Cube Project Portfolio
Criteria
1. The puzzle must be fabricated from 27 – ¾″ hardwood cubes.
2. The puzzle system must contain exactly five puzzle parts.
3. Each individual puzzle part must consist of at least four, but no more than six hardwood cubes that are permanently attached to each other.
4. No two puzzle parts can be the same.
5. The five puzzle parts must assemble to form a 2 ¼″ cube.
6. Some puzzle parts should interlock.
7. The puzzle should require high school students an average of ___5___ minutes/seconds to solve. (Fill in your target solution time.)
2. The puzzle system must contain exactly five puzzle parts.
3. Each individual puzzle part must consist of at least four, but no more than six hardwood cubes that are permanently attached to each other.
4. No two puzzle parts can be the same.
5. The five puzzle parts must assemble to form a 2 ¼″ cube.
6. Some puzzle parts should interlock.
7. The puzzle should require high school students an average of ___5___ minutes/seconds to solve. (Fill in your target solution time.)
Autobiography
Hello, my name is Breeyonna Williams and I'm a ninth grader at Southeast Raleigh Magnet High School. Currently I am a student in Introduction to Engineering and Design. I am in the Engineering Academy at my school because I want to be a Mechanical Engineering when I grow up.
Puzzle Design Challenge Brief
Client Fine Office Furniture, Inc.
Target Consumer Ages: High school aged
Designer __Breeyonna Williams__
Problem Statement
A local office furniture manufacturing company throws away tens of thousands of scrap ¾” hardwood cubes that result from its furniture construction processes. The material is expensive, and the scrap represents a sizeable loss of profit.
Design Statement
Fine Office Furniture, Inc. would like to return value to its waste product by using it as the raw material for desktop novelty items that will be sold on the showroom floor. Design, build, test, document, and present a three-dimensional puzzle system that is made from the scrap hardwood cubes. The puzzle system must provide an appropriate degree of challenge to high school students.
Target Consumer Ages: High school aged
Designer __Breeyonna Williams__
Problem Statement
A local office furniture manufacturing company throws away tens of thousands of scrap ¾” hardwood cubes that result from its furniture construction processes. The material is expensive, and the scrap represents a sizeable loss of profit.
Design Statement
Fine Office Furniture, Inc. would like to return value to its waste product by using it as the raw material for desktop novelty items that will be sold on the showroom floor. Design, build, test, document, and present a three-dimensional puzzle system that is made from the scrap hardwood cubes. The puzzle system must provide an appropriate degree of challenge to high school students.
Step 1: Brainstorming Puzzle Pieces
Activity 4.1a - Puzzle Part Combinations
In Activity 4.1a, the first part of the Puzzle Design Challenge, we were given up to six 3/4" wooden cubes and were asked to make a puzzle piece part that is made of six, five, four or three 3/4" wooden cubes. We were required to design 16 different puzzle piece parts.
Conclusion Questions
1. Why is it so important for a designer to think of multiple solutions to a design problem? It's important for a designer to think of multiple solutions to a design problem so that if one solution falls through, they have another solution to try.
2. What steps did you take to determine the exact number of possible combinations for each set of cubes? I determined the exact number of possible combinations for each set of cubes by designing many different puzzle piece designs so that almost anything could go together.
3. Why is it important to sketch your ideas on paper and sign and date the document? It's important to sketch my ideas on paper and sign and date the document because if I do this I can easily change my design and this proofs that it's my sketch.
2. What steps did you take to determine the exact number of possible combinations for each set of cubes? I determined the exact number of possible combinations for each set of cubes by designing many different puzzle piece designs so that almost anything could go together.
3. Why is it important to sketch your ideas on paper and sign and date the document? It's important to sketch my ideas on paper and sign and date the document because if I do this I can easily change my design and this proofs that it's my sketch.
Step 2: Possible Solutions
Activity 4.1b - Engineering Graphics
In Activity 4.1b, the second part of the Puzzle Design Challenge, we made 2 different designs for a 3 by 3 by 3 puzzle cube. Each puzzle cube had 5 puzzle pieces that each had from 3 to 6 3/4" wooden cubes in them. We first made it an isometric view of our puzzle pieces and our puzzle cubes. Then, we made multiview designs of our puzzle cube designs.
Conclusion Questions
1. Why is it important to have designs and drawings reviewed by peers? It's important to have designs and drawings reviewed by peers so that the maker of these works knows that their work can be interpreted by others and that they make sense.
