Project Title: 5th Century Studios
Project Timeline and Duration: 5 weeks
Grade Level: Secondary.
Unit Focus: This project is an introductory project that addresses priority Common Core Standards for Unit 1, Traditional Geometry, and Unit 5, Integrated Math Pathways.
It also focuses students on becoming familiar with the eight Mathematical Practices established in the Common Core Standards, and on practicing two key 21st Century skills, teamwork and communication.
In addition, students will practice using online technologies and non-print resources for Geometry. Read the Overview of Assessment [link] for details on project outcomes.
Critical Area: In this unit, students establish triangle congruence criteria, based on analyses of rigid motions and formal constructions. They use triangle congruence as a familiar foundation for the development of formal proof. Students prove theorems—using a variety of formats—and solve problems about triangles, quadrilaterals, and other polygons. They apply reasoning to complete geometric constructions and explain why they work.
Explore the Common Core State Standards: http://www.corestandards.org/
Suggested Priority Standards for Project 1:
G.CO.3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it into itself.
G.CO.6. Use geometric descriptions of rigid motions to transform figures and predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
G.CO.12. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic software, etc.) Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
Suggested Supporting Standards for Project 1:
G.CO.1.Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line distance along a line, and distance around a circular arc.
G.CO.2. Represent transformations in a plane using; e.g. transparencies and geometry software; describe transformations as functions that take points in the plan as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g. translation versus horizontal stretch.)
G.CO.4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
G.CO.5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g. graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
G.CO.7. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
G.CO.13. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Project Overview: This project introduces students to a brief history of Geometry, geometric terms, geometric shapes, and transformation and manipulation of shapes through understanding reflections, tessellations, and dilations. Students will form marketing teams to ‘sell’ Geometry by explaining key terms, demonstrating key shapes, and describing the significance of Geometry to an audience.
The Scenario and Challenge: Euclid, the ‘Father of Geometry,’ recently (well, not so recently…in the 3rd Century B.C.) decided to start a teen club for interested Geometry students. To attract the attention of youth, he has named his club The 5th Century Studios, in honor of, Plato, who lived two hundred years earlier. Euclid needs a marketing campaign to explain the importance of Geometry and the basic principles. This won’t be enough, however. He needs a clever marketing message to appeal to an audience who may not know how Geometry is used in the real world, or why it’s critical to so many areas of modern life. Fortunately, through the benefits of time travel, he can take advantage of the Internet. His goal is to market The 5th Street Studios to teenagers. To do this, he has invited several teams of young experts to compete for the prize of best presentation. Euclid will accept a webpage, a slide show, or an eye-catching poster, or flyer to get his message out. The product is up to you; it just needs to be provocative and informative.
He also knows he needs to update his message. Above Plato’s Temple was the inscription: “Only he who is familiar with geometry shall be admitted here.” That needs to be changed. He wants a new motto to go over the entrance to the teen club.
Your team has been chosen to enter the competition. Your challenge is to design and present a presentation that tells young people why Plato feels strongly about Geometry, and to use specific terms, shapes, and transformations to show what Geometry teaches us, why it’s useful, and where it applies to the world around us. You will also draft a motto for Euclid’s new club.
The Driving Question: How can we, as a team of young Geometry specialists, create a web page or presentation aimed at teens that combines geometric information and historical facts about Geometry to explain the significance of Geometry to their lives?