 # Lesson 9: Proportions, Radius and Arc (Mathematics)  Teacher Lesson Plan

Approximate length of time: about 30 minutes

Outline of the activity: Students will measure length of a circle’s diameter for 3 different size hula hoops or other circular objects. Record data. Calculate each circle’s circumference. Calculate area of each circle. Determine the relationship between radius and area.

Student materials: data sheet, string, calculator

Assessment/evaluation piece: Students will present findings on various hoop sizes - - - cumulative data presentation.

Teaser: Have the studentsbrainstorm times when you have had to calculate accurate proportions?

Challenge:

http://www.mathforum.org/library/drmath/view/58039.html

Student Worksheets

Name __________________________ Hula Hoop Activity #1

Comparing a circle’s circumference with its area and a circle’s radius with its area.

Materials:

• different size hula hoops or other circular object
• string
• meter stick

Procedure:

• Using the string, determine the diameter of the hoop.
• Calculate the circumference.
• Calculate the area.
 Hula Hoop Diameter Circumference C = πd Area A=πr2 1 2 3

• Using your calculations, what is the relationship between circumference and area of a circle?
• How much more pizza is there to eat in a 14-inch pizza vs. a 10-inch pizza? (Remember: you measured the diameter of the circle)
 Radius Area = pr2 14 inch 10 inch

Using your calculations from the 14-inch and 10-inch pizza, what is the relationship between the radius and area?

Name ________________________ Quiz
relationships in circles

1) A stepping stone has a radius of 5 inches. What is the relationship between that stepping stone and a stepping stone that has twice the radius (which means a radius of 10 inches)?

Standards:

National Science Standards

• All students should develop abilities necessary to do scientific inquiry and understandings about scientific inquiry.
• All students should develop an understanding of properties and changes of properties in matter, motions and forces and transfer of energy.
• All students should develop abilities of technological design and understandings about science and technology.
• All students should develop understanding of science and technology in society.
Materials Need:

Materials List

• chalk
• tape measure
• 5 sets of 3 circular items with different radii (hula hoops)
• A piece of string just little longer than the diameter of the largest hula hoop. Make sure it is shorter than the circumference.

Student materials:

• data sheet,
• string,
• calculators
Supplemental Files: Mathematics Proportions Info