Students really do say the funniest things. Here is a record of some comments, conversations, etc from the first semester. Enjoy!
**Me: If your swearing becomes habitual, then you will have to stay after school [instead of doing pushups].
Student: Does habitual count?
**Me: You’ll probably break that (using a badminton racket with a volleyball)
Student: If you break it, we won’t tell. Just bury it.
**Teacher 1: You need a sphere (best item for projectile motion)
Teacher 2: We could make spears!
**Student: Sometimes I feel like I’m too smart.
**Student: I’m not checking you out. I’m finding your derivative.
**Me: I can’t say the letter r.
Student: That explains why you sound like a pirate.
**Student: Do you know why it’s (the graphing calculator) trying to teach me French?
**Student: If you use big words like constitutes, it makes it seem like you use the word-a-day toilet paper.
**Student: What is this unidentified object on my [calculator] screen?
**Student: Can we turn the air off? [I’m freezing.]
Me: That’s the heat.
**Student: We pompous calc students should do great on the *pre-calc test
**Student: Is this the ruler ______ chewed on?
Me: Yes, but he hasn’t chewed on it this week.
Thursday, December 22, 2011
Friday, November 11, 2011
Is math invented or discovered?
I had my students write their initial thoughts on the question: Is mathematics invented or discovered? Then they had to read a few people's opinions, discuss their ideas with the class, and then write down their final thoughts. Here are three student responses:
I believe that mathematics is a combination of both discovery and invention. As Dr.Mellendorf had stated, “What was discovered was how to mold the model to fit reality. What was invented was the model itself.” It was discovered how to use mathematics. Yet, the processes and whatnot were invented. As Einstein once questioned, “How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?” Even Einstein believed that there had to be some for of math on the earth before we invented the process of mathematics.
The use of mathematics has been there since the beginning of time. However, it took human thought to develop forms of mathematics. For centuries, our world was using math without knowing what exactly it was called. People have always used forms of addition and subtraction without knowing the technical terms. Math hadn’t come out of thin air, it was discovered. We had just invented the processes and technical terms for the different areas of math. All in all, math has been on the earth since the day it was created. It just took humans some time to pinpoint exactly what mathematics was.
People say that it is there to be discovered, that if it was only invented
anyone could come out and say that 2+2=4. They say that math is there for us to discover. But yet
there are people out there that say math is invented, made by us, that math was not there before
humans. I am somewhere in between the two viewpoints on this topic. I believe that math has
always been there, created by God along with everything else to make the universe go round. I
believe that Newton discovered gravity, he did not invent it. But, I believe that we invented the
system, or the language, that we use to interpret mathematics, but not the “math behind the
math”. Take Newton and Leibnitz for example. Both discovered calculus around the same time,
yet when you look at their theorems, they have many different notations and ways of expressing
the same thing. The calculus they both discovered is the same thing, but they invented different
ways of interpreting it. It would be next to impossible for men who have virtually no way of
communicating to both invent the same thing around the same time. Say the great mathematicians
of old had decided that 1 was really 2 and 2 was really three. Wouldn’t that mean 2+2 would equal
3 when there were really only 2 objects there? (If we were adding objects) Theoretically if the
mathematicians wanted everything to equal tree, then our notation would be different types of
trees, but it would mean the same thing as what we have today. After reading Eugene Vigner’s
quote that said mathematics is a gift, when you think about it, it really is. Mathematics, along with
everything, is a gift from God, therefore not invented, but discovered.
I think that it is both. I believe that the actual concept of math was invented, but I would say that the inner workings of it must be discovered. I’m assuming that people first started to use math in order to make building and other such tasks less difficult, so like discovering fire, it made our lives easier. It’s a tool. Although on the other hand, mathematicians today are still looking to divulge themselves into deeper knowledge of the subject. A prime example of how parts of math have been discovered is Calculus. Regardless of whether or not it was Leibnitz or Newton who discovered it, the fact remains the same; Calculus was discovered. It’s these new discoveries that expand our knowledge of mathematic world.
