INTEGRATION WITH DANCE/MATHEMATICS
Submitted by Susan Hartley, Wake County Public Schools
Students will explore the relationship between Math and Dance.
Focus and Review
The students will discuss the use of the elements of dance and of composition (beginning, middle and end).
Statement of Objectives
Students will share ideas on how math can be used in dance- addition, subtraction, multiplication, division, geometry, area and volume, etc. Math can be utilized when working in groups and the numbers of people (sets) and patterns in space and with body shapes.
Students will "accumulate" movements- adding on movements to form a phrase.
Warm-up: Teacher will lead a warm-up utilizing geometric shapes - circles, arcs, line segments, diamonds, parallel lines, right angles, etc.
Students will form octets. Students number themselves 1-8. #1 creates a movement/shape and teaches it to the group. #2 creates a movement and "adds" it on to #1 movement, all perform. #3 add on to #2 and #1, etc.
The group chooses how to organize their composition. They set a beginning, a shape or entrance (one dancer enters, add another, add another). The middle consists of the performance of movement 1-8, or performance of 1, 1-2, 1-2-3, etc, or perform 8,7,6,5,4,3,2,1. The dance can also address the issue of 2 sets of 4 or 4 sets of 2 or a group of 8. The group will also create an ending. The students decide how their actions relate to each other and the group as a whole.
Students practice. Students perform for the class. Constructively critique each performance- how was math used.
Math can be rhythm, the use of grouping, or use of space. Math is found in all aspects of dance.
Submitted by Susan Hartley, Wake County Public Schools
7th and 8th grade
Math/ Algebraic Equations
Students will have an interdisciplinary experience applying their knowledge of algebra to movement.
Structure and Strategies for Teaching
Mathematics and movement might, at first glance, have little in common. Often students ask, "How can you dance math?" After a warm up utilizing geometric shapes and division, this lesson will experiment with algebra.
Warm-up: Have the students find good personal space on the floor and sit with their legs in a diamond shaped position (a symmetrical shape, body perpendicular to the floor, creating right angles, etc.). Using an upbeat 4/4 musical selection, "arc" the torso forward 8 counts, sideward 8 counts, backward 8 counts, and then the other side 8 counts. Divide the counts by 2 = 4 counts to each side; divide by 2 = 2 counts to each side; divide by 2 = 1 count to each direction. Change the legs to a parallel shape straight out in front of the body and repeat the combination of directional arcs and division of counts. Change the leg position once more to create a right angle with the legs on the floor and repeat the directional and division combination.
"The Equation": Teach "X" possibilities. "X" has the potential in this lesson of being any number "1" through "5". Either teacher generated or student generated, teach or create five movements. For example, the five movements could be wrap, spiral turn, reach, squat, and jump. These are your five possibilities of "X". Demonstrate the equation, 2X + 3 = 13. "X" equals 5, so you perform all five of the movements in any order, two times, then create 3 completely new movements. Students observing will identify all of the "X" movements performed twice (2X), and will observe three new movements (+3) to total a combination of 13 counts. Therefore, "X" = 5, and the equation as demonstrated is 2X + 3 = 13. Demonstrate the equation, 4X + 1 = 9. "X" equals 2, so you perform only two of movements in any order, four times, then create one new movement. Students observing will identify only two of the "X" movements performed four times (4X), and will observe one new movement (+1), to total a combination of 9 counts. Therefore, "X" equals 2, and the equation as demonstrated is 4X + 1 = 9.
Divide the class into groups of four. Give each group an equation remembering, "X" in this particular class can not be more than 5. (5X + 1 = 6, 2X + 4 = 8, X + 2 = 6, 3X + 3 = 12, etc.) Each group has a different equation and should keep it a secret from the other groups. Working independently of the other groups, they need to solve "X", decide what "X" movements they want to use, how many times they perform their "X", and how many "new" movements they need to create to demonstrate their equation. Then they need to decide how they are going to present their equation to the class - what floor pattern, a line, a circle, a semi-circle? Allow adequate time for creation and rehearsal.
Have each group perform their equation for the class, their audience. Ask them to perform it again so that the audience can notate what they see. Repeat the performance again, if necessary, then ask an audience member to share the equation that they observed and to solve "X". Reinforce that it takes a good observer to solve the equation but it also takes the clarity and the correctness of the performers in demonstrating the equation. Have each group share their equation as the audience notates what they see.
Culmination/ Final Forming
Have the students explain why this was, or was not a math class. Identify the mathematical forms that were used- equations, geometrical shapes, division, multiplication, counting, sequence, order, pattern, balance, symmetry and asymmetry.
Ideas for Extending the Lesson Have the students create the possibilities for "X". Have the "X" possibilities be more than 5. Have the students create their own equations to be performed. Add music (a slow tempo) for the performance.
Submitted by Jan Adams, Winston-Salem/Forsyth Schools
Explore shape with positive and negative space.
Symmetry statues and studies.
Dance combination reversals.
Statues with flips, slides.
Moving pathways, then mapping (big to little, little to big).
Pathway dances, machines.
Make sets of matched shapes or movements
What fraction of the whole class is doing a given movement? How would you represent that fraction as a percentage?
Shape puzzles - problem solving individually or in groups of two or more: "Create a statue with a partner with seven body parts touching the floor."
Matrix choreography: forward or backward steps add or take away tens. Lateral steps or take away ones. Make up a combination, then figure out what number you would land on if your beginning point was 1 - how about 14?
Predict, then measure how many steps, tiptoes, leaps it will take to cross a room. Discuss non-standard units of measure exemplified by different people's leaps.
Measure a variety of steps, crawls or leaps on a measurement chart.
Perimeter dances with a partner. Figure out a sequence of movement that leas you in a rectangle (i.e. 8 slides to right, 4 zigzag jumps back, 8 slides left, 4 zigzag jumps forward). Before you can perform it to music with your partner, you must figure out the perimeter and the area of your dance space.
Create a map of your school by sending two students out to measure with footsteps each hallway. You may also send students in to measure gym or media center or lunchroom. Then reduce their measurement to an agreed scale (i.e. 10 paces = 1 inch). Have them with their partner cut out a strip (for halls) or a rectangle (for large rooms) of paper and assemble map on large board. Create legend, including scale used.
* With vinyl numbers spread around room, dance or move to another number. Figure out an addition, subtraction, multiplication or division problem that has that number for an answer. Write down on paper. The paper will provide information for assessment.
Line graph dance. Record your dances through a simple line graph. Put movements along one side of chart and amount of time in units of 8 counts along bottom.
With vinyl numbers spread around room, put on music and hop, skip, dance to another number. When music is turned off, stop on the nearest number. What is the probability that you will land on an even number? A number above 6? With pencil and paper in hand, go through process 10 times. Gather data and find out.
Stand on a vinyl number. Notice the color you are on. As you move to another vinyl number, count the number of skips (or hops or walks, etc) that you are taking and you may only land on the same color. If you are moving to another number and someone gets to the color ahead of you, you must proceed to another vinyl square of your color. Count your skips, or hopes, or walks. Repeat 10 times and record the number of steps it took you to get there. What is the median number of steps that you took? The range? The mode?
Look at two shapes. How are they alike? How different?
Draw shapes using the least lines possible to capture body shape. Write down how shapes are alike, how they are different.
Look at a group of shapes or movement patterns. Group according to similar properties.
Create dances with rhythmic patterns. Interlock those patterns by creating dances "in canon."
Create movement patterns and movement tessellations.