Step 3: Working with Statistics
Activity 4.1c Mathematical Modeling
In Activity 4.1c, the second part of the Puzzle Design Challenge, we learned about the mathematics behind building models through examining the statistics behind cubes, puzzle pieces, and BXM bikes. We did this by making Excel spreadsheets based on the weights of 3/4" and 1" puzzle cubes and the minimum jump heights of BXM bikes of different weights.
activity_4.1c_mathematical_modeling.docx | |
File Size: | 137 kb |
File Type: | docx |
activity_4.1c_mathematical_modeling.xlsx | |
File Size: | 26 kb |
File Type: | xlsx |
Conclusion Questions
1. What is the advantage of using Excel for data analysis? The advantage of using Excel for data analysis because if you use Excel then you don't have to compute the math behind your data and you don't have to draw your own graph.
2. What precautions should you take to make accurate predictions? To make accurate predictions you should take the precaution of double checking your work or by using an electronic system to do your math.
3. What is a function? Explain why the mathematical models that you found in this activity are functions. A function is a relationship or expression involving one or more variables and the mathematical models that I found in this activity are functions because each input has a single output which is one of the rules of a function.
4. Are all lines functions? Explain. All lines aren't functions because certain lines like quadratic lines and straight lines can have inputs with more than one outputs.
2. What precautions should you take to make accurate predictions? To make accurate predictions you should take the precaution of double checking your work or by using an electronic system to do your math.
3. What is a function? Explain why the mathematical models that you found in this activity are functions. A function is a relationship or expression involving one or more variables and the mathematical models that I found in this activity are functions because each input has a single output which is one of the rules of a function.
4. Are all lines functions? Explain. All lines aren't functions because certain lines like quadratic lines and straight lines can have inputs with more than one outputs.
Step 4: Designing Pieces in Autodesk
CAD Drawings
Step 5: Creating Drawings in Autodesk
Autodesk Drawings
Step 6: Creating a Cube Presentation
Autodesk Presentations
One of the last parts of the Puzzle Design Challenge is to create presentations on Autodesk of our puzzle cubes being assembled. Below are videos of my two puzzle cubes being correctly assembled in Autodesk.
puzzle_cube_1_assembly.wmv | |
File Size: | 5 kb |
File Type: | wmv |
puzzle_cube_2_assembly.wmv | |
File Size: | 5 kb |
File Type: | wmv |
Step 7: Creating the Physical Model
Physical Model
Finally, after designing my cube and creating it in Autodesk, it was finally time to create the physical model. The physical model is three wooden cubes tall, three wooden cubes wide, and three wooden cubes long. It is made of five wooden pieces: one is purple, one is green, one is brown, one is blue and one is red. Below is a video from my YouTube channel of I showing how to put the puzzle cube together.
Step 8: Test Trials
After creating my physical model of my puzzle cube, I was required to have my peers solve my puzzle cube in order to estimate how long it would take a high school student to complete my puzzle cube. In addition to testing my peers, I also tested my parents for the purposes of having demographic outliers. Below is the Excel spreadsheet showing the data from my puzzle cube test trials and the statistics based on my data.
activity_4.1_test_trials.xlsx | |
File Size: | 16 kb |
File Type: | xlsx |
Excel Review
The slope of the treadline is -177.95x and the y-intercept is 606.7 because it represents what slope should be subtracted from. The slope is -177.95x because as the x value increases, the y value decreases. The slope being -177.95x means that with every attempt, the average solution time decreases by 177.95 times the number of attempts. The average solution time for the fifth attempt graphically based on the equation T(5) = -250.79533(5) + 606.7 is inaccurate because it is -647.27665 seconds which is impossible since there aren't negative seconds. This implies that it would take less than a second for a high schooler to solve the puzzle cube. The average solution time for the fifth attempt numerically based on the treadline equation T(5) = -177.95(5) + 606.7 is also inaccurate because it is -283.05 seconds which is impossible since there aren't negative seconds. This also implies that it would take less than a second for a high schooler to solve the puzzle cube. If a person's average solution time is 23 seconds, the number attempts in which they've solved the puzzle is graphically, based on the equation 23 = -250.79533 + 606.7, is 2 and numerically, based on the equation 23 = -177.95 + 606.7, is 3.
