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Desmos Drawing PBL: Mathematical Art Design
Due Date: May 14th by 8 pm
Project Overview:
In this project, you will create a meaningful and visually appealing design using mathematical equations. Your goal is to explore how different types of functions interact and combine to create artistic representations. This project will help you deepen your understanding of functions, transformations, and domain and range restrictions.
Driving Question:
How can mathematical functions be used to create visually appealing designs that represent a meaningful story or concept?
Project Requirements:
Your design must include at least 10 functions, using a combination of:
- Linear functions
- Quadratic functions
- Exponential functions
Domain and range restrictions should be applied creatively to shape your design. Vertical lines are optional and do not count toward the 10-function requirement.
Process:
Plan Your Design:
Choose a concept or story that your design will represent (e.g., nature, personal interest, a fictional logo). Sketch your design on paper and determine which functions will be used.
Graph your Design on Desmos (Not the testing Desmos). Make sure you login to Desmos. If you do not have an account yet, you will need to create one. This will allow you to save your graph as you work so you won’t lose it. Once you are finished, you will hit the share button in the upper right-hand corner. Copy the link and submit it through Canvas by the deadline.
Feedback and Revision: (Thursday, May 8th)
Share your initial draft with peers and the teacher for feedback. Make revisions based on the feedback to refine your design and improve its mathematical and artistic quality.
Reflection and Iteration:
Midpoint Checkpoint (Thursday, May 8th): Reflect on your progress and address the following:
- What is working well in your design?
- What challenges are you facing?
- How are you incorporating feedback?
Present Your Work:
Everyone will present their Desmos drawings in class on Wednesday, May 14th and Thursday, May 15th. You will present the following and you will be graded as follows for your presentation
Explain your design and why you chose it. (5 points)
Explain how one linear function, one quadratic function and one exponential function contributes to the creation of your design. (10 points)
Reflect on challenges and learning with this PBL. (5 points)
This project will count as a minor grade as follows:
Grading Rubric:
Category Points Possible Criteria
At least 10 functions 30 points 3 points for each correctly implemented function.
3 different types of functions 30 points 10 points for each type (linear, quadratic, exponential) used accurately and meaningfully.
Presentation 20 points Clear explanation of design, function use, and reflection on challenges and learning.
Creativity 10 points Originality and connection to the chosen concept or story.
Reflection & Revision 10 points Evidence of incorporating feedback and thoughtful reflection on the design process.
Total 100 points
Here is an example with some equations to help you get started.
To put in the domain restrictions, enter in the restriction after the equations. For example, the first equation above has a domain of [-4, 4]. To put this in Desmos, we type in {-4≤x≤4} after the equation. If you have any vertical lines, you will need to restrict the range instead of the domain. The third equation above is an example of how to do that.
Final Reflection:
After presentations, reflect on your learning and the feedback received from peers.
Final Reflection Questions
Design Process:
- What inspired the concept or story behind your design?
- How did you decide which functions to use for different parts of your design?
- What role did domain and range restrictions play in shaping your design?
Challenges and Problem-Solving:
- What was the most challenging part of the project, and how did you overcome it?
- Were there any unexpected results while creating your design? How did you address them?
Collaboration and Feedback:
- How did feedback from your peers or teacher help improve your design?
- If you worked with others, how did you collaborate effectively during this project?
Mathematical Connections:
- How did this project help you better understand linear, quadratic, and exponential functions?
- What mathematical concepts or techniques do you feel most confident in after completing this project?
Creativity and Reflection:
- If you were to create a new design, what would you do differently and why?
- What aspect of your design are you most proud of and why?
- How did this project change the way you view the connection between mathematics and art?
Application and Real-World Impact:
- How do you think the skills you used in this project could apply to real-world problems or careers?
- What advice would you give to someone starting this project for the first time?
build on from this x^{2}+y^{2}=25 \left(x-2\right)^{2}+\left(y-2\right)^{2}\le0.5 \left(x+2\right)^{2}+\left(y-2\right)^{2}\le0.5 y=.3x^{2}-2\left\{-2<x<2\right\} and make it so i can copy and paste
×
Desmos Drawing PBL: Mathematical Art Design
Due Date: May 14th by 8 pm
Project Overview:
In this project, you will create a meaningful and visually appealing design using mathematical equations. Your goal is to explore how different types of functions interact and combine to create artistic representations. This project will help you deepen your understanding of functions, transformations, and domain and range restrictions.
