4th Grade IEFA/Math Lesson
The Circle
Harcourt connection:
Unit 6, chapter 18
IEFA Essential Understanding 1:
There is great diversity among the 12 tribal Nations of Montana in their languages, cultures,
histories, and governments. Each Nation has a distinct and unique cultural heritage that
contributes to modern Montana.
IEFA Essential Understanding 3:
The ideologies of Native traditional beliefs and spirituality persist into modern day life as tribal
cultures, traditions, and languages are still practiced by many American Indian people and are
incorporated into how tribes govern and manage their affairs.
GFPS Geometry Mathematics Content Standard 4:
Students demonstrate understanding of shapes and an ability to use geometry.
GFPS 4th grade Geometry Mastery Statement:
Students will decompose and classify figures using 2-D shapes and identify their attributes and
identify in real-life situations.
Understandings: students will understand…
 Circles are an important symbol in Native American culture.
 Mathematical attributes of a circle.
Essential questions:
 What attributes do all circles share?
 Why are symbols used?
Students will be able to…
 Identify the attributes of a circle.
 Name circular symbols that are important in Native American culture.
Students will know…
 Circles are a unique shape with unique attributes. These attributes symbolize important
parts of Native American culture.
Assessment Evidence:
 Students will fold and/label their circle.
Learning Plan
Materials
8 inch circle di-cut
Circle pictures
Protractor
Gain Attention
1. Show students pictures of circular objects (sun, earth, nest, solar system, season cycle,
life cycle of a butterfly)
2. What do you observe about these objects? What do they all have in common?
State Objective and Rationale:
Today you will be learning:
1. Today you will be learning about the circle and how and why it is an important symbol
to the Native American culture.
a. Each culture has symbols that are important to them. Understanding an
important symbol of the Native Americans will help is understand their culture
better. They are a big part of our shared Montana culture .
2. We will also be looking at the circle mathematically and be able to describe it using the
correct terminology.
a. Using common terminology in mathematics helps us communicate our
mathematical ideas well with others.
Build background:
1. What do you notice about a circle?
2. How is it different than a square?
3. What are some of its attributes/characteristics?
4. Why do you think that the Native Americans chose a circle as an important symbol of
their culture?
Teaching:
1. Read aloud the poem “The Rock and Eagle Speaks. Put on the doc cam so they can read
along with you.
“The Rock and The Eagle Speaks”
All is a circle and a hoop within me.
If I speak in the language you taught me
I am all but one.
Look inside the circle and the hoop
You will see your relation and nations.
Your relation to the four legged
And the two legged
And the winged ones
And to the mother earth
The grandfather sun
The grandmother moon
The direction and the sacred seasons.
And the universe
You will find love for your relation.
Look further inside the sacred circle
And the sacred hoop
In the center of the circle and the hoop
You will feel the spirit
Of the great creator
He is in the center of everything
Learn about what you are
By observing what you are not.
2. What does the poem say about the significance/power of the circle?
3. Background: The Circle
Many American Indian tribes use symbols to remember key understandings of the natural
world. The circle is one such symbol. The shape of the circle can be used to explain and
understand the way our world works and to know our place in it. Circles have no beginning
and no end, therefore no point is more important than the point before or the point after. All
things are equal in the circle, thus all things are important.
The circle symbol can be found on several Montana tribal flags. Each flag’s circular symbol
is unique to that tribe. Below are the flags and what the flags symbol represents.
Blackfeet
Circle: Represents the cycle of life, people are
connected, always were, always will be, the circle
never ends. The many feathers equate the many bands
of the proud and numerous Blackfeet arranged in a
circle, beginning in a clockwise direction, as life is. The
sun rises in the East, circles to the West, the moon rises and sets in this circular motion, as is the
cosmos. Blackfeet people pitch the lodges with the doors to the East, knowing that we start life
with the circle in mind, it is perpetual.
http://www.blackfeetcountry.com/blackfeetflag.html
Rocky
Boy’s
The picture of this seal represents the circle of life on this reservation. Baldy Butte, the sacred
mountain of the Tribe: the Sun, representing life rising from the east, to greet the Sun Spirit each
morning from our homes and to wish for good health and life.
http://rockyboy.org/
Crow
The Emblem on the Flag is encircled. This
represents the Path of All Things. This Path is
clock-wise as is the Path of the Sun from the
northern vantage point.
http://www.crowtribe.com/emblem.htm
Fort Belknap
The circular shape of the shield symbolizes life itself,
as perceived by the Indian belief of the constant
cycle of life, each living thing dependent on each
other for life. The killing of the buffalo enables the
Indian to live and grow and when his mortal remains return to the earth, it serves as food for
the grasses of the prairie which in turn feeds the buffalo, thus ensuring the constant cycle of
life.
http://www.ftbelknap-nsn.gov/seal.htm
Science Teaching Examples:
Our seasons move in a circle, they happen in a continuous cycle with no beginning and no
end. One season is not more important than the one before or after. All 4 are necessary, thus
all 4 are equal in importance.
Water moves through a continuous circle: evaporation, condensation, precipitation, ground
water, evaporation… There is no beginning and no end. Each point in the cycle is just as
necessary as the point before and after.
Can you think of other circular systems?
4. Show a picture of some NA circles (Teepee, Ring for fire pit, medicine wheel, drum,
dream catcher, dancing in a circle at a pow wow.) What is a symbol? (Represents
something else)
5. Now that we know the circle is a significant symbol in the NA culture, let’s examine the
circle mathematically, because circles are everywhere!
6. Pass out circles to students. Have them turn and tell a neighbor their observations of the
shape itself. Share out loud a few. (These are called attributes of the circle!)
(Perhaps label circumference, radius, center and diameter here as they come up
in discussion)
7. Reinforce through whole class discussion that a circle has no beginning and no ending. It
is round. There are no corners or pockets. It continues and no one part is more
prominent than another.
8. Based on your knowledge of the attributes of the circle, does it make sense that the NA
culture chose this as an important symbol? How so?
9. Have students fold circle in half and trace the fold with a pencil. Make observations with
a neighbor. What can you tell me about the circle now? Share out loud (if not said):
a. We have created a line of symmetry.
b. The circle is divided into two equal halves or parts.
c. What we have just drawn in called the diameter of the circle. It is a line that runs
through the center of a circle from one side to the other.
d. Like the equator on earth.
10. Fold the circle again into quarters. Trace the fold with a pencil. Make observations with
a neighbor. What can you tell me about the circle now? What mathematical terms could
you use to describe what you see in the shape? Share out loud (if not said):
a. What we have created is another line of symmetry.
b. We formed four right angles. Each measure is 90 degrees. There are ninety
degree marks within this one quarter if a circle.
c. Put a dot at the intersection of the perpendicular lines. We call this the center of
the circle.
d. Show protractor and explain that if you line up the center point that every circle
can be measured using degrees. One degree is one equal part of a circle.
e. If there are 90 degrees in one part of the circle, how many degrees in the half
circle?
f. How many degrees in a full circle? Where in real life have you heard this term before?
Closure:
Where else do you see circles? What do these represent? Tell your neighbor something new
you learned about circles mathematically. Tell your neighbor something you learned about
circles in relation to the NA culture.