- Later on, we found that what made this so difficult to answer was the definition of “Math.” After a lot of discussing, we came to the conclusion that math can be defined as both the language of math, and how we use it / describe it, as well as the actual math itself. The actual math itself can be described as the truths and the fact that everything fits and how it works, which is discovered. The part that’s invented is the language of math.
I believe that mathematics is a combination of both discovery and invention. As Dr.Mellendorf had stated, “What was discovered was how to mold the model to fit reality. What was invented was the model itself.” It was discovered how to use mathematics. Yet, the processes and whatnot were invented. As Einstein once questioned, “How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?” Even Einstein believed that there had to be some for of math on the earth before we invented the process of mathematics.
The use of mathematics has been there since the beginning of time. However, it took human thought to develop forms of mathematics. For centuries, our world was using math without knowing what exactly it was called. People have always used forms of addition and subtraction without knowing the technical terms. Math hadn’t come out of thin air, it was discovered. We had just invented the processes and technical terms for the different areas of math. All in all, math has been on the earth since the day it was created. It just took humans some time to pinpoint exactly what mathematics was.
People say that it is there to be discovered, that if it was only invented
anyone could come out and say that 2+2=4. They say that math is there for us to discover. But yet
there are people out there that say math is invented, made by us, that math was not there before
humans. I am somewhere in between the two viewpoints on this topic. I believe that math has
always been there, created by God along with everything else to make the universe go round. I
believe that Newton discovered gravity, he did not invent it. But, I believe that we invented the
system, or the language, that we use to interpret mathematics, but not the “math behind the
math”. Take Newton and Leibnitz for example. Both discovered calculus around the same time,
yet when you look at their theorems, they have many different notations and ways of expressing
the same thing. The calculus they both discovered is the same thing, but they invented different
ways of interpreting it. It would be next to impossible for men who have virtually no way of
communicating to both invent the same thing around the same time. Say the great mathematicians
of old had decided that 1 was really 2 and 2 was really three. Wouldn’t that mean 2+2 would equal
3 when there were really only 2 objects there? (If we were adding objects) Theoretically if the
mathematicians wanted everything to equal tree, then our notation would be different types of
trees, but it would mean the same thing as what we have today. After reading Eugene Vigner’s
quote that said mathematics is a gift, when you think about it, it really is. Mathematics, along with
everything, is a gift from God, therefore not invented, but discovered.
I think that it is both. I believe that the actual concept of math was invented, but I would say that the inner workings of it must be discovered. I’m assuming that people first started to use math in order to make building and other such tasks less difficult, so like discovering fire, it made our lives easier. It’s a tool. Although on the other hand, mathematicians today are still looking to divulge themselves into deeper knowledge of the subject. A prime example of how parts of math have been discovered is Calculus. Regardless of whether or not it was Leibnitz or Newton who discovered it, the fact remains the same; Calculus was discovered. It’s these new discoveries that expand our knowledge of mathematic world.
- Later on, we found that what made this so difficult to answer was the definition of “Math.” After a lot of discussing, we came to the conclusion that math can be defined as both the language of math, and how we use it / describe it, as well as the actual math itself. The actual math itself can be described as the truths and the fact that everything fits and how it works, which is discovered. The part that’s invented is the language of math.
Tuesday, September 27, 2011
rough notes on interest rates, loans, etc
If you teach math, perhaps your students ask this: When will I ever need this in "real life?"*
We have been studying exponential growth and decay, and I was just waiting for this question. The past few days we have looked at car depreciation and why that is a big deal in "real life," but I wanted to take it up a notch.
Here are the rough notes for a project I am going to do with my advanced math students. I worked with my brother who is in the financial industry to help me design it. I still don't know how I am going to have the kids present what they learned to me. Perhaps I will do interviews, have them make a recording, or write a paper.
Project:
You need to take enough notes so that you'll be able to tell me what you learned. Take notes, screen shots, etc. so that you can reference them.
Read http://www.bankrate.com/finance/auto/the-price-of-long-auto-loans.aspx. What does it mean to be "upside down" in a loan?
Find a new car and use http://www.money-zine.com/Calculators/Auto-Loan-Calculators/Car-Depreciation-Calculator/ to figure out what value of car will be in 2 years. (I think we underestimated using 15% in class.) [Remember that you put in 0 for current age.]
