Class contact list spreadsheet from Gigi
14 years ago
Friday, December 18, 2009
Friday, November 27, 2009
Assignment #3: The other parts
Part 1 and 2:
http://erwinlee1980.blogspot.com/2009/11/assignment-3-math-project-on.htm
Part 1 and 2 (my pictures are here):
http://paulsiumaed314a.blogspot.com/2009/11/assignment-3-math-project-tessellations.html
http://erwinlee1980.blogspot.com/2009/11/assignment-3-math-project-on.htm
Part 1 and 2 (my pictures are here):
http://paulsiumaed314a.blogspot.com/2009/11/assignment-3-math-project-tessellations.html
Monday, November 23, 2009
Math and Sound Lesson Plan
Math and Sound Teacher Notes
Grade 12
Trigonometric Identities
Paul, Stanley, Erwin, and Gigi
Purpose: To show the trigonometric identity:
sin(2πf1t)+sin(2πf2t)=2 cos(2π (f1-f2)t/2)sin(2π (f1-f2)t/2)
in an auditory manner.
Students will hypothesis, predict and test which part of the wave is associated with the pitch and which part is associated with the beat or the volume.
Description of Activities: Students will be using Audacity (a free program) to generate sinusoidal sound waves. Playing two waves together is like playing the sum of the two waves. (This shows the additive property of waves.) Students will be investigating the beat phenomenon and the trigonometric identity: sin(2πf1t)+sin(2πf2t)=2 cos(2π (f1-f2)t/2)sin(2π (f1-f2)t/2) . They will be following their worksheet to guide them through the activity.
Sources: http://en.wikipedia.org/wiki/Beat_(acoustics)
Estimated time: 1-1.5 Classes or 1 Class and the rest is due for homework
Students are required to produce a page of answers and supporting graphs. Students will conclude cos(2π (f1-f2)t/2) is the part responsible for the amplitude (and thereby the beating) of the wave. The pitch of the wave is the part sin(2π (f1-f2)t/2) .
Marking Criteria: Students will be marked on the correctness of their answers. Students will also be given a mark on their participation in class out of a 4 point scale worth 25% of their total mark.
1- Did not participate
2- Participated 20% of the time
3- Barely meets expectation for participation
4- Meets expectation for participation
5- Exceeds expectation for participation
mathworksheetsound
Math and Sound Investigation
1) Open up Audacity. Go to Generate : Tone to create a tone also known as a sound wave. You can delete a sound wave by highlighting it and pressing delete. It is not recommended to have more than two sounds waves in your workspace at once. Try generating sound waves with different amplitudes, waveform and frequency.
2) At a fixed point in space, a basic sound wave (pure tone) can be represented by a sinusoidal function. One of the functional representation is Asin(kt).
Fill in the blanks with the following words: amplitude, frequency, volume, pitch
The _________________ of the function represents the loudness or _________________ of the sound.
The _________________ of the wave function represents the _________________ or how high or low the note is.
Copy and paste the above two statements with their answers onto separate file. You will print your answers at the end of class to hand in.
2) Investigate:
Generate a sine wave tone. Choose a frequency (call this n)
Generate another sine wave with frequency n+1.
Play the result.
What does it sound like? Record your answer.
You may hear a pitch change and a beating frequency.
Delete the wave with frequency n+1
Repeat the above and investigate with frequency n+2, n+3, n+10, n+20, n+100, etc
How does the pitch change as the second frequency increases?
How does the rate / frequency of the beat change?
Record your answers.
3) On graph paper, hypothesis what the wave would look like.
4) When you are listening to the waves together, it is like adding two sin waves.
sin2πf1+sin(2πf2) =
What is the trigonometric identity associated with this sum?
5) Hypothesis which part of the wave is associated with the amplitude (the beating) of the wave and which part is associated with the pitch.
6) Clear your workspace. Make two sound waves with different frequencies. Record this frequency. Using your hypothesis in question 5 predict the frequency of the beat and the frequency of the pitch. Use appropriate frequencies in which you can hear the beats.
7) Test your prediction by listening to the waves. Record how many beats you hear in 10 seconds. What are the experimental values of the beats? Is your hypothesis in 5 valid?
8) With the trigonometric identity found in 4, label which part is responsible for the beats and which part is responsible for the pitch of the waveform.
9) Plot out the sum in a graphing program or graphing calculator. You may need to plot twice: choose an appropriate scale for the beat and another for the pitch. Include your plots with your answers to hand in at the end of class.