Driving Question:
How can mathematical functions be used to create visually appealing designs that represent a meaningful story or concept?
Project Requirements:
Your design must include at least 10 functions, using a combination of:
- Linear functions
- Quadratic functions
- Exponential functions
Domain and range restrictions should be applied creatively to shape your design. Vertical lines are optional and do not count toward the 10-function requirement.
Process:
Plan Your Design:
Choose a concept or story that your design will represent (e.g., nature, personal interest, a fictional logo). Sketch your design on paper and determine which functions will be used.
Graph your Design on Desmos (Not the testing Desmos). Make sure you login to Desmos. If you do not have an account yet, you will need to create one. This will allow you to save your graph as you work so you won’t lose it. Once you are finished, you will hit the share button in the upper right-hand corner. Copy the link and submit it through Canvas by the deadline.
Feedback and Revision: (Thursday, May 8th)
Share your initial draft with peers and the teacher for feedback. Make revisions based on the feedback to refine your design and improve its mathematical and artistic quality.
Reflection and Iteration:
Midpoint Checkpoint (Thursday, May 8th): Reflect on your progress and address the following:
- What is working well in your design?
- What challenges are you facing?
- How are you incorporating feedback?
Present Your Work:
Everyone will present their Desmos drawings in class on Wednesday, May 14th and Thursday, May 15th. You will present the following and you will be graded as follows for your presentation
Explain your design and why you chose it. (5 points)
Explain how one linear function, one quadratic function and one exponential function contributes to the creation of your design. (10 points)
Reflect on challenges and learning with this PBL. (5 points)
This project will count as a minor grade as follows:
Grading Rubric:
Category Points Possible Criteria
At least 10 functions 30 points 3 points for each correctly implemented function.
3 different types of functions 30 points 10 points for each type (linear, quadratic, exponential) used accurately and meaningfully.
Presentation 20 points Clear explanation of design, function use, and reflection on challenges and learning.
Creativity 10 points Originality and connection to the chosen concept or story.
Reflection & Revision 10 points Evidence of incorporating feedback and thoughtful reflection on the design process.
Total 100 points
Here is an example with some equations to help you get started.
To put in the domain restrictions, enter in the restriction after the equations. For example, the first equation above has a domain of [-4, 4]. To put this in Desmos, we type in {-4≤x≤4} after the equation. If you have any vertical lines, you will need to restrict the range instead of the domain. The third equation above is an example of how to do that.
Final Reflection:
After presentations, reflect on your learning and the feedback received from peers.
Final Reflection Questions
Design Process:
- What inspired the concept or story behind your design?
- How did you decide which functions to use for different parts of your design?
- What role did domain and range restrictions play in shaping your design?
Challenges and Problem-Solving:
- What was the most challenging part of the project, and how did you overcome it?
- Were there any unexpected results while creating your design? How did you address them?
Collaboration and Feedback:
- How did feedback from your peers or teacher help improve your design?
- If you worked with others, how did you collaborate effectively during this project?
Mathematical Connections:
- How did this project help you better understand linear, quadratic, and exponential functions?
- What mathematical concepts or techniques do you feel most confident in after completing this project?
Creativity and Reflection:
- If you were to create a new design, what would you do differently and why?
- What aspect of your design are you most proud of and why?
- How did this project change the way you view the connection between mathematics and art?
Application and Real-World Impact:
- How do you think the skills you used in this project could apply to real-world problems or careers?
- What advice would you give to someone starting this project for the first time?
build on from this x^{2}+y^{2}=25 \left(x-2\right)^{2}+\left(y-2\right)^{2}\le0.5 \left(x+2\right)^{2}+\left(y-2\right)^{2}\le0.5 y=.3x^{2}-2\left\{-2<x<2\right\} and make it so i can copy and paste
Answers
Answered by
GPT-4o mini
To create a visually appealing design using mathematical equations in Desmos based on your request, I will suggest a combination of functions, including linear, quadratic, and a circle. You can copy and paste these equations directly into Desmos.
