Math
Is there a proof that shows that you can express any 3D printed object as layers of 2D planes?The
Project: Math Puzzles
The purpose of this activity is help students understand 3D forms through modeling and building math based puzzles.Software: Wolfram's Mathematica
Mathematica is an application that allows you to create 3D forms through manipulating mathematical equations.Software: Surfcad
Surfcad is a python proofofconcept CAD library written byto make models of mathematical objects. Surface is constructed based on mathematical functions.
Project: Tessellations
The purpose of this activity is help students understand 3D forms through modeling tessellations.Project: Polyhedra
The purpose of this activity is help students understand 3D forms through modeling polyhedrons.Project: Fractals
The purpose of this activity is help students understand 3D forms through modeling 2D and some 3D fractals.NYS Learning Standards for Mathematics, Science, and Technology:
Project  Standard 1  Standard 2  Standard 3  Standard 4  Standard 5  Standard 6  Standard 7 

Math Puzzles  √  √  √  √  √  √  √ 
Tessellations  √  √  √  √  √  √  √ 
Polyhedra  √  √  √  √  √  √  √ 
Fractals  √  √  √  √  √  √  √ 
Standard 1:
Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions.
Standard 2: Students will access, generate, process, and transfer information using appropriate technologies.
Standard 3: Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in realworld settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Standard 4: Students will understand and apply scientific concepts, principles, and theories pertaining to the physical setting and living environment and recognize the historical development of ideas in science.
Standard 5: Students will apply technological knowledge and skills to design, construct, use, and evaluate products and systems to satisfy human and environmental needs.
Standard 6: Students will understand the relationships and common themes that connect mathematics, science, and technology and apply the themes to these and other areas of learning.
Standard 7: Students will apply the knowledge and thinking skills of mathematics, science, and technology to address reallife problems and make informed decisions.
Standard 2: Students will access, generate, process, and transfer information using appropriate technologies.
Standard 3: Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in realworld settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Standard 4: Students will understand and apply scientific concepts, principles, and theories pertaining to the physical setting and living environment and recognize the historical development of ideas in science.
Standard 5: Students will apply technological knowledge and skills to design, construct, use, and evaluate products and systems to satisfy human and environmental needs.
Standard 6: Students will understand the relationships and common themes that connect mathematics, science, and technology and apply the themes to these and other areas of learning.
Standard 7: Students will apply the knowledge and thinking skills of mathematics, science, and technology to address reallife problems and make informed decisions.
NYS Learning Standards for CDOS:
Project  Standard 1  Standard 2  Standard 3a  Standard 3b 

Math Puzzles  √  √  √  
Tessellations  √  √  √  
Polyhedra  √  √  √  
Fractals  √  √  √ 

Standard 1:
Career Development
Students will be knowledgeable about the world of work, explore career options, and relate personal skills, aptitudes, and abilities to future career decisions.
Students will learn about the changing nature of the workplace, the value of work to society, and the connection of work to the achievement of personal goals.

Standard 2: Integrated Learning
Students will demonstrate how academic knowledge and skills are applied in the workplace and other settings.
Integrated learning encourages students to use essential academic concepts, facts, and procedures in applications related to life skills and the world of work. This approach allows students to see the usefulness of the concepts that they are being asked to learn and to understand their potential application in the world of work.

Standard 3a: Universal Foundation Skills
Students will demonstrate mastery of the foundation skills and competencies essential for success in the workplace.

Standard 3b: Career Majors
Students who choose a career major will acquire the careerspecific technical knowledge/skills necessary to progress toward gainful employment, career advancement, and success in postsecondary programs.