UCCI Course Description

Algebra Worksheets

Students solve and simplify simple proportions and evaluate and describe direct variation. Students work with rational expressions, ratios, proportion, and percent through problem sets and worksheets to prepare them for the first key unit project.

Scaling Images Through Algebra

Students create and scale an original mural design using colored pencils and grid structures. Students paint their artwork on a larger format. Using their scaled mural designs, students create ratios, proportions, and percents by comparing points in their original and scaled drawings. Students evaluate their drawings by solving proportions to validate the accuracy of their scaling. Students resize their image by using fractions with polynomials (rational expressions) and factoring techniques to investigate a variety of sizes their drawing might take.

Applying Scaling Techniques in Photoshop

In Photoshop, students take an existing image to scan and distort by keeping one of the dimensions a constant ratio and altering different parameters. Students use the techniques garnered in the Scaling Images Through Algebra Project to predict, describe, and interpret the outcomes of their scaled images. Students also apply different Photoshop techniques to alter and distort images and postulate the possible algebraic statements that might make the computer model possible. Students will add their creations and narratives to their electronic portfolio.

Using the lines that occur naturally in one-point perspective, students will identify and model linear relationships both algebraically and graphically.

Library Project

Students complete a one-point perspective pencil drawing based on the bookshelves in the library, and then finalize their drawing in ink, using watercolors for texture and shading. These drawing demonstrate vanishing point, size/distance, angles, texture, and shading. As students identify and explain object relationships and perspective, students also examine, identify, and represent linear models and develop a working knowledge of slope and intercepts. One-point perspective will be redefined by a system of linear equations. Students represent slope as variation, a constant rate of change, and as a tangent ratio in their drawings. Students will complete this assignment by learning to matt and frame one of their perspective drawings.

Students identify, represent, and manipulate rational and quadratic models by using specific parts of the human body from drawings by Da Vinci.

Da Vinci's Vitruvian Man

Students are introduced to the works of Leonardo Da Vinci through a brief historical overview of his time and importance. The Vitruvian Man is discussed as a representation of ideal human proportions described by the Roman architect Vitruvius. As the students identify and explain characteristics of the human body through Da Vinci's drawings, students also examine, identify, and represent parabolas through their ability to model rational and quadratic functions. Students develop the skills to manipulate different forms of quadratic equations. They learn the benefit of each form to explain features of the face and body.In this process students learn the algebraic and concepts needed to communicate quadratics algebraically and graphically such as completing the square, factoring methods, quadratic formula, and extracting square roots. Using technology such as graphing calculators, online graphing tools, and animation/modeling software, students demonstrate algebraically and graphically aesthetically pleasing proportions (i.e.-Golden Ratio) and quadratic solutions to these proportions. Students complete problem-sets, model parabolas, analyze systems of inequalities, quadratics in vertex forms, shifts of quadratics equations shifts, and reinforce rational equations using measurements and calculations derived from the Vitruvian Man.  

Contemporary Man or Woman

Students produce a digital photograph of themselves. Students measure the proportions of their own body and compare these to the measurements of the Vitruvian Man. Using graphing calculators and online graphing tools, students make algebraic transformations (graph shifts) by manipulations of these equations. Students develop an understanding of how the manipulation of equations changes the graphic representation and consequently the human characteristics and proportions. Students create models of themselves using 3D modeling software and manipulate the various characteristics to emphasize a chosen feature. The algebraic description of their shifts is attached and the work is added to their electronic portfolio.

Students will apply linear and absolute value functions to the mechanics of pinhole cameras and the manual use of digital cameras.

Pinhole Camera

Students represent angle of incidence by linear and absolute value functions. They will use piecewise functions and ratios formed by similar triangles and solve rational equations. Students then build, use, and develop their own pinhole cameras. Using one photograph produced with their pinhole camera, students will identify angles, proportions, parabolas, and hyperbolas.
 
Weekly History of Photography Worksheets

Students study the history of photography and the impact of technological changes through time. Each week students examine the different purposes and uses of photography (i.e. sociopolitical, advertising, propaganda, art) by completing worksheets that build their observational skills and understanding of history. A written, oral, or graphic reflection of the impact of photography will be added to their electronic portfolio.

Digital Photography

Function terminology and representations such as domain (dependent variable) and range (independent variable) will be applied to the mechanics of pinhole cameras and the manual use of digital cameras. After studying various genres (such as commercial photography, fine art photography, photojournalism, and studio photography), students create photographs using digital cameras on manual settings and emphasizing the 13 basics areas (self portrait, series, scenery, etc) of photography developing the skills to express their ideas artistically. Photoshop will be used to manipulate and enhance students’ images. Students also compare the workings of a digital camera to a pinhole/film cameras. Students matt their chosen photographs and add all photographs to their digital portfolios.

