Patterns, Fractions, and Geometry

by Debbie Koppman & Sandra Oby Sequoia Elementary School, Oakland

Patterns, Fractions, & Geometry

• This unit leverages art skills used in collage and bookmaking to further students’ understanding of specific math concepts focused on fractions and geometry. At the same time, the precision needed to understand the math concepts will be used to enhance students’ skills in art.

Why Art and Math?

• We learned as a faculty that many of our students are arriving at 5th

grade with an incomplete understanding of important math concepts, especially fractions. Without a better understanding of beginning concepts, students are completely lost when math concepts become more complicated. We felt that perhaps we could develop art/math integrated curriculum; our strategy is to leverage our students’ art skills to increase understanding in Math.

Understanding Goals • What is the relationship between patterns, geometry, and

fractions? • (OBSERVE, DEVELOP CRAFT, ENGAGE/PERSIST) • How can we use art skills to build understanding of fractions

and geometry, and how do skills in math inform artistic practice?

• (DEVELOP CRAFT, OBSERVE, ENGAGE/PERSIST, REFLECT) • How can we find relationships and make connections

between 2D and 3D shapes? • (STRETCH & EXPLORE, EXPRESS, ENVISION) • How have artists from multiple cultures used patterns,

fractions, and geometry? • (UNDERSTAND ART WORLD, REFLECT)

Common Core Content Standards: Math

• 3rd Grade: Recognize and generate simple equivalent fractions, e.g., 1/2=2/4 etc. Explain why the fractions are equivalent by using a visual fraction model.

• 4th Grade: Visualize, describe, and make models of geometric solids (e.g.,

prisms, pyramids) in terms of the number and shape of faces, edges, and vertices; interpret two-dimensional representations of three-dimensional objects; and draw patterns (of faces) for a solid that, when cut and folded, will make a model of the solid.

• 5th Grade: Solve word problems involving addition and subtraction of

fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. 5th Grade: Construct a cube and rectangular box from two-dimensional patterns and use these patterns to compute the surface area for these objects.

Cultural Inclusion Strategies

• We are planning to include many VTS discussions in our curriculum design. Our topic and our practice to make quilt-like things will offer many possibilities for showing work of artists from around the world, to include quilts, quilt-like cloths, and contemporary art.

How have artists from various cultures used patterns, fractions, and geometry?

What is the relationship between patterns, geometry, and fractions?

• Students will engage in 2 or 3 VTS discussions, looking at quilts from various traditions.

• What’s going on in this picture?

• What do you see that makes you say that?

• What more can we find?

How can we use art skills to build understanding of fractions and geometry, and how do skills in math inform artistic practice?

• Students will create a series of paper quilts, sequentially based on parts of the whole. (So we first create a quilt based on halves, then quarters, then eighths.)

Group Quilt based on Quarters (and Warm Colors)

• After creating collaborative quilts, students will engage in VTS discussions.

How can we find relationships and make connections between 2D and 3D shapes?

• Students will create one or more Star Books, with or without

pop-up additions.

What is the relationship between patterns, geometry, and fractions? How can we use art skills to build understanding of fractions and

geometry, and how do skills in math inform artistic practice?

• Students will create double-sided 8-fold origami books showing equivalent fractions.

These books offer teachers many possibilities to create variations on a theme!

Students will reflect on their own work in writing, and engage in a VTS discussion of student work.

Together we already have made great discoveries! This is where we all get to see the art/math relationships, and the interpretative

possibilities offered through art.

What’s going on in these pictures?

Students will create several origami structures, based in the folding pattern for eighths.

This seems to be a great way to get students engaged in the intersection between art and math.

Origami is fun, kind of mysterious, kind of art, based in math…

Students will create a 2D/3D Art/Math Toy, in the form of a 32-fold structure.

Students will create Math/Art sculptures, based in the work they have been doing with math/art books, quilts, fractions, origami

structures.

They will reflect on their own work in writing.

We have just started playing with these ideas.

We hope to get all of our classroom teachers using these paper folding Math/Art ideas next year!

Wish us luck!

Reflections: Debbie

• I am completely rededicated in an even stronger way to the idea of the importance of hands-on learning, as I am again even more aware of my own learning style, and the fact that I think with my hands, through making things, pretty much all the time.

• I was completely fascinated by the idea of creating

Art/Math integrated curriculum, and realized how little I really understand about Math.

• I am also rededicated to the value of ongoing collaboration between artists and classroom teachers. I feel that ongoing discussions about our work, our ways of learning, and our students’ challenges are invaluable, and helps all of us rethink our habits, practices, and curriculum design.

Reflections: Sandra

• This class reinforced my belief that art is such an integral part of learning whether it is math, science, language arts or social studies.

• The ongoing assessment throughout the unit allows for

immediate feedback which ensures that all students develop critical meta-cognitive thought processes.

• I feel that to instill in my students a focused work ethic is

important as well as the ability to make careful observations and this will serve them well in life. Equally important, I want my students to reflect on the comments of their classmates and to use those ideas to build upon their own.