Summary of Design Review
The design of my puzzle cube meets the design criteria because the puzzle has been constructed carefully, the blocks are aligned, the color matches the model, and the color is appropriately applied even if it doesn't enhance the puzzle. My design does "provide an appropriate degree of challenge to high school students" as stated in the design statement because the average solution time is 4 minutes and 18 seconds which almost reaches my goal for average solution time which is 5 minutes.
Step 9: Improve/Revise
I think I did a good job on designing a good puzzle cube that meets the criteria and is difficult for high school students to solve. The only thing that I would done better is that I would've colored the cube more and I would've tried to make puzzle cube pieces made of only four or five wooden cubes. Otherwise I believe that I made a puzzle cube that was difficult and nicely designed. I hope that you liked my final puzzle cube design!
Conclusion Questions
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 so that you don't make a mistake when building the final prototype which could lead to problems when it is applied in the real world and can waste valuable materials.
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. The assembly constraints that I used to constrain the parts of the puzzle to the assembly such that it did not move is flush and mate. The flush constraint aligns two surfaces with each other. For example, the front side of a puzzle piece is aligned with front side of another puzzle piece so that they're even with neither one ahead or behind the other. The degrees of freedom that are removed when flush is applied is if the flush is applied on the front, rear, right or left sides is left and right and forwards and backwards. When the flush is applied on the top and bottom sides, the degrees of freedom that are removed are up and down. The mate constraint joins two surfaces to each other. For example, the front side of a puzzle piece is connected to the right side of a puzzle piece. The degrees of freedom that are removed are up and down, left and right, and forwards and backwards.
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, "I used a design process to solve the problem at hand" it means that they used the design process in order to design the puzzle pieces accurately, put them together, make a proper physical model, and test out the puzzle cube on my classmates which properly follows the design process.
4. 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. For high school students, the rate of increase of solution time grows as the age of the person increases. With adults, the rate of decrease of solution time as the age of the person increases. This can be proven by the fact that a fourteen year old solved the puzzle faster than fifteen and sixteen year old people and a fifty year old took a longer time solving the puzzle than a fifty-one year old.
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. The equation using function notation that represents puzzle solution time in terms of age is T(a) = 248.7166a. T means average solution time, a means age of person solving my puzzle cube and 248.7166 is 248.7166 seconds. The slope of the function notation is based on the average solution time of the average solution time of each age to solve my puzzle cube. The equation using function notation that represents puzzle solution time on the first attempt in terms of age is T(a) = 387.444a and 387.444 is 387.444 seconds. The equation that represents puzzle solution time in terms of age for children and teens is T(a) = 267.082433a and the equation that represents puzzle solution time in terms of age for adults is T(a) = 221.17a. The equation that represents puzzle solution time on the first attempt in terms of age for children and teens is T(a) = 431.45a and the equation that represents puzzle solution time on the first attempt in terms of adults is T(a) = 321.435a.
c. Predict the solution time on the first attempt of a child who is 3 years of age. Show your work. Based on my equation for the puzzle solution time on the first attempt in terms of age for children, teens and adults, the predicted solution time on the first attempt of a child who is 3 years of age is 1,162.32 seconds because T(3) = 387.444(3) equals 1,162.32. But, based on my equation for the puzzle solution time on the first attempt in terms of age for children and teens, the predicted solution time on the first attempt of a child who is 3 years of age is 1,294.35 seconds because T(3) = 431.45(3) equals 1,294.35.
d. Predict the solution time on the first attempt of a person who is 95 years of age. Show your work. Based on my equation for the puzzle solution time on the first attempt in terms of age for children, teens and adults, the predicted solution time on the first attempt of a person who is 95 years of age is 36,807.18 seconds because T(95) = 387.444(3) equals 36,807.18. But, based on my equation for the puzzle solution time on the first attempt in terms of age for adults, the predicted solution time on the first attempt of a person who is 95 years of age is 30,536.325 seconds because T(95) = 321.435(95) equals 30,536.325.
e. Do these predictions make sense? Why or why not? These predicts do not make sense because I did not obtain solution times from a person of each age in order to get an accurate average solution time for the first attempt of solving my puzzle cube. Also, the puzzle cube solution time varies not only from age to age but also based on puzzle solving skills of the person, how much education the person has and what interests the person has. Lastly, the predictions don't make sense because based on the equations, a person who is sixteen years old would take much longer to solve the puzzle on a first attempt than it did for the people I tested who is sixteen years old on the first attempt.
f. What is a realistic domain for the function? A realistic domain for the function is 1 years of age to 100 years of age since children who are younger than 1 year old most likely can't solve a puzzle and people who are older than 100 years old might be too old to solve the puzzle. But, if I were trying to establish a realistic domain for the function based on the goal of the puzzle design challenge is 14 years old to 18 years old which are the ages of high school students.
g. Collect additional data to verify your mathematical model. I don't know of any additional data to verify my mathematical model.