Go to loan amortization sheet.
http://financialsoft.about.com/gi/o.htm?zi=1/XJ&zTi=1&sdn=financialsoft&cdn=compute&tm=32&f=10&su=p284.9.336.ip_p504.1.336.ip_&tt=11&bt=1&bts=1&zu=http%3A//www.mdmproofing.com/iym/products/loan-amortization/
Use 5.25% as the APR and 1/1/12 as the start date.
Compare total payment of loans for 3, 4, 5, 6, and 7 years. What happens to the total amount you have to pay? Why?
Compare your car value at 2 years to each of these loan values. What do you notice?
Read http://www.lendingtree.com/auto-loans/advice/buying-a-new-car/how-much-to-put-down-on-a-car/.
Now go back to the loan amortization sheet and put $5,000 down in the first payment. Now what do you notice? According to this article, can you be "upside down" in a loan even if you take out a 3-year loan?
Reflection questions
Why do most financial experts advise consumers to take car loans of 4 years or less?
Why do people take out loans for longer than 5 years and what can happen?
About what % of a car's value should you put down and why?
At my first job, I brought home approximately $23,000. Suppose my typical month of bills was $900, what advice would you give me if I wanted to buy a new car?
*I do acknowledge this is a valid and important question. I just wanted to set the tone of the blog. :)
We have been studying exponential growth and decay, and I was just waiting for this question. The past few days we have looked at car depreciation and why that is a big deal in "real life," but I wanted to take it up a notch.
Here are the rough notes for a project I am going to do with my advanced math students. I worked with my brother who is in the financial industry to help me design it. I still don't know how I am going to have the kids present what they learned to me. Perhaps I will do interviews, have them make a recording, or write a paper.
Project:
You need to take enough notes so that you'll be able to tell me what you learned. Take notes, screen shots, etc. so that you can reference them.
Read http://www.bankrate.com/finance/auto/the-price-of-long-auto-loans.aspx. What does it mean to be "upside down" in a loan?
Find a new car and use http://www.money-zine.com/Calculators/Auto-Loan-Calculators/Car-Depreciation-Calculator/ to figure out what value of car will be in 2 years. (I think we underestimated using 15% in class.) [Remember that you put in 0 for current age.]
Go to loan amortization sheet.
http://financialsoft.about.com/gi/o.htm?zi=1/XJ&zTi=1&sdn=financialsoft&cdn=compute&tm=32&f=10&su=p284.9.336.ip_p504.1.336.ip_&tt=11&bt=1&bts=1&zu=http%3A//www.mdmproofing.com/iym/products/loan-amortization/
Use 5.25% as the APR and 1/1/12 as the start date.
Compare total payment of loans for 3, 4, 5, 6, and 7 years. What happens to the total amount you have to pay? Why?
Compare your car value at 2 years to each of these loan values. What do you notice?
Read http://www.lendingtree.com/auto-loans/advice/buying-a-new-car/how-much-to-put-down-on-a-car/.
Now go back to the loan amortization sheet and put $5,000 down in the first payment. Now what do you notice? According to this article, can you be "upside down" in a loan even if you take out a 3-year loan?
Reflection questions
Why do most financial experts advise consumers to take car loans of 4 years or less?
Why do people take out loans for longer than 5 years and what can happen?
About what % of a car's value should you put down and why?
At my first job, I brought home approximately $23,000. Suppose my typical month of bills was $900, what advice would you give me if I wanted to buy a new car?
*I do acknowledge this is a valid and important question. I just wanted to set the tone of the blog. :)
Friday, August 19, 2011
One week down...How many more?
Well, we successfully made it through the first week of school. Yay! I told my students that today I felt jet lagged, and I hadn't even traveled anywhere. :) Honestly, it feels good to get back into the routine. I can't believe I am in my sixth year of teaching. It's been fun to reflect on how I've grown and yet, realize how much more I want to grow. I am trying some new things this year. My big project is Standards-Based Grading for Geometry and Algebra II. I'm sure I'll be blogging about that as the year goes on. I'm also serving as a mentor for a new teacher. I look forward to this role. I miss mentoring students like I did in Africa.
