this equation is: f(x) = 46.7(95)-81.7 = 4378.1 seconds.
e. These solutions do not make sense because in reality, a three-year-old would be too young to understand how this problem works and an older person would get it quickly.
f. A realistic domain for this function would be ages 10-20, because this puzzle is made for teens.
2. To constrain the parts of the puzzle in Inventor, I used the "Joint" and "Constraint" options. When "Joint" is applied, the pieces lock together and can no longer be moved. When "Constraint" is used, the pieces line up edge-to-edge, but can still be moved. I used mostly "Constraint" multiple times to make sure that all my sides of all my pieces matched up and were flush to each other.
3. When someone says, “I used a design process to solve the problem at hand” it means that they went through each step of the design process to solve their problem. For example, for my puzzle design challenge, I first graphically modeled it, then made prototypes and tested them before making my final cube. In the end, I evaluated what I did. This is the design process, and when someone uses it, they follow steps similar to this.
4. I found that female solvers were able to solve my cube faster than male solvers. The average time for male solvers for attempt 1 was about 10 minutes and 30 seconds, while the average for female solvers was about 8 minutes.
5. How does the age of the puzzle solver affect solution time?
a. I found that the rate of increase in solving time for attempt 1 was about 30 seconds higher for every year that the solver is older than 14. For example, a 14 year-old solved my cube in 8:32, while a 16-year-old solved it in 10:23.
b. An equation using function notation that represents puzzle solution time in terms of age where x represents age in years is f(x) = 46.7x - 81.7.
c. The solution time of a three year old, according to this equation is: f(x) = 46.7(3)-81.7 = 58.4 seconds.
d. The solution time of a 95 year old, according to this equation is: f(x) = 46.7(95)-81.7 = 4378.1 seconds.
e. These solutions do not make sense because in reality, a three-year-old would be too young to understand how this problem works and an older person would get it quickly.
f. A realistic domain for this function would be ages 10-20, because this puzzle is made for teens.