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        Math + Arts | Graph a Dance

        In this lesson, students will choreograph a figure for a square dance, graph it, and perform it.

        Lesson Summary

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

        1. Frame, Focus, and Reflection (view and discuss): students will explore the connections between two traditional arts, quilting, and square dancing.

        2. Short hands-on activity: students will graph a figure from a square dance.

        3. Project: students will choreograph a figure for a square dance, graph it, and perform it.

        Time Allotment

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

        2. Short hands-on activity: 1 class period

        3. Project: 2-3 class periods

        Learning Objectives


        I can represent the pathways of a dance by graphing points in the first quadrant of the coordinate plane.

        Arts and Humanities

        I can discuss and graph the use of the element of space (shapes and pathways) in dance.

        I can discuss the interrelationship between dance and visual art in terms of shape and pathways.

        I can perform a figure from a square dance.

        I can collaborate with my peers to choreograph a figure for a square dance.


        Graph paper

        Media Resources

        "Grand Square Dance," performed by the Berea College Country Dancers

        DanceSense: Elements of Dance

        DanceSense: Understanding Dance

        Introductory Activity

        Students should have been introduced to the idea that a graph has an x and a y axis.

        If students have not been introduced to Appalachian culture, explain that Appalachia is a region that includes the Appalachian Mountains and its foothills, including southeastern Kentucky. Explain that, like many regions, Appalachia has a distinctive culture that includes many traditional art forms.

        Learning Activities

        Frame, Focus, and Reflection

        Ask students if they have ever seen a quilt. Many quilters plot out their designs on graph paper, because they need to be sure their measurements and angles are precise.

        Explain that quilting is a traditional art form widely practiced in Appalachia and throughout Kentucky. Ask if they know anyone who makes quilts.

        Tell students they are going to watch a video of a dance that has a very geometric pattern. It’s called “Grand Square,” and it is a traditional American square dance. The square figure, which you’ll see several times in the dance, is also danced in English and French square dances called “quadrilles.” Explain that American square dancing is a traditional recreational dance that is especially popular in Appalachia as well as in other regions.

        Show the video “Grand Square.” (Also show the explanation before the dance for a cultural setting and basic information about the dance and dancers.)

        Explain that one element of dance is space. In this dance, shape, direction, and pathways are especially important.

        Show the video all the way through.

        Explain that a series of movements that is repeated is called a figure. Ask students to watch closely the figure that is repeated for every chorus of this dance.

        Watch just the first figure of the dance (the part where each dancer completes a square pathway and returns to their original position).

        Ask, the following questions: Did you notice the geometric patterns in the repeated chorus figure of the dance? What did you notice? What shape was each dancer making with their pathway? (square). Did you notice the turns the dancers made at the corners and in the center? What angle were these turns? (right angle). What did the dancers do when they met another dancer along their pathway?

        Short Activity

        Show the dance again, having students pay close attention to the angles and square pathways. Ask, “What else did you notice the dancers doing?” Answers might include:

        • There were figures in which the dancers crossed the square to dance momentarily in another place and then return “home.”

        • The chorus (square movement) used very angular pathways while the figures (crossing moves) used mostly curved pathways.

        • Dancers used different positions to hold on to a partner. Ask, “What similarities did you notice between the dance movements and pathways and the quilt pattern(s) we looked at?” Answers might include:

        • Patterns that cross through the center

        • Pathways/lines that stop at the center and turn at an angle

        • Geometric shapes such as squares, triangles & rectangles

        • Parallel lines

        • Right angles

        Pass out the "Graph a Dance" handout. Project it and lead students in identifying the points where the dancers were standing and the center point of the formation (at 4,4). Ask students to complete Section 1 on their own. Check their work.

        Point out that the dancers who stand at (0, 4) and (8,4) also move in a square pathway, moving four points in each direction. Look at the points you drew on your coordinate plane. Ask, “If we plotted the other two pairs of dancers’ movements, do you think you would have to draw more points?” (You would not—they follow the same lines in a different order—but allow students to figure this out with minimal direction if possible.)

        Play the beginning (chorus) figure of the video again to see how the dance relates to the students’ graphs.