It should be an exciting year. There is one certainty in education--you never know what the day will hold! :)
It should be an exciting year. There is one certainty in education--you never know what the day will hold! :)
Thursday, August 18, 2011
Guess my #
Number puzzles always fascinated me as a child. When I learned the algebra behind them,I liked them even more. :)
Now as a teacher, I like to start Alg/Alg II with this activity. The students are usually amazed when you first do them. Then you can draw them in so they don't mind writing and simplifying expressions because they want to know how it works. Here are some of the basic ones I started with:
Guess my Number
1. Pick a number between 1 and 100.
2. Double it
3. Add 100
4. Take half the result
5. Subtract the number you started with.
Number 2
1. Pick a number
2. Add 9
3. Multiply by 3
4. Subtract 6
5. Divide by 3
6. Subtract original number.
Number 3.
1. Pick a number.
2. Multiply it by 9
3. Subtract 18
4. Divide by 9
5. Subtract your original number.
6. Add 2
Then I have the kids write their own and show the algebra behind it. We are still at the basic stage, but I am still proud of their work during the first week of school.
(Dan Meyer has some great ones to help the kids move from completing puzzles to creating them.)
1. Pick a number
2. Multiply by 4
3. Subtract 10
4. Divide by 4
5. Add 5
6. Subtract number started with
1. Pick a number
2. Add 12
3. Multiply by 2
4. Subtract 4
5. Divide by 2
6. Subtract the number you started with
1. Pick a number
2. Subtract 3
3. Multiply by 3
4. Add 9
5. Divide by 3
6. Subtract the number you started with
1. Pick a number
2. Subtract 15
3. Divide by 5
4. Subtract 3
5. Multiply 5
6. Subtract the number you started with
1. Pick a number
2. Add 6
3. Multiply by 3
4. Subtract 3
5. Divide by 3
6. Subtract the number you started with
Now as a teacher, I like to start Alg/Alg II with this activity. The students are usually amazed when you first do them. Then you can draw them in so they don't mind writing and simplifying expressions because they want to know how it works. Here are some of the basic ones I started with:
Guess my Number
1. Pick a number between 1 and 100.
2. Double it
3. Add 100
4. Take half the result
5. Subtract the number you started with.
Number 2
1. Pick a number
2. Add 9
3. Multiply by 3
4. Subtract 6
5. Divide by 3
6. Subtract original number.
Number 3.
1. Pick a number.
2. Multiply it by 9
3. Subtract 18
4. Divide by 9
5. Subtract your original number.
6. Add 2
Then I have the kids write their own and show the algebra behind it. We are still at the basic stage, but I am still proud of their work during the first week of school.
(Dan Meyer has some great ones to help the kids move from completing puzzles to creating them.)
1. Pick a number
2. Multiply by 4
3. Subtract 10
4. Divide by 4
5. Add 5
6. Subtract number started with
1. Pick a number
2. Add 12
3. Multiply by 2
4. Subtract 4
5. Divide by 2
6. Subtract the number you started with
1. Pick a number
2. Subtract 3
3. Multiply by 3
4. Add 9
5. Divide by 3
6. Subtract the number you started with
1. Pick a number
2. Subtract 15
3. Divide by 5
4. Subtract 3
5. Multiply 5
6. Subtract the number you started with
1. Pick a number
2. Add 6
3. Multiply by 3
4. Subtract 3
5. Divide by 3
6. Subtract the number you started with
Saturday, June 4, 2011
What? You just said that? LOL
If you're a teacher, you know that students say the funniest things. A friend of mine encouraged me to keep a running list of these humorous moments. As the year winds down, I thought I'd share them with y'all.
Caution: Some of them may not be as humorous to the outside reader as context is everything. :)
*Miss Pettit, you always want to talk about math. (after I kept trying to get class to stop talking about movies)
*Excuse me Miss Pettit. I need to moonwalk.
*Miss Pettit, can I go get a pencil from my cereal box?
*Oh my gosh. I can’t concentrate when people talk about milk.
*Girls want real men...Men who eat beef jerky.
*Women.
