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LESSON PLAN

Ratios: Math + Art

“This project furthered exploration of difficult concepts

and pushed students to greater understanding of

concepts.” L E O F R A N C I S CO

OVERVIEW“Math is a language through which we tell specific stories about the world.” Sixth-grade students use visual artwork to represent math concepts. Students learn to recognize math not only in math books and worksheets, but also in the classroom, within artwork, and in daily experiences, and use art materials as manipulatives through which to present their own creative interpretations of math concepts.

ARTIST/TEACHER TEAMLeo Francisco/Jose Marcial

GRADE/SCHOOL6th Grade, Kellogg Elementary School, Chula Vista Elementary School District

DEMONSTRATION OF LEARNINGCutout collages

MATERIALSColored papers, glue, scissors, numerous art images (including works by Matisse and Mondrian)

VOCABULARYRatios, equivalent ratios, simplification

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LEARNING OBJECTIVESAcademic• Students develop understanding of representation of ratios.• Students discuss mathematic concepts seen in daily experience and artwork.

Arts• Students recognize and practice visual arts elements, especially composition.

Social development/critical thinking• Students work collaboratively and make group decisions.• Students speak clearly while sharing ideas with classmates.

LEARNING EXPERIENCES1/2 (Half ) Goal: Explore various representations of halves. Students begin their ratio explorations by folding rectangular pieces of paper in half, discovering there are only three ways to do so: vertically, horizontally, and diagonally. Next, students illustrate ½ by coloring half of their papers using different patterns and shading, exploring the myriad ways ideas can be represented. Assessment: Are students able to “read” images and identify/explain the mathematical concepts they represent?

Introduction to Ratios Goal: Use paper cutouts to visualize ratios. Students select one of the followings ratios: 2:3, 2:4, or 2:5. Each student is given a large, white paper background and two smaller paper sheets to be cut into ratio numbers. After discussing placement rules to ensure easy counting of pieces (pieces of the same color cannot touch each other), students experiment and finally arrange their pieces into representations of their chosen ratios before gluing pieces down for their final design. Assessment: Are students capable of recognizing ratios in other students’ artwork?

Two Ratios, Three Colors Goal: Create simultaneous representations of multiple ratios. Students begin planning multiple-ratio art pieces by selecting three colors and three different numbers for those colors. Students cut their papers into the appropriate numbers and try different compositions before gluing them into place. For the second part of this project, students build on their completed composition, adding the correct number of pieces to show an

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equivalent ratio. This activity may prove challenging for students, and may require a second class dedicated to revisions.Example: A student creates a composition using two oranges, three greens, and seven purples. If the student then adds enough papers to result in four oranges, he or she needs to keep the ratio intact by adding enough papers to the other categories to result in six greens, and fourteen purples. Assessment: Are students able to correctly represent their first ratios? Did final designs show an equivalent ratio to their original ones? Can students identify the ratios shown in peers’ artwork?

Art as Math Goal: Interpret art elements as examples of math concepts. Students challenged by previous ratio activities may need more practice relating mathematics to artwork. Using a list of ideas including geometry, position/arrangement, numbers, parts and whole, and greater than/less than, students view a vari-ety of art images through the lens of a mathematician, discussing examples of those ideas found within the images. Students generate observations accordingly (i.e., “I see quadrilaterals,” and “There are three times as many yellow pieces than there are blue pieces.”) Assessment: Are students able to describe artwork mathematically, using supporting details to justify their statements?

Back to Ratios Goal: Further develop understanding of ratios through collaboration. The class discusses ratios as seen in Matisse’s Icarus and a composition by Malevich. For Matisse’s piece, the teaching art-ist records ratios as called out by students, then uses these records as a foundation for creating a classwide collaborative cutout collage. Students then work in groups to examine Malevich’s painting, recording ratios as they see them, most often by colors but also by shapes. After recording these ratios, students make cutout collages expressing the same ratio. Assessment: Are students able to correctly record ratios from sample images? Do ratios depicted in group artwork match colors and numbers from the sample image?

Individual Work Goal: Generate individual equivalent ratios. Students use the lessons learned in previous weeks to work individually on collages that express the same ratios ex-plored during the week prior. Time and care are taken to calculate correct equivalent ratios, as well as to correct inequivalent ratios. Students may have difficulty with this step, failing to finish their work or creating an incorrect version. Assessment: Does student artwork show an equivalent ratio to the previous group project? Do recorded ratios match artwork?

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ACADEMIC STANDARDS CCSS English Language Arts: SL.6.1-2 ; Math: RP.A.6.1-3

CROSS-CURRICULAR STRATEGY APPLICATIONSContinuation: After familiarizing themselves with ratios, students can use similar visual arts techniques to complement learning a variety of math concepts, from geometry to algebra, division to multiplication, and area to perimeter. Arts activities can also be used to visualize word problems and fractions.