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## Math + Arts | Geometry in Dance

In this lesson, students observe symmetry, geometric shapes, and angles in two Early American dances, and then choreograph their own dance with symmetrical figures.

### Lesson Summary

There are three options for this lesson, depending on class needs and time available:

1. Frame, Focus, and Reflection (view and discuss): observe symmetry in dance and relate to paper folding.

2. Short hands-on activity: observe symmetry in dance and relate to geometric shapes and angles.

3. Project: compare and contrast two Early American dances, choreograph a dance with symmetrical figures.

### Time Allotment

1. Frame, Focus, and Reflection (view and discuss): half a class period

2. Short hands-on activity: half a class period

3. Project: 1-2 class periods

### Learning Objectives

Math

I can identify a right triangle. I can recognize and discuss the symmetrical attributes of squares, right triangles, and circles.

I can fold a square into progressively smaller right triangles.

I can use my body alone and in a group to create shapes and pathways that represent lines, angles, squares, and triangles.

Arts and Humanities

I can fold a piece of paper along lines of symmetry and discuss the art of paper folding.

I can recognize and reproduce the folding pattern in the singing game "Little Johnny Brown."

I can discuss the cultural context and symbolism of the singing game (dance).

I can recognize and discuss the use of space (pathways and direction) in the Lancers Quadrille.

I can compare the linear movements from the Lancers Quadrille to the folding method in the singing game "Little Johnny Brown."

I can compare and contrast two dances from the antebellum and Civil War era in terms of their cultural context.

I can perform a movement activity with my classmates that represents plane shapes and angles.

### Prep for Teachers

The basic elements of dance are space, time, and force. This lesson focuses on the use of space. As in math, the element of space in dance deals with area and volume. The flat space (such as the floor) a dancer or group of dancers use can be described in terms of total area (perimeter, circumference, area, circle, square, etc.) or in terms of pathway (the characteristics of the lines the dancers make as they move across their floor). Dance space is also described by levels, such as high, medium, and low, creating a three-dimensional aspect to space used in a dance.

Refer to these resources for more complete information:

DanceSense: Elements of Dance

DanceSense: Understanding Dance

### Supplies

Piece of notebook paper

Square piece of paper for demo, plus 1 square paper for each student

Protractors (if desired)

### Media Resources

PBS Cyberchase video: Digit in Pursuit

PBS Cyberchase game: Symmetrize

PBS Cyberchase video: The Secret of Symmetria

Video segment: Little Johnny Brown

### Introductory Activity

Students should know that a square is a plane shape with equal sides. Students should be introduced to different types of triangles, including right triangles. Students should be able to fold a piece of paper accurately in half vertically, horizontally, and diagonally, either alone or with some coaching.

### Learning Activities

Frame, Focus, and Reflection

Ask students if they have heard of the art form of origami. Focus on the fact that origami involves FOLDING paper to create shapes, some of which have a very realistic likeness to larger objects such as animals and plants.

Ask students what else they can think of that can be folded. Bed sheets, napkins, homemade greeting cards, and notes to pass in class might be a few ideas.

Tell the students that, when they fold things evenly, like folding a piece of notebook paper in half, they are using a line of symmetry. Demonstrate with a piece of paper folded lengthwise (“hot dog fold”) and width-wise (“hamburger fold”). If desired, have students do this along with you. This takes longer, of course, but offers a memorable hands-on experience.

Ask, “What other way could I fold this paper in half?” Try to get someone to offer the suggestion of folding it diagonally. Demonstrate that a diagonal fold won’t work well to divide a rectangular piece of paper in half. Ask, “What shape should this paper have in order for a diagonal fold to divide it in half?” Try to get someone to answer that it needs to be square.

Take out a square piece of paper. Fold it in half diagonally, both ways, and show the lines of symmetry you created. Hand out square papers to the students and ask them to fold along the vertical, horizontal, and diagonal lines of symmetry, like you demonstrated with your papers.

Short Activity

Tell students you’re going to show a short video of a teaching artist named Paula Larke instructing students in a traditional song and game called "Little Johnny Brown." Ask them to pay special attention to Ms. Larke’s explanation of the cultural context of the singing game and to the way Paula teaches the students to fold a piece of fabric and why it is folded that way.

Show the "Little Johnny Brown" video.

Ask students to recall the cultural context of the singing game. (It is a traditional singing game from the Georgia Sea Islands passed down in the African-American community that has been there since the days of slavery.)

Ask, “How was the “blanket” folded in the game?” (Fold the square diagonally across, then fold the resulting triangle in half, and continue to fold each triangle in half.)

Ask, “What did that series of folds change about the blanket’s shape?” (It ends up as a triangle, but it is smaller with each fold. This might be a chance to introduce the term “similar,” if you want.)

Ask, “Why did Paula say the blanket got folded that way in this game?” (To show the dancer’s ability to do a job precisely.)

Ask students to name other items that have to be folded in certain ways in order to get a job done correctly. Answers may include concert programs, fabric for upholstering, the American flag, a business letter, an envelope, a cardboard box, clothing in a store, reusable grocery bags, and others.

Show the video again and ask students to fold their square papers the same way the students in the video fold their fabric.

Tell students to open their folded papers so they are flat on the desks, and use a pencil or crayon to trace the lines they created when they folded the paper.

Ask what shapes are drawn on their paper now, and encourage several students to describe the shapes. Some will identify only (right) triangles and others may point out that two triangles together form a square. Others may see an eight-pointed starburst formed by the extra “Johnny Brown” folds. Take this in whatever direction you find helpful, depending on the amount of time you have to spend.

Ask what angles are formed by the intersecting folds, and what angles are formed by the folds that intersect with the edge of the paper. Use a protractor to measure the angles, if you want. Be amazed at the complexities a simple act of folding can produce!