(This was a class of a few girls and lots of boys.)
*Me: Are you okay?
Student: I can’t feel my arms. (after doing his pushups)
*I’m not gonna lie. My boxers are longer than your shorts.
*You know what that’s from? It’s from whipping our hair.(on why their neck and head hurt)
*I am right and you cannot argue with me. (end of student’s math paper)
*NASCAR is the lazy version of track.
*It makes me feel smart. (student talking about Sigma notation)
Student 2: It makes me feel like an alien.
Caution: Some of them may not be as humorous to the outside reader as context is everything. :)
*Miss Pettit, you always want to talk about math. (after I kept trying to get class to stop talking about movies)
*Excuse me Miss Pettit. I need to moonwalk.
*Miss Pettit, can I go get a pencil from my cereal box?
*Oh my gosh. I can’t concentrate when people talk about milk.
*Girls want real men...Men who eat beef jerky.
*Women.
(This was a class of a few girls and lots of boys.)
*Me: Are you okay?
Student: I can’t feel my arms. (after doing his pushups)
*I’m not gonna lie. My boxers are longer than your shorts.
*You know what that’s from? It’s from whipping our hair.(on why their neck and head hurt)
*I am right and you cannot argue with me. (end of student’s math paper)
*NASCAR is the lazy version of track.
*It makes me feel smart. (student talking about Sigma notation)
Student 2: It makes me feel like an alien.
Wednesday, May 25, 2011
Tunes, part tres
For my algebra class, the students had to create a song that covered a topic from the current school year. Here is the last example. Enjoy!
Graphing
Song: Friday
Seven a.m., going to math class
Gotta be smart, gotta go to school
Gotta know how to graph, gotta get a pencil
Graphin’ everything, the pencil’s always moving
Tickin' on and on, everybody's workin'
Gotta get y by itself
Gotta draw my lines, I see my answer, my answer
B is the y-intercept
M is the slope
Y is the answer
This is so easy
It's Graphing, Graphing
Gotta get down on graphing
y=mx+b, bbbbb
Graphing, Graphing
Gotta know graphin’
Y=mx+b, bbbb
Graphin' and, graphin' (Yeah)
Graphin' and, graphin' (Yeah)
Math, math, math, math
Lookin' forward to the solution
2:37, we're getting out of class
Knowin’ so much, I can do my homework
Math, Math, thinkin’ about math
You know what it is
I got this, you got this
My calculator is by my right
I got this, you got this
Now you know it
B is the y-intercept
M is the slope
Y is the answer
This is so easy
It's Graphing, graphing
Gotta get down on graphing
Y=mx+b, bbbb
Graphin, graphin
Getting down on graphing
Y=mx+b, bbbb
Graphing
Song: Friday
Seven a.m., going to math class
Gotta be smart, gotta go to school
Gotta know how to graph, gotta get a pencil
Graphin’ everything, the pencil’s always moving
Tickin' on and on, everybody's workin'
Gotta get y by itself
Gotta draw my lines, I see my answer, my answer
B is the y-intercept
M is the slope
Y is the answer
This is so easy
It's Graphing, Graphing
Gotta get down on graphing
y=mx+b, bbbbb
Graphing, Graphing
Gotta know graphin’
Y=mx+b, bbbb
Graphin' and, graphin' (Yeah)
Graphin' and, graphin' (Yeah)
Math, math, math, math
Lookin' forward to the solution
2:37, we're getting out of class
Knowin’ so much, I can do my homework
Math, Math, thinkin’ about math
You know what it is
I got this, you got this
My calculator is by my right
I got this, you got this
Now you know it
B is the y-intercept
M is the slope
Y is the answer
This is so easy
It's Graphing, graphing
Gotta get down on graphing
Y=mx+b, bbbb
Graphin, graphin
Getting down on graphing
Y=mx+b, bbbb
Tunes, part deux
For my algebra class, the students had to create a song that covered a topic from the current school year. Here is example two of three. Enjoy!
