# Introduce the Project and Generate Interest

1. Introduce the challenge. This project teaches students the basics of triangles, such as types, congruence, proofs, and similarity, by asking each student to create a poster, drawing, or personal adornment such as a fingernail design, piece of jewelry, or tattoo that uses at least two different triangular shapes. The product must meet the criteria for ‘beautiful’—that is, it must display symmetry or other design elements that make it attractive.

2. Describe the scenario and the task. Clarify, if necessary
The challenge in this project is for students to use triangular shapes to create a piece of art that they can defend as ‘beautiful.’ They must craft and think through their criteria for their artwork, rather than merely create it, and be able to explain the criteria to peers. In the early stages of the project, students will explore triangles in art to learn how this shape has influenced artistic design.

Students should choose their own art piece. The choices will vary with classes and teacher discretion. Possibilities include: a poster for a room; a piece of fine art; an image of a person represented in triangles; a drawing of a mandala; fingernail art; or a tattoo. Each piece will be individually designed. However, students will work throughout the project in small cohorts as they proceed on their design.

Students must also be able to answer the Driving Question by demonstrating that their art piece is ‘beautiful,’ according to criteria they will develop with their cohort. They must also be able to explain the kinds of triangles and how they were used in one other piece of art created by another student.

The Art of Triangles Project is designed to engage students in the study of geometry by having them use their knowledge of congruence and similarity in various types of triangles to create artwork. Students will be expected to know how triangles have influenced art and symmetry, and how they can use triangles in their own designs. They must be able to discern and describe triangles in a piece of artwork, and explain the properties of the four types of triangles. They must also know how to bisect triangles and prove theorems for triangles.

The project will conclude with an exam and a gallery of creations. Students will view the gallery of designs and reflect on them.

The crucial aspect of the project is the final product. Students will be expected to use their knowledge and skill to create a poster, drawing, or personal adornment that employs triangles to make it ‘beautiful.’ Students should be able to describe, in their own words why their product is ‘beautiful.’ Other students must be able to identify and explain the use of triangles in the artwork.

3. Frame the task with the Driving Question. How can I use a variety of triangles to create a poster, drawing, or personal adornment that meets the criteria for ‘beautiful’ artwork?

4. Describe the concepts that students will learn as they complete the project. The project will teach the four kinds of triangles and the theorems and procedures associated with triangles, including bisectors, similarities, and proofs.

5. If using Curriki Geometry for your students, invite them to the site.

6. Have your students review the student materials available to them. You may also choose to download and print some of the resources for distribution as a student packet.

7. Anchor rubrics. Students should understand project grading and rubric language.

If your students have no or little experience with PBL, you may have to begin the first day by explaining the process. They can also watch the video Project Based Learning: Explained (approximately 4 minutes) or a video on PBL and mathematics (approximately 30 minutes).

## Tips and Tools

Generate interest in the project by using an Entry Event. Examples:
Have students view Cezanne’s The Card Players and identify the triangular shapes in the painting.
Show and discuss examples of triangles in art. Students may also view these on their own.

• If your or students would like to change or refine the Driving Question, use this Protocol for Refining the Driving Question.
• It’s critical to a good start that students understand they will be assessed on (1) geometry content; (2) mathematical practices; (3) teamwork; (4) presentations.

The Project Rubric includes a ‘Breakthrough’ category at the bottom of the rubric, which has been left blank to recognize unusual creativity and design. This section can be filled in by the teacher, or by students after discussion with cohorts.

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