Introduction
Find out how to correctly identify the parts and the angle measures of a circle in this complex lesson on Circles and Arcs. Throughout this journey you will master how to solve real world problems using geometry.
Task
You will be creating/completing a sequence of activity's. Each activity will help to improve your knowledge on Circles and Arcs. After creating/completing the activites you will have a full understanding of Circles and Arcs. You will be required to apply your knowledge to create your own real life situation.
Process
You will be working on several different activity's through out this journey. You may work alone, or with a partner. Your first task will be to create a series of problems with a low level of difficulty concerning circles and arcs. The questions you create should gradually become harder. You may use the websites listed below for reference.
http://www.mathwords.com/a/arc_circle.htm
http://mathworld.wolfram.com/MinorArc.html
For your first task, you are to create a series of problems that describe the relation of the angles contained with in a circle. For example, the measure of an angle that is 120 degrees is a minor arc. And the measure of an angle that is 240 degrees is a major arc.
You will draw your own circles using a protractor and create your own angles. There will be no technology used. You may use white printer paper.
You will be creating 10 questions centered around major and minor arcs. These questions are designed to help you learn all you need to know about circles and arcs.
You will be drawing a total of 50 circles. Every ten circles you create will be centered on a different concept of circles and arcs. There is much to know!
For your second task, you are to create a series of 10 problems concerning the arc addition postulate. The arc addition postulate states that the measure of the arc formed by two adjacent arcs is the sum of the measures of two arcs. For example, measure abc = measure ab + measure bc.
Keep in mind that the problems should gradually become harder as you write them. This should be a complex lesson and upon completion you should have a deep understanding of circles and arcs.
For your third task, you are to create a series of 10 problems based around the diameter of a circle. The diameter should be shown and the circle should contain a total of four angles adding up to 360. Two of the angles should be given to help calculate the other two missing angle measures.
For your fourth task, you are to create a series of 10 problems using theorem 10-9. Theorem 10-9 states that the circumference of a circle is x times the diameter. In other words C= Pi multiplied by Diameter or C= 2 multiplied by Pi multiplied by Radius.
For your fith task, you are to create a series of 10 problems based around theorem 10-10. Theorem 10-10 states that the length of an arc of a circle is the product of the ratio measure of the arc divided by 360 and the circumference of the circle. In other words the measure of the arc divied by 360 multiplied by (2 multiplied by Pi multiplied by Radius) or Measure of arc divided by 360 multplied by (Pi multiplied by Diameter).
You should have a total of 50 problems minimum.
Evaluation
You must have 50 circles drawn with neat craftmanship. I will be evauating your problems and making sure the problems gradually grow more difficult. Every set of (10) problems should be based on the concept given in the process.
4
Execellant craftmanship. More than 50 circles drawn. Problems gradually become harder.
3
Fair craftmanship. 50 circles drawn. Problems gradually become harder.
2
Good cratmanship. Less than 50 circles drawn. Problems are mixed on different levels of difficulty but do not become gradually harder.
1
Poor craftmanship. Less than 50 circles drawn. Problems are all at the same level.
Conclusion
Circles and arcs are everywere, and it's important to be able to find there angle measures. I hope this complex lesson has deepened your uderstanding of circles and arcs and taught you how to solve real world problems using geometry.
Credits
Hi, my name is Jenna Lee Escalante and I love to make art and poetry. I love classic horror movies. Coffee is my favorite drink and I enjoy perfecting my cursive and learning to read calligraphy.
I picked the topic Circles and Arcs for my webquest because I found it easy to apply to a real world situation. The world is made up of shapes, even the earth is circlular! I am also an artist so shapes are very familiar to me, I work with them a lot.