10) Find two frequencies f1, f2, in which a period of the beat is 10 times larger than the period of the oscillations (part responsible for the pitch). Show your work. Graph the sum of sin2πf1+sin(2πf2) .
Extension Questions:
Go to http://www.mindspring.com/~j.blackstone/dist101.htm. Scroll down to the applet. Play around with the applet and record how the sound changes. Does the perceived pitch change? In other words, if you tried to hum the note does it change as you change the wave?
Monday, November 16, 2009
Memorable Moments from Practicum
I sort of can't find where the sheet I wrote was so I'll try to just type for eight or so minutes.
Memory 1:
I was asked if I was a new student in the grade 9 class science class. Granted my sponsor teacher had a policy of not outright saying this new person was but just showing by interactions and presentations, I think this student wanted to spite me. She was a bit catty and chatty. I had dressed up very professional the last day and this second day I was wearing nice pants and a leather jacket. Anyways, I decided not to play her game if she was playing a game and just told her I was a student teacher. My sponsor teacher said that there are sometimes students coming in and out and peer tutors helping out in the class. I knew this was going to happen.
Memory 2:
I had taught my math sponsor's two classes. The first was a grade 11 class and the 2nd was a grade 9 class. I wanted to do TPS with the students. I made a mistake with the grade 11 class and they went crazy. They didn't do their seatwork and didn't want to present to the class after. I talked with my FA and SA after the lesson. I learned now I need to set expectations and stress these expectations. I needed to stress that they needed to work and at the end I would choose randomly a person to go and present to the class. I deliberately wrote out the words I was going to say so that I was emphasize on the SHARING part of TPS. My SA stressed that if the students are working harder than the teacher, the teacher is working too hard. Thus, with all this in mind, my grade 9 class went much smoother even though they were grade 9s. I also learned from the ToC that day, if you confiscate a cell phone, keep it hidden in a drawer or in a pocket or the phone will be stolen or lost.
Memory 1:
I was asked if I was a new student in the grade 9 class science class. Granted my sponsor teacher had a policy of not outright saying this new person was but just showing by interactions and presentations, I think this student wanted to spite me. She was a bit catty and chatty. I had dressed up very professional the last day and this second day I was wearing nice pants and a leather jacket. Anyways, I decided not to play her game if she was playing a game and just told her I was a student teacher. My sponsor teacher said that there are sometimes students coming in and out and peer tutors helping out in the class. I knew this was going to happen.
Memory 2:
I had taught my math sponsor's two classes. The first was a grade 11 class and the 2nd was a grade 9 class. I wanted to do TPS with the students. I made a mistake with the grade 11 class and they went crazy. They didn't do their seatwork and didn't want to present to the class after. I talked with my FA and SA after the lesson. I learned now I need to set expectations and stress these expectations. I needed to stress that they needed to work and at the end I would choose randomly a person to go and present to the class. I deliberately wrote out the words I was going to say so that I was emphasize on the SHARING part of TPS. My SA stressed that if the students are working harder than the teacher, the teacher is working too hard. Thus, with all this in mind, my grade 9 class went much smoother even though they were grade 9s. I also learned from the ToC that day, if you confiscate a cell phone, keep it hidden in a drawer or in a pocket or the phone will be stolen or lost.
Group Microteaching
(from a long time ago!)
Group Microteaching Lesson Plan
Bridge: Our hook? Everyone loves the out of the norm problem solving. We'll have the students pair up and work on one of three problems for 5-7 minutes. They'll be using string to make lines of best fit.
Learning Objectives: Students will turn data from word problems based on real life and make a table. Students will have hands on experience on making a best fit line from the data they plot. Students will then extrapolate from the fit to answer other questions.
Teaching Objectives: Students will work in pairs. Students will be responsible for presenting their solutions.
Pre-Test: Ask students if they remember graphing from previous years.
Participatory Activity: There are three different worksheets for this activity. Each worksheet will have the students graph out a different type of graph.
Linear Function: Data is already given to the student. Students will plot out the relationship between payment for a plumber's rates at different hours.
Reciprocal Function: A class wants to buy the teacher $100 gift. The amount each student has to pitch in depends on the number of students that want to pitch in.
Quadratic Function: You want to carpet the floor. What is the area of the square of the carpet if we vary the length of the square?
Students will have to answer questions about their scenario and graph out the data. Students will plot out the data and do a best fit. Students would then have to answer questions based on their fit.