Project

Refer to the square papers that were folded in the Short Activity. Ask students to imagine they were the size of an ant and could only walk on the fold lines. Would they always be walking in a straight line? (Yes) Would they ever be able to walk in a curved line? (No, not if the paper is folded correctly and all the lines intersect at the center of the square.)

Tell the students they are going to see a video of dancers performing the Lancers Quadrille, an English dance that was the most popular dance in America during the Civil War era.

Ask them to watch especially how the dancers move in shapes and pathways and to notice the square, line, and triangle patterns in the dance. Point out that, in dance, shapes can be made by individual dancers walking in a certain pathway, by a group of people standing in a certain formation, or by a group of people moving from one formation to another in a specific way. Notice the symmetry in the dance, similar in many ways to the symmetry of the shapes and lines on the students’ square papers.

Read this excerpt from the Background Essay that accompanies this video on the KET website:

The symmetry and sweeping figures make this an elegant dance and show off the long skirts of the ladies—after all, a dance was a place to see and be seen, to meet people, and to flirt. Socialization was an important part of dance in Civil War America, and movements of the Lancers allow for dancers to interact with each other face-to-face.

Ask them to recall that the singing game Little Johnny Brown also originated in the 1800s but among a different group of people. Ask them to compare and contrast the two dances in terms of pathways. Ask them to consider if socialization was an important purpose for each dance. Do they imagine the people who danced Little Johnny Brown in the 1800s would have been dressed in the same way as the people dancing the Lancer’s Quadrille? How would the lifestyle of these two different groups of people have been different? How is that reflected in the dances?

Divide students into groups of eight, and ask them to work out a way to create the pattern of lines on their square papers using their bodies. They may use ideas from the Lancers as inspiration if they want. They may choose to stand in place and use outstretched arms to create the shapes on the paper. They may choose to move in pathways that follow the lines (folds) on the paper. They may choose a combination of techniques. Any idea is correct, as long as it contains an identifiable connection to the lines and shapes created by the paper folds. You might allow students to use fabric squares, ribbon, yarn, or other props to help create shapes and/or lines. It is not necessary for the students to use movement in this part of the activity. Some may choose to, and others may not; either way is OK for now.

When the groups are ready, ask them to share their ideas with each other by demonstrating their techniques.

Discuss each of the performances using the following questions for the observers to answer:
1. How did this group show the lines and/or shapes on the paper?
2. How did this group show the angles on the paper?
4. What could make this presentation even more interesting?

1. What was challenging about doing this activity?
2. How did you end up making the decision to use space in the way you did?

When all the groups have presented, ask students to discuss how they might create a dance for the whole class using each of the groups’ ideas. Would they present the group movements in order? Should they happen all at the same time? Should the whole class combine to be one large group, or should the groups stay separate?

Help keep the discussion on track, maybe even writing down ideas on the board and trying to come up with a final choreography plan. Discuss the type of music that could be used for the dance, and make a list of some tunes/songs that would work. Choose a single piece of music by voting or some other method.

Depending on your space constraints, you can end the project here, without trying the group “dance.” If you don’t have space to try the dance, just listen to the music and narrate the choreography. Use some or all of the discussion questions below to process the experience.

If you have space, get the students up and try the dance! Discuss what worked and what didn’t, and try it again. Do the dance as many times as you think necessary to make the activity feel successful.

If you have the technology, film the dance and watch the best run-through as a class.

Discuss the experience using the following questions:
1. How was this experience more, or less, challenging than the smaller group activity?
2. If you were a choreographer, how would you costume your dancers for this dance?
3. How would you make this dance longer, so it could stand alone as a performance (between two and four minutes in total length)?

Formative Assessment

What are the indicators of student progress toward or achievement of each learning target?

Math Assessment Problems

Teacher observation during lesson

Arts and Humanities

Frame, Focus, and Reflection: teacher observation

Short hands-on activity: teacher observation

Project: teacher observation, exit slip

Program Review

Where does this fit in? How should you document it?

This activity contributes to your school’s overall efforts in art programming in several areas, depending on whether you implement just the Frame, Focus, and Reflection portion or you implement the entire project.

Document with lesson plan and samples of student-generated problems and scripts. If possible, record performances or take pictures of performances.

Curriculum and Instruction: Aligned and Rigorous Curriculum

a) To what extent does the school ensure that the arts curriculum encompasses creating, performing and responding and is fully aligned with the Kentucky Core Academic Standards?

b) To what extent does the school ensure that the arts curriculum provides for the development of arts literacy in all four arts discipline and also utilizes the Common Core Standards for English/Language Arts?

c) To what extent does the school ensure that the school’s curriculum provides opportunities for integration as natural cross-curricular connections are made between the arts and other content areas?

d) To what extent does the school ensure that the arts curriculum includes the study of representative and exemplary works of dance, music, theater and visual arts from a variety of artists, cultural traditions and historical periods?

Curriculum and Instruction: Instructional Strategies

a) To what extent do teachers systematically incorporate all three components of arts study: creating, performing and responding into the arts?

b) To what extent do teachers provide models of exemplary artistic performances and products to enhance students’ understanding of an arts discipline and to develop their performance/production skills?

c) To what extent do arts teachers provide for the development of artistic theory, skills, and techniques through the development of student performances or products that are relevant and developmentally ap propriate for students?

Curriculum and Instruction: Student Performance

a) To what extent are students actively engaged in creating, performing and responding to the arts?

b) To what extent do students use written and verbal communication to objectively reflect on exemplary exhibits and live or technologically provided performances as classroom assignments?

Lesson Creators: Jennifer Rose, Emily Jackson, Dean Cornett, Dawn Hibbard, and Judy Sizemore

Producer:

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