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 |
Diameter |
Circumference |
Area |
|
1 |
|||
|
2 |
|||
|
3 |
Answer the following questions:
- 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 |
|
|
10 |
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)?
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 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
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