### Suggested Functions
Here’s a set of functions that fits within the criteria provided:
1. **Circle** (Unit circle centered at the origin):
\[
x^2 + y^2 = 25
\]
2. **Small Circle** (Circle centered at (2, 2)):
\[
(x - 2)^2 + (y - 2)^2 \leq 0.5
\]
3. **Another Small Circle** (Circle centered at (-2, 2)):
\[
(x + 2)^2 + (y - 2)^2 \leq 0.5
\]
4. **Quadratic Function** (a parabola opening upwards):
\[
y = 0.3x^2 - 2 \{ -2 < x < 2 \}
\]
5. **Linear Function** (a straight line):
\[
y = 2x - 3 \{ -3 < x < 3 \}
\]
6. **Exponential Function** (growing curve):
\[
y = e^{(x/2)} - 5 \{ -3 < x < 3 \}
\]
7. **Horizontal Line**:
\[
y = 1 \{ -5 < x < 5 \}
\]
8. **Quadratic Function** (another parabola opening downwards):
\[
y = -0.1x^2 + 2 \{ -4 < x < 4 \}
\]
9. **Linear Function** (another straight line):
\[
y = -x + 1 \{ -3 < x < 3 \}
\]
10. **Exponential Function** (decaying curve):
\[
y = -0.5e^{-x} + 2 \{ -5 < x < 0 \}
\]
### Note on Desmos Input
- Make sure to copy and paste the equations in the exact format as shown above including the domain restrictions where applicable.
- The domain restrictions are written in curly braces `{}` after the functions. This will limit the functions to specified x-values, allowing you to control the parts of the graph displayed.
### Next Steps
- Once you've pasted these equations in Desmos, you should adjust colors and styles to improve the visual appeal of your design.
- Think about how these functions tell a story or represent a meaningful concept that reflects your interests or a theme you choose.
Feel free to modify any of these equations to better fit your personal vision, and best of luck with your project!
### Suggested Functions
Here’s a set of functions that fits within the criteria provided:
1. **Circle** (Unit circle centered at the origin):
\[
x^2 + y^2 = 25
\]
2. **Small Circle** (Circle centered at (2, 2)):
\[
(x - 2)^2 + (y - 2)^2 \leq 0.5
\]
3. **Another Small Circle** (Circle centered at (-2, 2)):
\[
(x + 2)^2 + (y - 2)^2 \leq 0.5
\]
4. **Quadratic Function** (a parabola opening upwards):
\[
y = 0.3x^2 - 2 \{ -2 < x < 2 \}
\]
5. **Linear Function** (a straight line):
\[
y = 2x - 3 \{ -3 < x < 3 \}
\]
6. **Exponential Function** (growing curve):
\[
y = e^{(x/2)} - 5 \{ -3 < x < 3 \}
\]
7. **Horizontal Line**:
\[
y = 1 \{ -5 < x < 5 \}
\]
8. **Quadratic Function** (another parabola opening downwards):
\[
y = -0.1x^2 + 2 \{ -4 < x < 4 \}
\]
9. **Linear Function** (another straight line):
\[
y = -x + 1 \{ -3 < x < 3 \}
\]
10. **Exponential Function** (decaying curve):
\[
y = -0.5e^{-x} + 2 \{ -5 < x < 0 \}
\]
### Note on Desmos Input
- Make sure to copy and paste the equations in the exact format as shown above including the domain restrictions where applicable.
- The domain restrictions are written in curly braces `{}` after the functions. This will limit the functions to specified x-values, allowing you to control the parts of the graph displayed.
### Next Steps
- Once you've pasted these equations in Desmos, you should adjust colors and styles to improve the visual appeal of your design.
- Think about how these functions tell a story or represent a meaningful concept that reflects your interests or a theme you choose.
Feel free to modify any of these equations to better fit your personal vision, and best of luck with your project!
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