Exponent Rules
Song: Black and Yellow
CHORUS
Yea uh-huh you know what it is
Mathematician, mathematician, mathematician
Every time I multiply, I add
Mathematician, mathematician, mathematician
Yea uh-huh you know what it is
Mathematician, mathematician, mathematician
Every time I divide, I subtract
Mathematician, mathematician, mathematician
When you times, you gotta remember to add
Mathematician, mathematician, mathematician
When you divide, always remember to subtract
Mathematician, mathematician, mathematician
VERSES
Exponent rules, always crazy
Use all forms, don’t get lazy
Add when multiplying, subtract when dividing
If you don’t get it, keep trying
It’s not hard to be learnin’
Just get that brain juice burnin’
Remember what term goes with what
So you won’t be confused and stuck.
CHORUS
Yea uh-huh you know what it is
Mathematician, mathematician, mathematician
Every time I multiply, I add
Mathematician, mathematician, mathematician
Yea uh-huh you know what it is
Mathematician, mathematician, mathematician
Every time I divide, I subtract
Mathematician, mathematician, mathematician
When you times, you gotta remember to add
Mathematician, mathematician, mathematician
When you divide, always remember to subtract
Mathematician, mathematician, mathematician
Exponent Rules
Song: Black and Yellow
CHORUS
Yea uh-huh you know what it is
Mathematician, mathematician, mathematician
Every time I multiply, I add
Mathematician, mathematician, mathematician
Yea uh-huh you know what it is
Mathematician, mathematician, mathematician
Every time I divide, I subtract
Mathematician, mathematician, mathematician
When you times, you gotta remember to add
Mathematician, mathematician, mathematician
When you divide, always remember to subtract
Mathematician, mathematician, mathematician
VERSES
Exponent rules, always crazy
Use all forms, don’t get lazy
Add when multiplying, subtract when dividing
If you don’t get it, keep trying
It’s not hard to be learnin’
Just get that brain juice burnin’
Remember what term goes with what
So you won’t be confused and stuck.
CHORUS
Yea uh-huh you know what it is
Mathematician, mathematician, mathematician
Every time I multiply, I add
Mathematician, mathematician, mathematician
Yea uh-huh you know what it is
Mathematician, mathematician, mathematician
Every time I divide, I subtract
Mathematician, mathematician, mathematician
When you times, you gotta remember to add
Mathematician, mathematician, mathematician
When you divide, always remember to subtract
Mathematician, mathematician, mathematician
Tunes
For my algebra class, the students had to create a song that covered a topic from the current school year. Here is one example. Enjoy!
Equation of a line
Song: Forget You
Song 1:
I’m getting kinda frustrated with y=mx+b and I’m like forget you
Ms. Pettit’s helping me out but still I’m kinda confused and I’m like
Forget you and forget math too
I said if I wasn’t smarta this’d be a lot harda
Ha, now aint that some shhhh
But I need to get my homework done even though it’s no fun
So I’m like forget you
So, m’s the slope
Now isn’t that just dope
As for b, it’s the y-intercept
But I didn’t know
Straight’s the only way to go
Between two points, that is
I pity the fool who doesn’t know these rules
Oh
Well
Ooooh, I’ve got some help for you
Yeah, go tell all your little friends
Chorus:
I’m getting kinda frustrated with y=mx+b and I’m like forget you
Ms. Pettit’s helping me out but still I’m kinda confused and I’m like
Forget you and forget math too
I said if I wasn’t smarta this’d be a lot harda
Ha, now aint that some shhhh
But I need to get my homework done even though it’s no fun
So I’m like forget you
Line 2:
So before you go solo
Make sure that you know
To put rise over run
Another piece of info
Is it’s gotta be in slope
Intercept form to work
I pity the fool who doesn’t know these rules
Oh
Well
Oooh, I’ve got some news for you
I’m a graphing beast now
Equation of a line
Song: Forget You
Song 1:
I’m getting kinda frustrated with y=mx+b and I’m like forget you
Ms. Pettit’s helping me out but still I’m kinda confused and I’m like
Forget you and forget math too
I said if I wasn’t smarta this’d be a lot harda
Ha, now aint that some shhhh
But I need to get my homework done even though it’s no fun
So I’m like forget you
So, m’s the slope
Now isn’t that just dope
As for b, it’s the y-intercept
But I didn’t know
Straight’s the only way to go
Between two points, that is
I pity the fool who doesn’t know these rules
Oh
Well
Ooooh, I’ve got some help for you
Yeah, go tell all your little friends
Chorus:
I’m getting kinda frustrated with y=mx+b and I’m like forget you
Ms. Pettit’s helping me out but still I’m kinda confused and I’m like
Forget you and forget math too
I said if I wasn’t smarta this’d be a lot harda
Ha, now aint that some shhhh
But I need to get my homework done even though it’s no fun
So I’m like forget you
Line 2:
So before you go solo
Make sure that you know
To put rise over run
Another piece of info
Is it’s gotta be in slope
Intercept form to work
I pity the fool who doesn’t know these rules
Oh
Well
Oooh, I’ve got some news for you
I’m a graphing beast now
Saturday, January 29, 2011
Investigations (not wasted days)
My classes have been doing investigations (or will be doing investigations) based on ideas we have come across in the world outside the mathematics classroom. We haven't analyzed the data yet so I have no idea what it will show. I used to fear that these would be "wasted" days in the math classroom. Now I want to have more of these days. Why? I want my students to read/see something and ask questions.
