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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.