Arts/Math Integration Project

A unique cross-discipline focus on a broad spectrum of mathematical topics connected to artistic projects.

On July 1, 2007, the Washington State Board for Community and Technical Colleges (SBCTC) was awarded a two-year $150,000 grant from the Ford Foundation for the Arts/Math Integration Program. Drawing on its experience managing the Transition Math Project (TMP) – a cross-sector, public/private venture funded by the State Legislature and the Gates Foundation – the SBCTC solicited, reviewed and selected two proposals from teams that demonstrated the local support, content expertise and most promise for sustainability.

The end result of the work is a unique cross-discipline focus on a broad spectrum of mathematical topics connected to artistic projects. Our collection of the seven different projects is ready-to-run and accessible through this website. Each project includes annotated activities aimed at instructors or workshop coordinators and a collection of activity sheets (electronic) for use by students or workshop participants.


Educational Service District 105

Yakima Valley ProjectOn the East side of Washington, the Yakima Valley’s Educational Service District 105 serves one of the most diverse regions in Washington State. The ESD’s proposal to design a set of integrated art/math modules – aligned to the College Readiness Standards – was strengthened not only by their current work with the TMP but also by their local Art Fusion project funded through the U.S. Department of Education.


Project TIME

project timeOn the West side of Washington, Project TIME has led an art in math initiative that also draws on their work as a TMP local project. Project TIME is a partnership of Green River Community College, K-12 school districts, and 4-year universities and examines issues around transitions in mathematics while facilitating student progress in mathematics from one sector to another.




Projects

Lessons will focus on the development of a school-based art piece or project. This activity can be used as a class or school project. Using math and art, Legacy Project students will work in small teams to identify ways of enhancing their school environment for learners, families, staff and visitors and to develop, design, and implement realistic and artistic solutions.Projects will be aligned with the Math College Readiness Math Standards and Washington state Arts Essential Academic Learning Requirements.

The Legacy Project is a challenge for the senior class to work as a cohort to identify and solve campus problem to enhance the school environment. Students identify a need of the school campus to enhance the school environment for learners, families, staff and visitors and develop, design, and implement a solution to that need. The Legacy Project contains components of the TALONS (senior portfolio). Credit can be earned or retrieved in math, art, science, social issues, CWP, or as an elective based on student credit evaluation in consultation with advisory teachers.

OBJECTIVES

  1. Work with a cohort to identify and solve a campus problem by enhancing the school environment using math and art.
  2. Meet the Washington State graduation requirements in mathematics and art.
  3. Complete designated T.A.L.O.N.S. (E.A.G.L.E. High School senior project) components.
  4. Demonstrate attitudes and skills of active citizenship.

MATH STANDARDS
3, 5, and 6

RESOURCES

“Got Math Art Journal?” will allow the student in a math or art class to create a journal that will include math concepts and art work.  This will be an introduction to two art elements, line and shape. The project is based on 10 journal entry lessons which provide instruction in specific art concepts and math skills.

The use of art journals is used by artists as meaningful expressions of ideas, concepts and insights. These lessons will engage students in the artistic process of journaling (writing and illustrations) with Algebra 2 as an integrated method of note taking while learning art concepts. These lessons are linked to the Math College Readiness Standards. Specifically, students will be asked to solve various types of equations and inequalities numerically, graphically, and algebraically; interpret solutions algebraically and in the context of the problem; distinguish between exact and approximate answers and express these equations in their art journals.

OBJECTIVES

Students will complete the 10 entries in the Math Art Journal as measured by achieving a score of 3 or 4 on the visual art CBPAs.

CRMS: 3.1, 3.4, 5.2, 8.2, 8.4

SAMPLE PROCEDURES

  • Procedures for specific instruction are identified in each of the 10 developed lessons plans which represent the following entries.
  • Blind contour drawing or continuous contour line drawing
  • Adding detail to the blind/continuous contour line drawing
  • Drawing a visual of the history of numbers
  • Geometric or organic shapes are created when a line meets
  • Introducing primary colors
  • Introducing secondary colors
  • Picture graphing
  • Basic graph forms
  • Looking at art – write and equation
  • Geometric series

RESOURCES

Game Design and Probability are addressed through 2D visual arts instruction. The purpose of this project is to demonstrate knowledge and understanding of art elements and principals and the math concept of probability. The art lessons include three units of study which also address the math College Readiness Standards. Students will use their understanding of the elements of art and principals of design as well as use empirical/experimental and theoretical probability to investigate, represent, solve, and interpret the probability and/or counting techniques and provide evidence of learning.

During the development phase of this project the following criteria were kept in mind: Materials must be higher than a 10th grade level and must be able to prepare students for a secondary education.