        Try moving through the chorus figure. Select eight students to stand in square-dance formation in the classroom. Use tape to “draw” an x and y axis and intersecting lines from (4, 0) to (4,8) and from (0,4) to (8,4). Position the dancers so that each pair is standing at the end of one of the intersecting lines. The students at (4,8) and (4,0) will move four steps forward toward the intersection, while the students at (0,4) and (8,4) will separate from each other and move four steps to the outer corners first. Work with the students to translate what they saw on the video and graphed on their handouts into actual movements for themselves. Hint: every dancer is moving in mirror image to their partner and to the dancer directly across from them in the formation.

        Repeat with another eight students until all students have had a chance to participate.


        Show the segment of KET "Understanding Dance" that deals with culture from 8:50 to about 13:23. Explain that sometimes a dance might have different purposes in different circumstances. For example, the video that students watched of the Grand Square was a performance, so in that case it would be considered artistic expression, but when people get together to square dance for fun, it is a recreational dance.

        Explain that square dancing is a traditional recreational dance with numerous variations worldwide. In general, square dances begin with four couples standing on the sides of a square and facing the center. A couple does not have to be boy-girl and being a couple in a square dance does not imply any romantic involvement! The basic movement in square dancing is walking. Dancers walk forward or backward following pathways and making turns. As their pathways bring them face to face with another dancer, they might bow, slap hands, or even link arms and twirl about. Sometimes they might join hands and move together in a new direction. There are endless variations.

        A series of movements that is always repeated in the same order is called a figure. Tell students, “You have just graphed and danced a figure!”

        Now, divide the class into groups with eight or fewer students per group. Each group is going to invent a new figure, practice dancing it, graph it, and then perform it. Each figure will begin with four couples standing in the same position as the dancers in the figure you graphed.

        1. Two dancers are standing at (4, 8).
        2. Two dancers are standing at (4, 0).
        3. Two dancers are standing at (0, 4).
        4. Two dancers are standing at (8, 4).

        The couples can move together or the partners can separate, but every dancer must walk in at least two directions and must turn at least once. The dancers can walk along the perimeter of the square or they can walk into and/or cross the center. All of the movements must happen within the square defined by the four points.

        Have students work with you to develop a rubric for scoring the dances the teams create.

        Unless you have a class of 16 or 24 students, groups will have to be relatively fluid as they “borrow” dancers from other teams to develop, practice, and perform their figures.

        Extension: Add music and have the class divide into groups of eight and dance each of the figures that have been choreographed. Practice a few times and then invite the principal, other classes, parents, the school council, and/or local media to attend a performance.

        Formative Assessment

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

        Math Assessment Problems

        I can represent the pathways of a dance by graphing points in the first quadrant of the coordinate plane.

        Arts and Humanities

        I can graph the use of the element of space (shapes and pathways) in dance.

        I can discuss the interrelationship between dance and visual art in terms of shape and pathways Assessment Strategy.

        I can describe the interrelationship between dance and visual art in terms of shape and pathways.

        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 figures. 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 appropriate 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 identify a purpose and generate original and varied art works or performances that are highly expressive with teacher guidance?

        c) To what extent do students, with teacher guidance, routinely use creative, evaluative, analytical, and problem solving skills in developing and/or reflecting in their artistic performances and products?

        d) 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?

        Formative and Summative Assessment: Assessments

        a) To what extent do teachers utilize formative and summative arts assessments for individual students and performing groups that are clearly aligned with the components of the Kentucky Core Academic Standards and authentically measure a specific concept, understanding and/or skill and lead to student growth?

        b) To what extent do teachers guide students to use developmentally or grade level appropriate peer review and critique to evaluate each other’s work?

        Formative and Summative Assessment: Expectations for Student Learning

        a) To what extent do teachers utilize exemplar/models to encourage students to demonstrate characteristics of rigorous work in the appropriate art form in most instructional lessons/units?

        b) To what extent do teachers share clearly defined rubrics or scoring guides with students before creating, performing, or responding assignments or other assessments; and students have the opportunity to provide input into the scoring guide?

        Formative and Summative Assessment: Assessment for Teaching

        To what extent do students regularly reflect on, critique, and evaluate the artistic products and performances of others and themselves as is grade level and age appropriate?


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


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