DANCE THE DEPENDENT VARIABLE—GEOMETRIC FUNCTION DANCES

In Geometric Functions activities students create, manipulate, and experience function concepts by treating geometric transformations as functions with points as their variables.

In this two-part activity, students perform dances based on the translation, reflection, rotation, and dilation function families. In part 1, teams of students practice and perform physical dances with one student as the independent variable, another as the dependent variable, and the remaining students as choreographers. In part 2, pairs of students use Sketchpad to perform virtual dances, with one student moving the dependent variable and the other student acting as coach and recorder.

OBJECTIVES

In this activity students will:

• Work with a team to practice and then perform several function dances chosen from the reflection, rotation, dilation, and translation families.
• Dance the role of an independent variable either by moving freely or by moving along a restricted domain.
• Dance the role of a dependent variable, moving in coordination with the independent dancer to maintain the function rule.
• Coach the independent and dependent dancers to help them maintain the function rule.
• Drag a point to keep it in the role of dependent variable for an animated independent variable.
• Observe, analyze, and record the relative rate of change of the two point variables.
• Compare the shapes traced by an independent variable restricted to a domain and a corresponding dependent variable, distinguishing between similar shapes and congruent shapes.

COMMON CORE CONNECTIONS
Mathematical Practices

(1) Make sense of problems and persevere in solving them; (2) Reason abstractly and quantitatively; (3) Construct viable arguments and critique the reasoning of others; (4) Model with mathematics; (5) Use appropriate tools strategically; (6) Attend to precision; (7) Look for and make use of structure; (8) Look for and express regularity in repeated reasoning.

Content Standards

8.F1,2; 8.G1; F-IF1,2,9; G-CO2; G-SRT1