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.
- 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.
- 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?
- 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.