"Is this true?"
"Could we prove it?"
"What would happen if...?"
My students aren't independently there yet, but I hope I can guide them there.
Current investigation 1: We looked at the Noah basketball website http://www.noahbasketball.com/optimal_arc.php
and the press it is getting http://www.youtube.com/watch?v=2FEmBY-n71Y to set up an investigation in advanced mathematics. We used flip cameras(?) to videotape students shooting 10-20 shots. We shot from the free-throw line, three-point line, and half court. Next week we will analyze the data to see if it fits the Noah site and discuss why our results match/don't match as well as drawbacks in our data collection.
Upcoming investigation 2: The math and physics involved in sledding. I need to collaborate with the physics teacher to get some equations so we know what data to collect. Now hopefully we get a fresh batch of snow soon. (It's Iowa so I'm sure I won't have to wait too long.)
I also hope to fit quadratic models into this investigation as well. Snowballs will need to be used...Oh boy, I think this will test my classroom management strategies, but I can't wait!
"Is this true?"
"Could we prove it?"
"What would happen if...?"
My students aren't independently there yet, but I hope I can guide them there.
Current investigation 1: We looked at the Noah basketball website http://www.noahbasketball.com/optimal_arc.php
and the press it is getting http://www.youtube.com/watch?v=2FEmBY-n71Y to set up an investigation in advanced mathematics. We used flip cameras(?) to videotape students shooting 10-20 shots. We shot from the free-throw line, three-point line, and half court. Next week we will analyze the data to see if it fits the Noah site and discuss why our results match/don't match as well as drawbacks in our data collection.
Upcoming investigation 2: The math and physics involved in sledding. I need to collaborate with the physics teacher to get some equations so we know what data to collect. Now hopefully we get a fresh batch of snow soon. (It's Iowa so I'm sure I won't have to wait too long.)
I also hope to fit quadratic models into this investigation as well. Snowballs will need to be used...Oh boy, I think this will test my classroom management strategies, but I can't wait!
Monday, January 10, 2011
My favorite math lesson
So I guess it's time to start fulfilling my "New Year's Resolution." We'll see how long it lasts. :) Basically, I want to post a weekly blog about something that is happening in my classroom. If you are a new reader, please understand that this blog was previously my location for describing my missionary experiences in West Africa and then a place to post ramblings as I transitioned back into American culture.
Enjoy :)
The Sine Function
Here is my favorite math lesson to teach and I get to cover it at VM next week! It's over the sine function and how it is created from the unit circle values. I love hands-on activities, and I had that "Aha" moment when I completed the activity the first time.
(Note: This was adopted from an NCTM article that appeared many years ago. They used cooked spaghetti. Perhaps someone has the original article and can share the link with everyone!)
Supplies: Bulletin board paper (a large piece) and pull-n-peel licorice
My preparation beforehand:
Take a large piece of bulletin board paper and draw a large set of axes. Then make a circle with the radius equal to the length of one-pull-n-peel licorice strand. Create a unit circle marking the standard points. (I usually have my students fill in the point values and the radian measurement.)
