Unit Summary
Students learn to graph
linear equations and choreograph dance moves to demonstrate them. For
example, students modeling the function y=x² hold both arms above their
head (similar to the way a referee in a football game would indicate a
touchdown), and they use a graphing calculator to create corresponding
figures and graphs. Each dance is comprised of nine equation poses
choreographed to music. Students videotape or photograph their dances, and
combine these visual elements with screen shots of the equations and
graphs into an electronic presentation.
Curriculum-Framing Questions
- Essential Question
How can we communicate through
movement?
- Unit Questions
How do we read equations and
graphs?
How do we represent linear equations in different ways?
- Content Questions
How does a linear function
differ from a quadratic function?
How does changing the y-intercept
in an equation change the graph of the equation?
Assessment Processes
View how a variety of
student-centered assessments are used in the Choreographing Math Unit Plan.
These assessments help students and teachers set goals; monitor student
progress; provide feedback; assess thinking, processes, performances, and
products; and reflect on learning throughout the learning cycle.
Instructional Procedures
Introducing
the Project
Ask students to discuss what communicating
mathematically means. Engage students in discussion as they offer
their ideas and opinions. Discuss how mathematical communication includes
understanding, expressing, and conveying ideas orally, in writing,
graphically, and algebraically. Introduce the idea that students will also
learn how to communicate their mathematical understanding through movement
by creating a dance comprised of nine equation poses.
Pose the
Essential Question, How can we communicate through movement? Have
students record this information in math journals and share ideas with the
class.
Set the stage for the project by modeling a variety of
functions with your arms. Play a popular song on the radio and move to the
beat of the music. Ask students if they can identify the functions you
model. For example, stretch your arms out at a diagonal to model the
equation y=x. Invite students to join you by getting out of their seats
and modeling a few basic functions to the beat of the music. Challenge
them to name the equations of the functions they are modeling.
Distribute the student handout and go over basic expectations for the
project, including selecting equations, choreographing the dance, choosing
music, and collecting visual elements of both the poses and the
corresponding graphs and equations. Encourage students to supply props and
costumes. Distribute and discuss common lines using the Common Lines Reference, a sheet of common graphs.
Getting to Work
Hand out the project rubric and the group task rubric so students are aware of project
expectations. Check for student understanding and answer questions as
needed. Students use the group task rubric to self and peer-assess their
participation while working in groups. Allow two days for students,
working in small groups, to discover families of linear functions by
completing the graphing activity on a graphing calculator. After groups
complete the activity and discuss their findings with the class, have them
complete a four-question investigation so you can assess their understanding thus
far. Make necessary adjustments to bring all students to a common point of
understanding. Throughout the unit, teach formal lessons to develop
students' understanding of linear equations.
Pose the Unit
Question, How do we represent linear equations in different ways?
Discuss ideas as a class. Then, begin a series of lessons to teach
students to identify slope and write equations in standard form,
point-slope form, and slope-intercept form. Have students document
understanding of these concepts in their math journals. Collect journals
and provide students with feedback. Use the journal entries to reteach
concepts as needed.
Begin the dance choreography part of the
project by reviewing the student handout. Show part of a sample presentation to demonstrate ways students might
represent their functions. Have students reconvene into small groups. Make
sure groups have a recording of their music as they choreograph their
moves. Ask students to get their songs approved before bringing in music
and starting work on their presentations. Graphing calculators will be
useful for exploring the various functions they may want to model. Have
students choose equations and develop corresponding poses for their
dances. Have them experiment with the order of poses and the dance
elements between each pose. Instruct students to graph each equation on a
separate sheet of graph paper. When all of the groups have their
choreography established, ask each group to turn in an outline of their
group’s dance sequence to you. Review each outline and make necessary
recommendations and comments to each group.
When the dances are
ready, have students begin developing the multimedia slide presentations.
Invite other school personnel to help students work on their projects. The
dance instructor, physical education teacher, media center specialist, and
video production teacher may be assets.
Give students digital
cameras to take pictures of their poses as well as their graph and
equation sketches. Have students draft 3- to 5-minute long slideshow
presentations. Hand out the slideshow presentation checklist to students and make sure
all students understand required expectations. Have students review and
refine their presentations, and practice their delivery with one another.
The groups can give feedback to each other using the peer assessment sheet.
Performing and
Presenting
Plan for students to perform their dances and
present their multimedia presentations. Invite other classes, parents, and
administrators to watch. If your school has a video production class,
allow students to film the dances and broadcast them into the various
classrooms.
Revisit the Essential Question, How can we
communicate through movement? Have students record their ideas in
their math journals and make sure they provide concrete examples from the
unit. Use these entries in final assessment.
Prerequisite Skills
- Graphing ordered pairs, relations, and equations
- Solving problems by making a table
- Identifying the domain, range, and inverse of a relation
- Determining if a relation is a function
- Writing an equation to represent a function given its table of
values
- Analyzing linear equations
Differentiated Instruction
Resource
Student
- Modify work requirements if necessary
- Provide extra time to complete assignments (possibly during resource
classes)
- Provide additional support from teachers and
parents
Gifted Student
- Encourage the student to investigate more advance functions, such as
sine and cosine functions
- Require the student to include more advanced technical attributes in
the slideshow presentation
English Language Learner
(ELL)
- If possible, have the student work in groups with bilingual students
who are more proficient in English
- Use sample projects to provide visual aids
- Provide music suitable to the student's culture
Credits
Brenda Levert teaches mathematics at the
Academy for Academics and Arts in Huntsville, Alabama. Levert's classroom
was featured in An Innovation Odyssey, a collection of stories of
technology in the classroom, Story 152: Choreographing Math. A team of
teachers expanded the plan into the example you see here.