Purpose
The purpose of this analysis project is to help students to develop analysis skills; specifically, how to evaluate data using Microsoft Excel. This part of the Puzzle Cube Challenge utilizes spreadsheet software to have students create scatterplots with data they have collected, and calculate standard set-of-data functions (mean, median, mode, and range) that are derived from that data. Students learn how to incorporate technology into contemporary settings to find useful data quickly and accurately. This is a useful skill for deriving patterns out of data that appears to make no sense.
The pictures shown below are the representations of the stats I collected for my puzzle cube from test subjects. The stats were created on Microsoft Excel. This is the final stage of the project: analyzing data, and then if needed, making changes to the product. (My product seems to be unmarketable, considering the fact that around 15 people gave up on it and most of the people who solved it took a long time to do so.)
Conclusion Questions/Answers
1. Why is it important to model an idea before making a final prototype?
It is important to model an idea before making a final prototype because it shines a different light on the design, and may show any mistakes you missed before. Having an idea laid out in 3-D as something you can hold and can highlight any problems that were previously hidden from view. If mistakes are found, the idea can be modified, and the prototype has a much higher chance of coming out the way it was intended to be. In addition, if a prototype is created using a lot of money, and it had errors, then a new one has to be created, using that money again. If a model is fabricated, it might not need as much money, but the same errors could be detected. To further add to the topic, the creation itself of the model may reveal construction errors that could mess up the production of the final design product later on.
2. Which assembly constraint(s) did you use to constrain the parts of the puzzle to the assembly such that it did not move? Describe each of the constraint types used and explain the degrees of freedom that are removed when each is applied between two parts. You may wish to create a sketch to help explain your description.
I used two constraints to accomplish this task: The mate constraint and the flush constraint.
The mate constraint binds two planes that contain the faces of the objects you wish to constrain together. However, since the planes are bound, not the faces only, the objects can move anywhere on that plane. This removes the degrees of freedom that allow the objects to move away or closer to each other (if you were looking at them from above, they could not move vertically towards you or away from you).
The flush constraint binds two planes of surfaces to completely intersect, so the faces are parallel to each other. Thus, the object can move about side to side, and up and down, but not front or back. This removes the degrees of freedom that dictate movement of the objects' constrained faces ahead or behind each other (if you were looking at them from above, they would not be able to move so that the constrained face stays in a straight line with the other constrained face).
3. Based on your experiences during the completion of the Puzzle Design Challenge, what is meant when someone says, “I used a design process to solve the problem at hand”? Explain your answer using the work that you completed for this project.
When someone says they used a design process to solve a given problem, they are referring to the fact that the completion of their project was completed using a set procedure and method. A design process is meant to help generate and create the best product possible. The design process I used to complete this puzzle cube project was the PLTW-designated process. This process has individual steps used for developing ideas, creating the product, and refining it so it will come out with as many desirable traits as possible. Because of the PLTW-designated design process, I brainstormed ideas for each individual part, created two different models, chose the better one, and tested it to record data on its properties, all according to the design process I followed. Thus, my project was created based on the procedure laid out in the design process I was using.
4. How does the gender of the puzzle solver affect solution time? Be specific and provide evidence to support your answer.
According to my data, the solution time of the solver seems to peak during Trial 1 if they are male, and the solution time is highest during Trial 2 when the solver is female. In addition to this conclusion, it seems like the solution time for Trial 2 for females is higher than the solution time for Trial 2 is for males.
Supporting evidence: While Grant, Nathan M., Joseph C., and Rohith M. all had their Trial 1 times as their longest, Joseph C. had his longest trial time during Trial 3, and Shahnaz C. had her longest trial time during Trial 2. Shahnaz C.'s Trial 2 solution time was the highest in all my data collected (higher than the males who underwent my experiment).
Disclaimer: This data is a very small sample and is extremely limited, and as such, my conclusion is not strongly supported by factual evidence.