Overall project will be a module containing 2-4 weeks of materials. One to two component(s) will be chosen from the Washington State Transition Mathematics Project College Readiness Mathematics Standards and support materials must help students prepare to meet that standard by providing evidence of learning.

OBJECTIVES

Students will develop a true understanding of how probability can be used to develop a fair game. Students will develop a game that is consistent and measurable as well as enjoyable. Use group work to achieve goals and develop a team approach to game development.

CRMS:
Probablility and Statistics: 6.1

RESOURCES

The process of creating a small clay sculpture that will be open-face cast into glass involves the understanding and utilization of geometric formulas for perimeter, area and volume. The casting process involves work with algebraic formulas, graphs of linear functions and understanding and interpreting graphs of two variables.

Math Key Concepts/Goals:

  • Geometric Formulas: Volume, Area, Perimeter, Surface Area
  • Graphing: interpretation of graphs, relation between two variables, and creation of graphs
  • Graphing Geometric Figures: reflections, translations, symmetry
  • WASL (Washington Assessment of Student Learning) Practice
  • Linear Functions: relationship between graphical, tabular and symbolic form

CRMS:
Number sense: 4.3, Geometry: 5.2, 5.3, Algebra: 7.3, Functions: 8.2, 8.4

WASHINGTON MATH STANDARDS:
A 1.4, 1.6, G .5, .6, M1.0, 1.0 B, 1.3, 1.4

STUDENT ACHIEVEMENTS

At the end of this unit the students will know and be able to:

  1. Calculate volume and surface area of molds and determine the amount of material needed to create sculpture.
  2. Create linear equations from tables.

PRE-REQUISITE KNOWLEDGE/SKILLS:
1. Knowledge of graphing in two dimension

SAMPLE ACTIVITIES:

  • 2-D Sketch and 3-D Clay Model Activity
  • Volume and Surface Area Application Problems
  • Hot Tub Problem Worksheet
  • 400 Meter Race News Story & Worksheet
  • Bus Trip Worksheet
  • *Several activities adapted from previously released math WASL test questions

RESOURCES

Mathematics is a critical component of animation in general and computer games in particular.

Target audience:

  • Grades 9 – 12
  • Students needing motivation in Algebra and Geometry
  • Students needing additional real-life applications for Algebra II, Precalculus, and Trigonometry topics with a “wow” factor

CRMS:

PS/Reasoning: 1.2, Communication: 2.3, Probability/Stats: 6.2

WASHINGTON MATH STANDARDS:
M1.2, M1.3, M2.5, M2.6

ACHIEVEMENTS:

At the end of the chapter students will know and be able to:

  • Describe position of an object on a coordinate system.
  • Illustrate how a position of a point is denoted differently in a computer animation.
  • Convert numbers into different bases and understand how hexadecimal numbers are used to represent RGB colors in computer graphics.
  • Explain how ratios and proportions are used in computer simulation.
  • Adapt a piece of computer or calculator code to change direction, color or speed in an animation.
  • Use vectors to describe direction and movement in games.
  • Describe how matrices can move a figure to a new position.
  • Describe and illustrate the parallax effect.

SAMPLE ACTIVITIES:

  • Introductory problem: Racing Away
  • Animation Worksheets #1, #2, #3
  • Video 02 and Cornell Notes for Video 02
  • Hexadecimal Numbers and RGB color website
  • Flip Book
  • Where in the World is Wally’s Treasure

RESOURCES

Music can be modeled and refined/changed with mathematics.

Target audience:
Students needing additional real-life music applications for Algebra II, Precalculus, and Trigonometry topics with a “wow” factor that includes: function notation, translation of functions, application/translation of sine functions.

CRMS:
Functions 8.2b, 8.2c, 8.3a, 8.6d, and 8.6e

ACHIEVEMENTS

At the end of the chapter students will know and be able to:

Write a tune on Finale Notepad.
Use translations to change a melody.
Analyze how a particular translation will affect a tune or a function.
Use logger pro to tune a musical instrument.

PRE-REQUISITE KNOWLEDGE/SKILLS:
Graphing

OBJECTIVES

Students will develop a true understanding of how probability can be used to develop a fair game. Students will develop a game that is consistent and measurable as well as enjoyable. Use group work to achieve goals and develop a team approach to game development.

RESOURCES

ceramic
The project involves integrating the creation of ceramic vases with geometric concepts from mathematics. The mathematics concepts include measurement skills in length, area, volume, shrinkage and absorption calculations, scaling, and tessellation patterns with symmetry, and transformational geometry. The art components include designing, measuring, dimensioning and building a vessel from a template guideline or a designated extrusion form. The process of creating the vase, drying the clay, firing the vase in a kiln (“bisque”) and doing a final glaze firing, will demonstrate real world mathematics concepts.