Post-Test: One student representing a different worksheet will present their scenario and their graphs. They explain and discuss their graph and give answers to their questions.
Summary: Students are learning from their worksheets and their peers. They will learn hands on one of the ways to do a best fit curve. At the presentation, students will be able to see the different types of graphs. Students will also learn the different types of real life problems, the mathematics they know already can handle.
Group Microteaching Reflection
I was feeling quite nervous and excited that day as we had to present in front of the whole class and that it was the last day of class before our short term practicum. One of our biggest enemies is timing. How will we gauge whether the majority of the class has finished their worksheet and that we should move on? If they are finished or not finished, they still look like they are busy chatting away. I think if their was a blank backside to their work sheet, we could get them to turn it over and sit quietly or for them to draw on it. We may have given them 2 extra minutes but in a 20 minute activity, that is a lot of time.
We didn't tell our class that this was a grade 8-9 activity. When the students presented, we had our trustworthy students answer in the class. In a real class situation, I learned from my practicum that before I hand out the activity, I would have to make sure all students are responsible for presenting and that they would be randomly called up to present their findings. Our first student that presented gave answers above and beyond the grade level and using big mathematical terms to explain the problem. I was mortified and a bit tired so I was quite stunned. I did not know what to do. The student became the teacher and was messing up the time allotement for the activity. If my mind was more cleared, then I would have stepped in and ask the student just to explain the scenario and how it relates to the graph that he has drawn. We wanted more on how the curve looked: Was it straight? Did it increase or decrease? All in all, that was probably our biggest problem of the presentation. In our responses, other students noted this problem. They did however also noted the relavency of the activity to real life.
Group Microteaching Lesson Plan
Bridge: Our hook? Everyone loves the out of the norm problem solving. We'll have the students pair up and work on one of three problems for 5-7 minutes. They'll be using string to make lines of best fit.
Learning Objectives: Students will turn data from word problems based on real life and make a table. Students will have hands on experience on making a best fit line from the data they plot. Students will then extrapolate from the fit to answer other questions.
Teaching Objectives: Students will work in pairs. Students will be responsible for presenting their solutions.
Pre-Test: Ask students if they remember graphing from previous years.
Participatory Activity: There are three different worksheets for this activity. Each worksheet will have the students graph out a different type of graph.
Linear Function: Data is already given to the student. Students will plot out the relationship between payment for a plumber's rates at different hours.
Reciprocal Function: A class wants to buy the teacher $100 gift. The amount each student has to pitch in depends on the number of students that want to pitch in.
Quadratic Function: You want to carpet the floor. What is the area of the square of the carpet if we vary the length of the square?
Students will have to answer questions about their scenario and graph out the data. Students will plot out the data and do a best fit. Students would then have to answer questions based on their fit.
Post-Test: One student representing a different worksheet will present their scenario and their graphs. They explain and discuss their graph and give answers to their questions.
Summary: Students are learning from their worksheets and their peers. They will learn hands on one of the ways to do a best fit curve. At the presentation, students will be able to see the different types of graphs. Students will also learn the different types of real life problems, the mathematics they know already can handle.
Group Microteaching Reflection
I was feeling quite nervous and excited that day as we had to present in front of the whole class and that it was the last day of class before our short term practicum. One of our biggest enemies is timing. How will we gauge whether the majority of the class has finished their worksheet and that we should move on? If they are finished or not finished, they still look like they are busy chatting away. I think if their was a blank backside to their work sheet, we could get them to turn it over and sit quietly or for them to draw on it. We may have given them 2 extra minutes but in a 20 minute activity, that is a lot of time.
We didn't tell our class that this was a grade 8-9 activity. When the students presented, we had our trustworthy students answer in the class. In a real class situation, I learned from my practicum that before I hand out the activity, I would have to make sure all students are responsible for presenting and that they would be randomly called up to present their findings. Our first student that presented gave answers above and beyond the grade level and using big mathematical terms to explain the problem. I was mortified and a bit tired so I was quite stunned. I did not know what to do. The student became the teacher and was messing up the time allotement for the activity. If my mind was more cleared, then I would have stepped in and ask the student just to explain the scenario and how it relates to the graph that he has drawn. We wanted more on how the curve looked: Was it straight? Did it increase or decrease? All in all, that was probably our biggest problem of the presentation. In our responses, other students noted this problem. They did however also noted the relavency of the activity to real life.
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