Raster vs. Vector

Students investigate how quadratics are used to create vector images/drawings. Students create an example of the triangles used to describe a truetype font and demonstrate how the curves are applied to fabricate a seamless font curve and add their project/observations to their electronic portfolio.

Students will refine and deepen their understanding of key concepts in both algebra and art.  Students will identify their own areas of strength and areas that need reinforcement.

Refining and reinforcing concepts is spiraling the content by continuing to curve or return back to a topic. A spiral curriculum, by moving in a circular pattern from topic to topic, seeks to catch students when they first become ready to learn something and pick up other students the next time the topic occurs. The first four units introduce the main content. The refining comes in this unit and this half of the course. These spiraling activities develop depth of understanding and breadth of overall interconnectedness of the algebra content. Unit 5 is intended to allow students some time for "pure" algebra and "pure" art work to both reinforce and introduce concepts appropriate to each discipline.

Algebra Review

Using benchmark tests, students are assessed for areas of algebraic strength and weakness. Results are analyzed by individual students and by class. Students have access to this data and are reflect in writing and orally on their specific areas of need. Using specific skill packets, students can fill in the gaps in their algebraic knowledge. Class-wide areas of need are addressed by classroom re-teaching.

Abstract Composition

Students identify and refine the basic elements of art to create an abstract artwork emphasizing line, shape, positive and negative spaces, texture, movement and direction, shading, size, and color to create aesthetically pleasing compositions. No representational images will be permitted in this piece. Students will add this work to their portfolio.

Students will analyze cost, baseline operating costs, and profit margin in the art industry using systems of equations and exponential growth and decay. Students will learn about the impact of artistic message, marketing, and the media.

Art Show Budgeting

Given a sample budget, students analyze cost, baseline operating costs, and profit margin using systems of linear equations and exponential growth and decay. Students will model their operating costs by linear and exponential representation. Students will learn about the impact of artistic message and the media. Students will research costs of and profit margin of artworks in different regions. They will create a sample budget for a student art show using information from their research.

Careers in Art Paper

Students self-assess the style of their own artwork and explore possible career options, educational pathways, and different markets. Students research various art venues (such as internet, galleries, studios, museums) and examine potential markets for merchandising their artwork (self-owned business, subcontracting, contests). Students write a two-page paper based on their research.

Matting and Mounting

By utilizing algebraic methods and measurement, students prepare and mount one of their art pieces for display and show.

Famous Artists and Styles Presentation

Students investigate an artist whose artwork they admire and the market that supported the artist. Students produce a narrated 2-3 minute video showcasing a minimum of 13 pieces of the chosen artist’s work, and a biography of the artist’s life, including a piece of artwork the student likes most and explaining why.   

This unit is designed for students to self-assess their algebraic mastery and artistic understanding through demonstration of their portfolio and digital media presentation.

Final Student Portfolio (Algebra and Art)

The culminating portfolio consists of the student's previous key artwork assignments, which demonstrate the student's overall algebraic mastery. Examples of work included:

• Toolkits (graphic organizer) of interrelated math topics
• Key unit projects
• Learning logs (Cornell notes)
• Homework
• Class activities
• Self and peer critiques
• Assessments including oral, partner quizzes, unit exams, midterms, and finals.

Final Presentation Integrating Algebra and Art

Students focus on one of the previous projects completed in the course to create a 3-5 minute digital media presentation (using one of the following methods: FinalCut, Dreamweaver, Podcast, MovieMaker, live@edu, Google Docs) that teaches a lesson on how algebra and art relate. 

Final Examination

This unit includes the final examination for the course.

Through a final culminating project, students apply and demonstrate theoretic algebraic concepts acquired throughout the course. Students revisit perspective drawing, producing an artistic work which uses two-point perspective. Students discuss both the mathematical and artistic elements of these works bridging from algebra into initial geometric concepts.

Final Two-Point Perspective Drawing

Students survey the use of perspective across cultures and history. Students then identify and apply the elements of two-point perspective by creating an artwork (styles varying from a realistic rendering of a building to an urban art piece) that demonstrates proper use of scale, angle, shading, texture, and details. Students present the drawing as the final project in their individual portfolios.

Bridging Algebra to Geometry

Students identify in their Two-Point Perspective Drawings key algebraic concepts they have learned in the course. Students are introduced to key geometric concepts such as polygons (triangles and quadrilaterals), similarities, properties of parallel lines, and area and volume, and identify these concepts on their drawing.