TIME FRAME: 6 days

Target Audience:

  • Grades 9 – 12
  • Students needing additional practice or review with:
  • Using geometric formulas
  • Geometric transformations, (rotations, reflections, etc.)

CRMS:
Number sense: 4.3, Geometry: 5.2, 5.3

WASHINGTON MATH STANDARDS:
M1.3, M1.4, M1.1B

ACHIEVMENTS:

At the end of this unit students will know and be able to:

  • Design and construct a vase which follows the cutout guideline the student premeasured and designed earlier or the extrusion selected.
  • Calculate volume and surface area of the vase and determine the amount of material needed to create vase.
  • Determine the volume and surface area of vase.
  • Determine the percent of shrinkage in the four stages of the vase (wet, dry, bisque firing and glaze firing).
  • Describe the patterns on the vase in terms of tessellations, symmetry, and transformational geometry using terms like “rotation” “reflection” “translation” “glide reflection” “rotational symmetry” “reflective symmetry”.
  • Utilize scaling to draw a two-dimensional image of the three-dimensional object
  • Reflect on process of designing Measuring, Dimensioning, and Building Process.

SAMPLE ACTIVITIES:

  • Origins of Clay and Clay Stages
  • Hand-building Techniques Geometric Analysis Worksheet

RESOURCES

The Art/Math Integration project consisted of 6 High School teachers, 2 College faculty members, 1 Writer/Trainer on A/M modules and 1 Regional Math Coordinator. Of the 10 participants there were 7 current or former Math teachers and 3 current or former Art teachers. All participants had a minimum of 10 years classroom experience. Below is a summary of lessons learned from the project.

When implementing art-math modules, intentionally build in time for on-going student feedback and student-led planning. Knowledge of the dynamics of effective student group work, as described in complex instruction, is useful for helping ensure student buy-in. Teachers exposed to and comfortable with some level of experimentation in the classroom and who can shift the classroom focus from one of general pedagogy to one that is particularly connected to their own students will find interdisciplinary activities more manageable despite time constraints.

This is what teachers said:

  • “The work was almost entirely student-led, buy-in was very high and student body interest was great. It was a challenge to keep up with where the students were going, sometimes frustration was high on the student or teacher side, but the rewards were worth it. Being flexible is the key to success.”
  • “I had a very limited understanding of what could be possible. This project helped me experiment and think outside the box.”
  • “To be prepared for students changing the direction of their project required us to be ready for almost anything. We teachers planned for many scenarios.”

Build interdisciplinary courses and modules around established, agreed upon standards for each content area. Clearly and frequently state the broad goals of the work with all participants.

This is what one teacher said:

  • “Our teachers have long experience working across disciplines to integrate content and were aware of logistical challenges in pulling such programs together. We wanted to make sure that the Legacy Project was firmly grounded in both art and math standards. The Art and Math Integration Project provided support in terms of time and expertise from our regional coordinators as well as opportunities to learn from the other project participants in our region.”

Leverage existing school structures, policies and schedules to help ensure implementation and sustainability of arts/math modules.

This is what teachers said:

  • “The project allowed students to finish parts of their senior project, and get credit in math or art."
  • “Many of our alternative school students enjoy art and are deficient in math credit. Our teachers collaborate informally. The Legacy Project (E.A.G.L.E Transition Math Project initiative) provided support for teachers to collaborate systematically to develop an integrated curriculum to enable our students to meet graduation requirements in a meaningful way.”

In the Arts/Math Integration project, successful efforts were ones where teachers reflected on interdisciplinary work as a unique opportunity to re-examine a discipline’s big ideas, teaching approaches, and the use of tasks and examples. It was viewed as an opportunity to explore alternative methods, and reflect on student learning and instructional priorities in new ways by drawing on and from other disciplines.

This is what some teachers shared as reflections on their work:

  • “I learned a lot about how art instructors evaluate student learning and how they establish learning outcomes. I was surprised by the varying level of mathematics that is utilized in an art classroom; from basic mathematics and geometry to trigonometry and pre-calculus topics.”
  • “Our commitment to interdisciplinary approaches to content has been strengthened by our participation in the Art and Math Integration Project. We also saw how the skills developed through art and math content areas can be used in "real" projects that can benefit the community (service learning). School wide (district wide) support greatly enhances chances of success and multiplies the effect beyond the actual participants.”

For initiating or continuing integration efforts, a strong case needs to be explicitly made for how interdisciplinary efforts support and connect to district and student achievement goals. This will help ensure that time and resources can be directed to support these efforts.

This is what teachers said:

  • “I feel that this program has merit. It has the potential to augment any school districts math program. The challenge would be finding the open-minded administration to take the steps forward or to use Integrated Math.”
  • “Art and math faculty need more time together to collaborate and communicate during this creative process.”