“Math Projects” Assignment

(#6) Math 10 Project: Geometry of Design

group: Michelle, Meghan, Paul

This is certainly an interesting project from the point of view of math appreciation.  There are many students who are turned off by algebra and numbers, and for them this playful visual exercise can do a great deal to draw them in to the world of math.  The practicality of this project may be called in to question, as there is notoriously short time in class.  However, this may be a criticism of the school’s scheduling more than the assignment itself, which is wonderfully enriching and deserves more time than it will inevitably be allotted.



Strengths:

• Requires very little base knowledge.  This makes it accessible to everyone in the class.  It may inspire the struggling students to see a project in which their previous weaknesses in mathematics are not compounded.
• Combines math, history, nature and art.  Let’s face it, most people find art and history far more interesting than mathematics.  Showing how math can relate to the these “fun” subjects will go a long way towards showing students how enjoyable math can be.
• This project enables students to choose their own piece of art or object from nature, which allows for broad ranges of interest.  
• After students complete this project they will see how mathematics is in so many different aspects of everyday life that they probably did not realize before.  One of the main outcomes of this project is math appreciation.   

Weaknesses or Constraints:

• Students may be able to find geometric shapes in well known art on the Internet.  This will prevent the student from playing around with shapes and tracing paper to find geometry in the item themselves.
• Perhaps the topic might be too narrow and not really interest all students.
• Project will be hard to cram into a busy curriculum as it is time-intensive and does not cover many PLOs.

Possible Modifications, Adaptations or Extensions:

• One possible modification of the project is having the students orally present the steps they took to finding geometry as opposed to the step by step write up. This might benefit some students, that  are more comfortable verbalizing their process than writing out the steps. Another advantage is students will have a chance to share their findings with their peers.
• Perhaps students could then make their own piece of art work which is based on geometric shapes or mathematical ratios.  

Our Project:

Math12 Project: Mathematics in Art Design

Grade Level: We chose to do this project in Math 12 because geometry is no longer in the curriculum and this is a great enrichment project for these math students who have knowledge about geometric and trigonometric and shapes.
Our project will span two classes over a period of one week.

Purpose:  The purpose of this project is for students to understand and see how mathematics is within many works of art, even though it is not obvious.  The planning of many pieces of art includes mathematical shapes, calculations and ratios.  Students will play around with and sketch geometric shapes, the golden rectangle, logarithmic spirals etc. and see how they can be manipulated to form interesting compositions.  Students will develop their own work of art which is based on their chosen mathematical elements. 
    

Description of Activities:

Day 1:   

• Show students examples of famous art which contains and is based on geometric shapes or ratios.  There will be a PowerPoint presentation or overheads with examples and also a hand-out for students which includes: the Mona Lisa, the Parthenon, Egyptian art, Mondrian, daVinci etc.  
• After students see how these basic shapes and ratios are behind the planning of many works of art students will learn how to draw, using a compass and ruler, these basic geometric shapes.  Some shapes they will practice drawing are the golden rectangle, logarithmic spirals, polygons, stars and possibly trigonometric functions.
• Students will decide by the end of this class which geometric shape(s) or ratio(s) they want to use to construct their artwork drawing.  

Homework:  Students plan and sketch their artwork drawing.  


Day 2 (One Week Later):  

• Students make their drawing on large poster board.  The drawing can be done in markers, charcoal or pastels.  By the end of the class students should be able to have their work finished.  If the project is being done in the art room then students could use other materials such as paint, collage, etc.  

Sources:
Kimberly Elam (2001). Geometry of Design: Studies in Proportion and Composition. (NY: Princeton Architectural Press.)
Miranda Lundy (1998).  Sacred Geometry. (NY: Walker & Co.)


Timeline of Project:  Two classes separated by a week.  Students are required to plan their artwork between the two classes and come to the second class with a complete plan so that they have the maximum amount of time to complete the artwork in the second class.



Students are Required to Produce:  

• a large composition drawing which incorporates at least one mathematical element in the planning.  
• all their planning materials such as sketches of shapes, rough drafts and rough work of their final composition.
• A written or spoken explanation of the mathematics involved.

Marking Criteria: Rubric (20 marks total)

Use of Class Time (3 marks)

• 0 - Absent
• 1 - Come to second class without plan, make poor use of class time
• 2 - Come to second class without plan, make good use of class time
• 3 - Come to second class with plan, make good use of class time

Presentation (2 marks)

• 0 - Unfinished or missing
• 1 - Poor effort, obviously done at the last minute
• 2 - Decent to good effort.  Most students will receive this mark.

Mathematical Content (10 marks)

• 0 - Missing
• 2 - No apparent mathematical content
• 4 - Mathematical concept attempted but incorrectly applied (such as an unmeasured freehand spiral)
• 6 - Mathematical concept properly applied, but with errors in explanation.
• 8 - One mathematical concept properly applied and explained
• 10 - More than one mathematical concept properly applied and explained

Completeness (5 marks)

• 1 mark for each of the following completed on time: Planning materials, rough draft, explanatory piece
• 2 marks for final draft submitted on time

Justification for Rubric: Since this is a math class and not an art class, the artistic component is negligible.  The largest component is the mathematical content.  It follows a linear progression where 0 marks are earned for doing nothing, and 8 marks are earned for doing the minimum.  An extra 2 can be gained by going a little bit beyond.  The students would, of course, be made aware of this beforehand.  It is expected that most students will attempt to incorporate 2 mathematical concepts, and even if they completely mess one of them up, they’ll still achieve 8 out of 10.  We feel that marks should not be difficult to obtain on enrichment projects such as this.