Big Idea:
To help students understand the definition and motivation for radians and the relationship between radians and degrees while using the computer.
Standards:
GSE Framework:
M(G&M)-AM-7 Uses radian measure appropriately when solving problems; converts between radian measure and degree measure; and understands why radian measure is helpful. (K-12 Mathematics NH Curriculum Framework)
Common Core Math Standards:
F.T.F.1: Understand the radian measure of a circle as the length of the arc on the unit circle subtended by an angle.(Common Core Math Standards)
ISTE Standards:
1. Creativity and innovation - Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology.
a. Apply existing knowledge to generate new ideas, products and processes.
b. Create original works as a means of personal or group expression
4. Critical Thinking, Problem Solving, and Decision Making
a. Identify and define authentic problems and significant questions for investigations.
b. Plan and manage activities to develop a solution or complete a project.
Lesson Objectives:
- Students will understand and be able to explain the math lesson: Introduction to Radians using the computer.
- Students will be able to recognize that there are three different ways of expressing angle; degrees, radian decimals and radian fractions.
- Students will be able to calculate arc length from radian angle measure.
- Students will be able to create the ratio of concentric arcs.
- Students will be able to describe an angle and convert to radian and degree measure.
Materials:
- Laptops or computers
- Earbuds
- Internet Access
- School gmail accounts
- Slips of blank paper
- Pencil
- Scissors
- Printer
- String for each student (enough for the circumference of two circles of different sizes)
Anticipatory Set:
In order to get the students attention on the upcoming lesson, the teacher will ask the students the following questions.
- Have ever used the computer to learn math?
- How they would describe and measure an angle?
- What professions may have the need to measure and use angles?
- Do you know what degrees and radians are?
- Does the word radian sounds like radius?
- Tell the students that they are going to study trigonometry which is made up of three Greek words. Do you know what the greek words are and what they mean? (Tri-three, gonya - sides, metron - measure. Trigonometry - the measure of triangles)
Procedures:
1. Tell the students that they will be learning about the degree and radian measure of angle and how to convert between degrees and radians. Tell the students that they will be using a computer to access the lesson Introduction To Radians.
2. Have the students log into their school account. The students will go to the link titled Introduction To Radians which was emailed to them prior to class. The teacher will pass out a piece of white paper for each student and will read the instructions to procedure 3. The students will begin to watch and listen to the tutorial titled Introduction to Radians. Remind the students to use their earbuds as they use the computer.
3. The teacher is to instruct the students that as they navigate thru the lesson, they must answer the two problems under the sub-headings; Radians and arc length and Degrees to radians. Each student will show all their work on a separate piece of white paper that they recently received from the teacher. Each student must put their name and date at the top of the paper. All answers must be circled. The students will be graded using 1. Tell the students that they will be learning about the degree and radian measure of angle and how to convert between degrees and radians. Tell the students that they will be using a computer to access the lesson Introduction To Radians.
2. Have the students log into their school account. The students will go to the link titled Introduction To Radians which was emailed to them prior to class. The teacher will pass out a piece of white paper for each student and will read the instructions to procedure 3. The students will begin to watch and listen to the tutorial titled Introduction to Radians. Remind the students to use their earbuds as they use the computer.
3. The teacher is to instruct the students that as they navigate thru the lesson, they must answer the two problems under the sub-headings; Radians and arc length and Degrees to radians. Each student will show all their work on a separate piece of white paper that they recently received from the teacher. Each student must put their name and date at the top of the paper. All answers must be circled. The students will be graded using the attached rubric. This rubric can also be found in a link emailed to them prior to class. The teacher will collect each students work when everyone is done answering the questions.
4. When the students are done the computer lesson, have them form small groups of three to five students. Each group must create a challenging mathematical problem relating to the lesson and provide a solution key. The groups must be creative and come up with a challenging problem that addresses the following four questions:
- How do you find the arc length given the angle in radians and the radius?
- How do you find the ratio of concentric arcs given the radius and the distance between the two arcs?
- After finding the ratio of concentric arcs, how do you find the angle in radians and the length of the second concentric arc?
- How do you convert an angle in radians to degrees?
5. Each group is to exchange their problem with another group and they are to work together to solve the problem. Each group will go back to the group who originally gave them the problem to check to see if their solution to the problem is correct.
6. ACTIVITY: Upon completion of the group work, the teacher will ask the students; What is the relationship between the circumference and the diameter? The teacher is to create a classroom discussion revolving around this question. The teacher will then give each student two pieces of string. The students will then access their circle worksheet that was emailed to them in a link prior to class. The students will cut the string to the length of the diameter for each circle shown on the circle worksheet. They will see how many times it will go around the circumference of a circle. It should be able to go around approximately 3.14 times on each circle. This exercise will show how the diameter and radius are related to the circumference.
7. The teacher will pass out another piece of white paper and each student will put their name, date and title of the lesson (Introduction to Radians) on the top of the paper. The teacher will ask the students to reflect on todays lesson and list all the important aspects of the lesson. Encourage the students to show formulas and list definitions along with mathematical drawings. The teacher will collect this paper as the students leave the class.
8. As the students leave the class, the teacher will tell the students how wonderful they are and wish them a great day.
Closure:
1. Students will be assessed on their response to the two problems titled: Radians and arc length and Degrees to radians that they were required to complete during the computer tutorial. The students are required to show all work and circle their answer. The attached rubric will be used to assign a grade.
Modifications/Accommodations:
1. Students who struggle with the lesson will be allowed to work with a partner who demonstrates higher academic abilities.
2. Students that struggle during the lesson will be allowed to ask the teacher for help or ask a classmate for help. This will be allowed throughout the lesson but not while the students are answering the two problems that are presented on the computer.
3. Students that may need more time or extra help can come after school for further assistance.
4. All IEP and 504 modifications and accommodations will be followed.
6. ACTIVITY: Upon completion of the group work, the teacher will ask the students; What is the relationship between the circumference and the diameter? The teacher is to create a classroom discussion revolving around this question. The teacher will then give each student two pieces of string. The students will then access their circle worksheet that was emailed to them in a link prior to class. The students will cut the string to the length of the diameter for each circle shown on the circle worksheet. They will see how many times it will go around the circumference of a circle. It should be able to go around approximately 3.14 times on each circle. This exercise will show how the diameter and radius are related to the circumference.
7. The teacher will pass out another piece of white paper and each student will put their name, date and title of the lesson (Introduction to Radians) on the top of the paper. The teacher will ask the students to reflect on todays lesson and list all the important aspects of the lesson. Encourage the students to show formulas and list definitions along with mathematical drawings. The teacher will collect this paper as the students leave the class.
8. As the students leave the class, the teacher will tell the students how wonderful they are and wish them a great day.
Closure:
1. Students will be assessed on their response to the two problems titled: Radians and arc length and Degrees to radians that they were required to complete during the computer tutorial. The students are required to show all work and circle their answer. The attached rubric will be used to assign a grade.
Modifications/Accommodations:
1. Students who struggle with the lesson will be allowed to work with a partner who demonstrates higher academic abilities.
2. Students that struggle during the lesson will be allowed to ask the teacher for help or ask a classmate for help. This will be allowed throughout the lesson but not while the students are answering the two problems that are presented on the computer.
3. Students that may need more time or extra help can come after school for further assistance.
4. All IEP and 504 modifications and accommodations will be followed.
No comments:
Post a Comment