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. The assembly constraints that I used to constrain the parts of the puzzle to the assembly such that it did not move is flush and mate. The flush constraint aligns two surfaces with each other. For example, the front side of a puzzle piece is aligned with front side of another puzzle piece so that they're even with neither one ahead or behind the other. The degrees of freedom that are removed when flush is applied is if the flush is applied on the front, rear, right or left sides is left and right and forwards and backwards. When the flush is applied on the top and bottom sides, the degrees of freedom that are removed are up and down. The mate constraint joins two surfaces to each other. For example, the front side of a puzzle piece is connected to the right side of a puzzle piece. The degrees of freedom that are removed are up and down, left and right, and forwards and backwards.
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, "I used a design process to solve the problem at hand" it means that they used the design process in order to design the puzzle pieces accurately, put them together, make a proper physical model, and test out the puzzle cube on my classmates which properly follows the design process.
4. 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. For high school students, the rate of increase of solution time grows as the age of the person increases. With adults, the rate of decrease of solution time as the age of the person increases. This can be proven by the fact that a fourteen year old solved the puzzle faster than fifteen and sixteen year old people and a fifty year old took a longer time solving the puzzle than a fifty-one year old.
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. The equation using function notation that represents puzzle solution time in terms of age is T(a) = 248.7166a. T means average solution time, a means age of person solving my puzzle cube and 248.7166 is 248.7166 seconds. The slope of the function notation is based on the average solution time of the average solution time of each age to solve my puzzle cube. The equation using function notation that represents puzzle solution time on the first attempt in terms of age is T(a) = 387.444a and 387.444 is 387.444 seconds. The equation that represents puzzle solution time in terms of age for children and teens is T(a) = 267.082433a and the equation that represents puzzle solution time in terms of age for adults is T(a) = 221.17a. The equation that represents puzzle solution time on the first attempt in terms of age for children and teens is T(a) = 431.45a and the equation that represents puzzle solution time on the first attempt in terms of adults is T(a) = 321.435a.
c. Predict the solution time on the first attempt of a child who is 3 years of age. Show your work. Based on my equation for the puzzle solution time on the first attempt in terms of age for children, teens and adults, the predicted solution time on the first attempt of a child who is 3 years of age is 1,162.32 seconds because T(3) = 387.444(3) equals 1,162.32. But, based on my equation for the puzzle solution time on the first attempt in terms of age for children and teens, the predicted solution time on the first attempt of a child who is 3 years of age is 1,294.35 seconds because T(3) = 431.45(3) equals 1,294.35.
d. Predict the solution time on the first attempt of a person who is 95 years of age. Show your work. Based on my equation for the puzzle solution time on the first attempt in terms of age for children, teens and adults, the predicted solution time on the first attempt of a person who is 95 years of age is 36,807.18 seconds because T(95) = 387.444(3) equals 36,807.18. But, based on my equation for the puzzle solution time on the first attempt in terms of age for adults, the predicted solution time on the first attempt of a person who is 95 years of age is 30,536.325 seconds because T(95) = 321.435(95) equals 30,536.325.
e. Do these predictions make sense? Why or why not? These predicts do not make sense because I did not obtain solution times from a person of each age in order to get an accurate average solution time for the first attempt of solving my puzzle cube. Also, the puzzle cube solution time varies not only from age to age but also based on puzzle solving skills of the person, how much education the person has and what interests the person has. Lastly, the predictions don't make sense because based on the equations, a person who is sixteen years old would take much longer to solve the puzzle on a first attempt than it did for the people I tested who is sixteen years old on the first attempt.
f. What is a realistic domain for the function? A realistic domain for the function is 1 years of age to 100 years of age since children who are younger than 1 year old most likely can't solve a puzzle and people who are older than 100 years old might be too old to solve the puzzle. But, if I were trying to establish a realistic domain for the function based on the goal of the puzzle design challenge is 14 years old to 18 years old which are the ages of high school students.
g. Collect additional data to verify your mathematical model. I don't know of any additional data to verify my mathematical model.