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 translate a dance pattern into a graph.
2. Short hands-on activity: students will step through the first figure of a traditional square dance and relate it to graphs.
3. Project (view and discuss): students will use a graph to choreograph a dance figure, perform it for their classmates, and translate a classmate’s graph into a dance.
1. Frame, Focus, and Reflection (view and discuss): 1 class period
2. Short hands-on activity: 30 minutes
3. Project: 1-1/2 to 2 class periods
I can calculate absolute value on a horizontal and vertical number line.
I can express movement on a number line as addition using absolute value.
Arts and Humanities
I can discuss the purposes of dance.
I can discuss shape as an element of dance.
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 on a plane. Dancers and their “resting” positions can be compared to points on a coordinate plane, and pathway in dance can be compared, to some degree, to a line on a graph connecting coordinate points.
This lesson also discusses the purposes of dance—why people dance—and humanities in dance—how dance is influenced by the cultural context of the dance. The "Grand Square" is a traditional American square dance, which is a type of recreational dance done for fun, socialization, and exercise.
"The Absolute Value of Dance" handout
Graph paper with large grids
Students should have been introduced to the idea that a graph has an "x" and a "y" axis and four quadrants in which points may be plotted using coordinate pairs.
Students understand that the numbers to the left of the origin (intersection of the x and y axes) and underneath the origin are represented as negative integers, and the numbers to the right and above the origin are represented as positive integers.
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 it’s called "Grand Square," and that it is a very geometrical dance. The square figure, which is seen 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.)
Ask students to describe the geometric patterns they observed in the dance.
Show the beginning of the dance again, from the opening position through the beginning figure of the dance in which each dancer follows pathways that create a square.
Pass out "The Absolute Value of Dance" handout and ask the students to complete it on their own or with a partner. Check their work.
Show 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 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. Work with the students to translate what they saw on the video and graphed on their handouts into actual movements. Repeat until all students have moved through the pattern. Hint: every dancer is moving in mirror image to their partner and to the dancer directly across from them in the formation.
Show the "Elements of Dance" from the beginning to 2:25.
Discuss the shapes in "Grand Square," both the formation of the dancers and the pathways they follow.
Divide class into groups of four and distribute graph paper. Tell each group that they will choreograph a dance on graph paper with four dancers performing geometric dance patterns. You can assign the dancers’ starting positions and/or parameters for the shapes the dance will create and the directions of the dancers’ pathways, and/or the absolute value of their movements. Or, you can lead a class discussion to allow students to determine the requirements for the dance. In either case, the students should have a clear rubric to follow. Each group should graph itsdance and practice it to make sure that their graphs accurately express the pathways that the dancers will follow.
Groups will perform their dance patterns for each other.
You might ask the audience to graph each dance and calculate the absolute value of the dancers’ movements.
You might ask the groups to exchange dance graphs and challenge them to figure out how to perform the other group’s dance from the graphs.
What are the indicators of student progress toward or achievement of each learning target?
Math Assessment Problems
Review answers on "The Absolute Value of Dance" handout.
Review the graphs that students create in terms of your assignment or the class-generated rubric.
Arts and Humanities
Bell ringer or exit slip: what are three reasons that people dance?
Describe the element of shape in the dance "Grand Square." What is the job of a choreographer?
Teacher observation of student performances: do the students move along the pathways to create the shapes in the first figure of "Grand Square"? Do the students move along the pathways to create the shapes they have graphed?
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 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 enhances 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?
Formative and Summative Assessment: Assessments
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?
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?
Lesson Creators: Jennifer Rose, Cheryl Burchfield, and Judy Sizemore