Students will investigate several circular objects
in order to understand the meaning of pi and solidify the formulas of a
Topic: Geometry and Measurements of a circle
Grade Level: 6th grade
Student Lesson name and URL: Pi in your face
Math Measurement and Geometry
1.0 Students deepen their
understanding of the measurement of plane and solid shapes and use this
understanding to solve problems:
1.1 Understand the concept of
a constant such as p; know the formulas for the circumference and area
of a circle.
1.2 Know common estimates of p(3.14;
22/7) and use these values to estimate and calculate the circumference
and the area of circles; compare with actual measurements.
Activities -Go Here for Student Work
Students will understand
the vocabulary of a circle: center, diameter, radius, chord, arc, circumference,
Student measure circumference
to nearest millimeter.
Students will compare the area
of each object found.
After given one measurement students
will be able to find the circumference and area.
Students will use a spreadsheet
to organize measurements of 5 round objects. Suggestions are soup cans,
soda containers, basketball count, garbage cans, tape rolls, ect...
Students will take a pretest, and list daily occurrences of circles.
What do you know about circles?
In teams of 2-3, list all
the places you might see a circle today.
Day 1 - Vocabulary
Students will make a game, crossword puzzle, word search or other activity
for the following words:center, diameter, radius, chord, arc, circumference,
pi, area, central angle
Day 2 - Switch It- Students give their work to someone else
to do. This is the review.
Materials Needed: various round objects, string, and ruler. Have students
make a spreadsheet or graph as shown here.
At least five objects will be used. Measure to the nearest millimeter
Collect several objects the
students listed. Set up a spreadsheet or have student make one.
What is the value for the ratio?
Review - Take
the students out to the basketball courts. Each team of 4-5 students
need one circle. Ask them to show in the circle circumference,
diameter, radius, arc and area.
Activity - Materials: Graph paper, soda can, transperancy graph
Area- It won't fit on graph paper! Circles don't fit nicely on
graph paper. On the overhead trace the bottom of a soda can. Place
graph transperency of it. Can you figure out how many square centimeters
there are. What are some of the problems you run into? Discuss
There is a formula for the area of a circle. Area = ? * r * r.
Let's do it as a class. Write the examples and answers down If the
radius is 5, find the Area. Do on overhead. Check. Give the following radii
and diameters. Check progress and then review as class R = 6,
R= 3, R = 7 D= 8, D= 10, D =4, *D =7
What are the formulas we use for a circle?
C=d*3.14 Or C=2(r)(22/7) A = 22/7(r)(r)
Pi can be 3.14 or 22/7 it depends on how accurate you need to be.
3 Station Test.
3 Station test.
Station One - Show
these definitons and illustrate them: center, diameter, radius, chord,
arc, circumference, pi, area, central angle
Station Two - Show
the steps to find the Area of a circle if the diameter is 8, and another
if the radius is 5.
Station Three -Show
the steps to find the Circumference of a circle if the diameter is 10,
and another if the radius is 3.
The rubric for all required
student work is under Your Grade
Resources & Supplementary Materials
There is a great AIMS activity
called Magic Circle. Here is the AIMS web site http://www.aimsedu.org/
Evergreen Union School District
Location Cottonwood CA