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        Math + Arts | Rotation, Reflection, and Translation in Dance

        In this lesson, students choreograph a dance figure by creating a dance graph with descriptions of rotation, reflection, and translation; perform it for their classmates; and translate a classmate’s dance map into a performance.

        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 discuss the purposes of dance and describe the opening position of a traditional square dance in terms of rotation, translation, and reflection.

        2. Short hands-on activity: students will engage in a mirroring activity and then step through the first figure of a traditional square dance and describe the pattern in terms of rotation, reflection, and translation.

        3. Project: students will choreograph a dance figure by creating a dance graph with descriptions of rotation, reflection, and translation; perform it for their classmates; and translate a classmate’s dance map into a performance.

        Time Allotment

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

        2. Short hands-on activity: 1 class period

        3. Project: 2 class periods

        Learning Objectives


        I can accurately describe movement as a series of rotations, reflections, and translations.

        Arts and Humanities

        I can discuss the purposes of dance.

        I can discuss space as an element of dance, including shape, direction, and pathway.

        I can collaborate with my peers to choreograph and perform a dance pattern.

        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 placement and movement on a plane. Dancers and their “resting” positions can be described, to some extent, in terms of rotations and reflections, and the dance pattern in terms of rotations, reflections, and translations.

        This lesson also discusses the purposes of dance—why people dance. The "Grand Square" is a traditional American square dance, which is a type of recreational dance done for fun, socialization, and exercise.


        "Rotation, Reflection, and Translation in Dance" handout

        Masking or gaffer’s tape

        (Note: Gaffer’s tape stays in place better than masking tape and can be removed easily, leaving no residue or stain. Your school custodian might have some or know where it can be ordered. It can also be purchased online.)

        Media Resources

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

        DanceSense: Elements of Dance

        DanceSense: Understanding Dance

        Introductory Activity

        Students should have been introduced to the terms rotation, reflection, translation, and line of symmetry.

        Learning Activities

        Frame, Focus, and Reflection

        Ask students why people dance. Allow some time for discussion, then show "Understanding Dance" from 8:50 to the end.

        Explain that most dances fall into one of three categories: artistic expression (like ballet or modern dance), ceremonial dance (like some Native American dances that express a spiritual belief), and recreational (dance that is performed for fun, exercise, or socialization).

        Tell students they’re going to watch a video of a recreational dance, a traditional American square dance.

        Explain that the dance is called "Grand Square," and that it is a very symmetrical dance. The square figure, which you’ll see several times in the dance, is also danced in English and French square dances, called quadrilles.

        Show "Grand Square." (Show the explanation before the dance if you want to, for a cultural setting and basic information about the dance and dancers.) Show the beginning of the dance again, freezing on the opening position.

        Distribute "Rotation, Reflection, and Translation in Dance" handout and review the instructions. Have students mark the position of each dancer on the graph, playing close attention to placing the X and Y dancers on the proper side of the axis line. Project the Teacher Version on your Smartboard or project a blank grid and mark the positions of the dancers.

        Ask if Couple B is a reflection—or mirror image—of Couple A. Although at first glance the couples appear to be reflections of each other, if you pay attention to the X and Y, it is clear that the positions of X and Y are reversed.

        Divide students into small groups with at least two boys and two girls in each group.

        Challenge them to create a series of directions that would result in the Y dancers being directly across from and facing each other and the X dancers being directly across from and facing each other. Instruct them to write detailed directions using the terms rotate for turning and translate for moving straight forward in one direction. Tell students that they must indicate the degrees and direction of rotation (such as, “Rotate 90 degrees to the right”). They should work this out on their graph paper and by acting out the movements.

        Allow each group to share their solution with the class. One student should read the directions while teammates act out the rotations and translations. Keep track of how many different solutions the students come up with.

        Short Activity

        Show the beginning (chorus) figure of the video again, just long enough to see each dancer make one square pattern and return to their starting position. Before showing, tell students to focus on one dancer and follow that dancer’s movements. As a group, describe the dancer’s movements using the terms rotate and translate.

        Show the same segment again, asking students to focus on the dancer directly across from the dancer they watched the first time and to notice how the two dancers’ movements are mirror images of each other. As a group, describe the second dancer’s movements using the terms rotate and translate.

        Explain that you are going to practice mirroring. This is an exercise used by dancers and theater artists to help them develop focus and cooperation. Ask students to stand up and face you and to move in an exact mirror image of you. If you raise your right arm, the students should raise their left arms. If you bend to the left, the students should bend to the right. Practice large and small movements staying in one place.

        Explain that these movements (bend, push, pull, sway, twist, reach) are nonlocomotor movements. Now, you are going to make a locomotor movement, and you want students to mirror your movement, so they need to be sure that they are in a position where they can step forward and backward. If you step forward leading with your right leg, they should step forward leading with their left leg. Practice stepping forward and back several times.

        Next, try rotating 90 degrees and taking a step forward. Then rotate 180 degrees and return to your original position. Ask students to describe what you just did using the terms rotate and translate.

        Clear a space large enough for students to stand facing one another in pairs with room to swing their arms. Tell them that one student will lead and the other follow, mirroring their partners exactly. Tell them to use nonlocomotors movements only.

        Switch leaders and have them continue making and mirroring nonlocomotor movements.

        Tell them to take a step apart from their partner and try some small locomotor movements (no more than one step in any direction, unless you have lots of room).

        When they seem comfortable with mirroring, show the video segment one more time and ask them to observe how the dancers who begin directly opposite one another mirror one another’s movements.

        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 position the dancers so that each pair is standing at the end of an axis line, four steps from the center. The students at the ends of the y axis will move four steps forward toward the origin first, while the students at the ends of the x axis will separate from each other and move four steps to the outer corners first. Repeat until all students have moved through the pattern. Remember: every dancer is moving in mirror image to their partner and to the dancer directly across from them in the formation.


        Show "Elements of Dance" from the beginning to 2:25.

        Discuss the shapes in "Grand Square," both the formation of the dancers and the directions and pathways they follow.

        Divide class into groups of four and distribute graph paper. Tell each group that they will choreograph a dance figure with four dancers performing geometric dance patterns and record it on graph paper. The dance figure should have 16 steps. Each dancer’s movements should be reflected by at least one other dancer. The dance should include rotations and translations. Each dancer should write a description of their movements using the terms rotate, translate, and/or reflect.

        Project the "Reflect, Rotate, Translate & Dance!" Scoring Rubric. Discuss your expectations with students. If you want, you can ask for student input in editing the rubric.

        Allow time for students to choreograph a dance figure and record it on graph paper and in writing.

        Groups will perform their dance patterns for each other.

        As an extension, you might ask the groups to exchange dance graphs and descriptions and challenge them to figure out how to perform the other group’s dance from the graphs.

        Formative Assessment

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

        Math Assessment Problems

        Bell ringer or exit slip: write a definition of rotation

        Scoring Rubric

        Arts and Humanities

        Bell ringer or exit slip: what are three reasons that people dance?

        Scoring Rubric

        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 the lesson plan and samples of the student-generated dance graphs.

        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 integra tion 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 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 Stan dards; 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, Kayla Hibbard, and Judy Sizemore


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