5. How does the age of the puzzle solver affect solution time?
It is important to model an idea before making a final prototype because it shines a different light on the design, and may show any mistakes you missed before. Having an idea laid out in 3-D as something you can hold and can highlight any problems that were previously hidden from view. If mistakes are found, the idea can be modified, and the prototype has a much higher chance of coming out the way it was intended to be. In addition, if a prototype is created using a lot of money, and it had errors, then a new one has to be created, using that money again. If a model is fabricated, it might not need as much money, but the same errors could be detected. To further add to the topic, the creation itself of the model may reveal construction errors that could mess up the production of the final design product later on.
2. Which assembly constraint(s) did you use to constrain the parts of the puzzle to the assembly such that it did not move? Describe each of the constraint types used and explain the degrees of freedom that are removed when each is applied between two parts. You may wish to create a sketch to help explain your description.
I used two constraints to accomplish this task: The mate constraint and the flush constraint.
The mate constraint binds two planes that contain the faces of the objects you wish to constrain together. However, since the planes are bound, not the faces only, the objects can move anywhere on that plane. This removes the degrees of freedom that allow the objects to move away or closer to each other (if you were looking at them from above, they could not move vertically towards you or away from you).
The flush constraint binds two planes of surfaces to completely intersect, so the faces are parallel to each other. Thus, the object can move about side to side, and up and down, but not front or back. This removes the degrees of freedom that dictate movement of the objects' constrained faces ahead or behind each other (if you were looking at them from above, they would not be able to move so that the constrained face stays in a straight line with the other constrained face).
3. Based on your experiences during the completion of the Puzzle Design Challenge, what is meant when someone says, “I used a design process to solve the problem at hand”? Explain your answer using the work that you completed for this project.
When someone says they used a design process to solve a given problem, they are referring to the fact that the completion of their project was completed using a set procedure and method. A design process is meant to help generate and create the best product possible. The design process I used to complete this puzzle cube project was the PLTW-designated process. This process has individual steps used for developing ideas, creating the product, and refining it so it will come out with as many desirable traits as possible. Because of the PLTW-designated design process, I brainstormed ideas for each individual part, created two different models, chose the better one, and tested it to record data on its properties, all according to the design process I followed. Thus, my project was created based on the procedure laid out in the design process I was using.
4. How does the gender of the puzzle solver affect solution time? Be specific and provide evidence to support your answer.
According to my data, the solution time of the solver seems to peak during Trial 1 if they are male, and the solution time is highest during Trial 2 when the solver is female. In addition to this conclusion, it seems like the solution time for Trial 2 for females is higher than the solution time for Trial 2 is for males.
Supporting evidence: While Grant, Nathan M., Joseph C., and Rohith M. all had their Trial 1 times as their longest, Joseph C. had his longest trial time during Trial 3, and Shahnaz C. had her longest trial time during Trial 2. Shahnaz C.'s Trial 2 solution time was the highest in all my data collected (higher than the males who underwent my experiment).
Disclaimer: This data is a very small sample and is extremely limited, and as such, my conclusion is not strongly supported by factual evidence.
5. How does the age of the puzzle solver affect solution time?
- a. Make a specific statement related to the rate of increase or decrease of solution time with respect to age. Provide evidence that supports your statement.
There seems to be no solid, reliable factual correlation between the age of the participant and their solution time for each Trial.
Supporting evidence: The data for Joseph C. and Rohith M. is substantially different, despite their same age. Grant C.'s and Nathan M., - b. Write an equation using function notation that represents puzzle solution time in terms of age. Be sure to define your variables and identify units.
Because there seems to be no correlation between puzzle solution time and age, an equation cannot be written.
Puzzle solution time is represented by seconds.
Age of test subject is represented in years. - c. Predict the solution time on the first attempt of a child who is 3 years of age. Show your work.
No function available to be able to do so. - d. Predict the solution time on the first attempt of a person who is 95 years of age. Show your work.
No function available to do so. - e. Do these predictions make sense? Why or why not?
These predictions I have made as parts (c) and (d) of question 5 make sense. The evidence I have collected is highly variegated and irregular, and has no correlation between age of puzzle solver and puzzle solution time that I have noticed. - f. What is a realistic domain for the function?
A realistic domain for the function (if one could be conceived) would be approximately (units in seconds): 5 ≤ x ≤ 2700 - g. Collect additional data to verify your mathematical model.