Introduce lesson by asking them how we graph functions
1. Explain sine, cosine etc are functions. Ask them why we can’t call it a function on the circle.
2. Explain to the students how the circle was made.
3. Complete the following in groups.
Pull-n-peel Trigonometry
1. For the marked points, label the angles on the circle. (Use radians)
2. Place the string along the circle with one end at 0 radians and transfer the radian marks from the circle to the string.
3. Stretch the string along the line and transfer the marks on the string to the line. The end of the string that was at 0 radians on the circle must be placed at the beginning of the line. Label all the new points with the radian measures.
4. Use the pull-n-peel (pnp) to form a right triangle on the circle. (Pretend we are using pnp instead of drawing all the triangles.)
5. Move the piece of pnp that is the vertical leg of the triangle to the line and place it perpendicular to the line at the appropriate radian measure.
6. Now make a dot on the paper at the top of the piece of pnp to show the length of the vertical leg of the right triangle.
7. Do this for all the points.
a. Remember to think about values on the axes as well as what the triangles would look like in the 3rd and 4th quadrant.
b. Also, think about all the triangles and whether you need to construct them all.
8. Show Miss Pettit what your new graph looks like. Then connect all the points.
Questions:
1. What does the graph look like? Why?
2. What would the graph look like if you used the horizontal legs of the triangle instead of the vertical ones? How do you know?
3. What concept did you use to create the scale on the x-axis?
4. What would happen if we wanted to continue the graph. What value would be at 5π/2?
At -π/2? How do you know?
5. Explain why you really only needed to make 3-6 triangles instead of 14-17.
6. Explain how the sine function is created. Be specific. It is important that you know this.
Enjoy :)
The Sine Function
Here is my favorite math lesson to teach and I get to cover it at VM next week! It's over the sine function and how it is created from the unit circle values. I love hands-on activities, and I had that "Aha" moment when I completed the activity the first time.
(Note: This was adopted from an NCTM article that appeared many years ago. They used cooked spaghetti. Perhaps someone has the original article and can share the link with everyone!)
Supplies: Bulletin board paper (a large piece) and pull-n-peel licorice
My preparation beforehand:
Take a large piece of bulletin board paper and draw a large set of axes. Then make a circle with the radius equal to the length of one-pull-n-peel licorice strand. Create a unit circle marking the standard points. (I usually have my students fill in the point values and the radian measurement.)
Introduce lesson by asking them how we graph functions
1. Explain sine, cosine etc are functions. Ask them why we can’t call it a function on the circle.
2. Explain to the students how the circle was made.
3. Complete the following in groups.
Pull-n-peel Trigonometry
1. For the marked points, label the angles on the circle. (Use radians)
2. Place the string along the circle with one end at 0 radians and transfer the radian marks from the circle to the string.
3. Stretch the string along the line and transfer the marks on the string to the line. The end of the string that was at 0 radians on the circle must be placed at the beginning of the line. Label all the new points with the radian measures.
4. Use the pull-n-peel (pnp) to form a right triangle on the circle. (Pretend we are using pnp instead of drawing all the triangles.)
5. Move the piece of pnp that is the vertical leg of the triangle to the line and place it perpendicular to the line at the appropriate radian measure.
6. Now make a dot on the paper at the top of the piece of pnp to show the length of the vertical leg of the right triangle.
7. Do this for all the points.
a. Remember to think about values on the axes as well as what the triangles would look like in the 3rd and 4th quadrant.
b. Also, think about all the triangles and whether you need to construct them all.
8. Show Miss Pettit what your new graph looks like. Then connect all the points.
Questions:
1. What does the graph look like? Why?
2. What would the graph look like if you used the horizontal legs of the triangle instead of the vertical ones? How do you know?
3. What concept did you use to create the scale on the x-axis?
4. What would happen if we wanted to continue the graph. What value would be at 5π/2?
At -π/2? How do you know?
5. Explain why you really only needed to make 3-6 triangles instead of 14-17.
6. Explain how the sine function is created. Be specific. It is important that you know this.
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