Mother: We're going to drive you there.Daughter: I can fly.
M: I know. But we want to drive you. Time for us to talk. I like that they want the freshman and sophomores to live on campus.D: We'll see.
Me: (I tell them about Tastea and how I wish it were closer.) Okay, let's start with something you might be more familiar with, Starbucks. I love that now I live within walking distance from one! Do you know the different sizes that they have there?Class: (When I refer to "class," I don't mean the whole class, of course, but somebody in the class joins in on the conversation.) Tall, grande, venti.M: Do you know exactly how much liquid each size holds? (They make various guesses. I bring out the 3 sizes that I got from Starbucks so they have a visual.) I normally order a tall mocha frappuccino, let's say the price is $3.50. Do you think the venti, which is twice the volume of the tall, would cost twice as much, or $7.00?C: No.M: Why not?C: You normally get a better deal with a bigger size.M: What do you mean by a "better deal"?C: (All their answers show me that they understand the idea of more bang for your buck. Then finally someone says...) Lowest unit price!M: Right! That's why so many families go to Costco. Buying in bulk normally saves us money because the item has the best unit price. Well, we're talking about Starbucks now, so buying more is a better deal, but drinking more is not so good for our body. Let's fill in this sheet. (I pass out this 2-page worksheet.) How do we calculate unit price? What place value should we round it to? How do you write thirty-one-cents-per-ounce?
M: Tastea has three sizes: mini, gigantic, and even more. Their teas can also be purchased by the "partea jug," which holds a gallon. I've given you the prices of the 10-ounce minis for the three different types of drinks, your job is to figure out the prices of the other sizes. You'll work in small groups to figure out these out. So, do you think the gigantic will cost twice as much as the mini because it holds twice as much?C: No. It'll cost less.M: How much less? Well, that's your group's job to come up with the best estimate. We have Starbucks' prices for their three sizes, you could look at how they price their drinks. But here's the sweet deal for you. You and your group mates do the math that you need to, then write down your first estimation right here in this column. Bring your paper up to me (only the "captain's" paper), give me a few seconds to figure out the percentage that your estimation is off by, and I'll write it in this column and give you back your paper. What percent do you want to see, large or small? What if your estimation were the actual price — what percent would I write there?
I learned how to work backwards with percentages and try to get the number spot on. I also learned how business would price things by dropping the price by the perfect amount. My number sense got a lot better from all the multiplying, dividing, and reasoning. It was very difficult, which I'm very happy about.The teamwork was probably the hardest part of the project. M and I are very competitive, and we got different answers a lot. I learned how to work together with others a lot better, and it doesn't move your team along to place blame and argue. I'm really grateful we did this project because it was very hard and worthwhile. It was a great use of three days!***I learned how to use different data to get answers. Also, we have to see a pattern. This Tastea assignment was really fun. I enjoyed it and look forward to another. Teamwork is really important even though people can't agree, you got to support it. If your group gets it wrong, but your answer was right, you can't blame someone or put them down because probably they will get some right for you. So always stay positive to your teammates and encourage them.
Version A: 18 likes, 14 dislikes
Version B: 18 likes, 14 dislikes
Version C: 15 likes, 17 dislikes
LIKES: (see above)
DISLIKES: Not understanding the question, or "I'm a visual learner, so I like Version B better."
LIKES: It's visual. It's easy.
DISLIKES: Too fast and hard to follow. One student, "The movement is distracting and confusing. I feel like it's too abrasive and violent. Math should be more elegant than this."
LIKES: You just count the number of candies. It's visual.
DISLIKES: Too fast to follow. It seems too easy. There's space between the candies. One student, "You can't get the exact answer... And the leftover space in one shape may be more than the leftover space in the other."
I collect all their papers before telling them which version I like. I like Version A for its simplicity. I'm curious if the stated question is enough information for them to understand. This student's reason nails it for me: "It allows me to think the way I want to and not be misled by a moving picture."
So, one from the kids.This [Version C] is the most "real-world" solely because of the fact that it involves a material object which in this case is the candy. However, the thing you're solving for in this question is not very "real-world" at all. Personally, I don't care at all if a problem is "real-world" or not; I just like to solve problems.
If a problem didn't have to do with "real-world" I will still do it if I like it. It doesn't really matter.
I don't think any of these problems are "real world" math problems. I like how they make me think. But I don't think I need them in the "real world."
I wouldn't care if it is a real-world problem because I was there to learn. I think all versions can be a real-world problem because it can be needed in some situations.I feel like all of these problems are real world... But honestly it doesn't matter at all to me. It doesn't matter if it's real world or not, it doesn't affect me wanting to solve the problem.
Me: What is the distance between these two points?Class: Eight.M: How did you get eight?C: Subtract.M: What about this one? The points are at -3 and 9.
C: The distance is twelve.M: This one?C: Thirty-two.M: Good. Distance is always positive... How did you find the distance between the points again? What operation did you use?
C: Subtraction!M: Then I'm going to add an equation below each number line showing subtraction. Is that okay?M: So, the distance between 5 and 13 is 8. Then, what is the distance between 13 and 5?C: EightM: Woah! It's the same? Meaning I can write the equation either way?
Me: Given two points, you can tell me the distance between them. So now I’m going to give you just one of the two points but tell you the distance between them, and you find the missing point x.
C: x is ten.
M: Yea, ten works. Let's try to read this open sentence. How would you say it?
C: x minus six... The absolute value of x minus six is four.
M: Hmmm. Oh, you say the words 'absolute value' because they're there. Let's try again without saying those words. Use the word 'distance' instead.
C: The distance of x minus six equals four.
M: Let me show you again the first one that I'd asked you. I remember just asking you, 'What is the distance between 5 and 13?' What did I not say even though it's there?
M: Right. Let's not add stuff we don't need. You know naturally that finding distance implies subtraction. So, say the equation again.
C: The distance between x and six is four.
M: Or you could say...? Can we switch the points around?
C: The distance between six and some point x is four.
M: Alright. Is 10 the only answer for x? We are trying to find a point on the line that makes the equation true. So, let's use the number line to solve this. Because we know 6 is one of the points, let's locate it. We need to find the other point that would be a distance of 4 away from 6. So, it could be to the right of 6, or to the left of 6. Where does this put us at?
M: Oh, why isn't the point -6? I see a 'minus six' in the equation.
C: Remember, that minus is for subtracting. We need it there to find distance.
M: I remember. We need it.
We do a few more of these. Enough to bore us, need something new.
M: Let's try this.C: No subtraction sign.M: And you said we needed it. Then create it. Make it happen without changing the problem of course.C: Change it to minus minus...
We do a few more of these. Enough to bore us, need something new again.M: What does this problem say now?C: The distance between x and negative eight equals five.
Then we do a batch of these:M: What about this?M: Nothing terribly exciting. The other point(s) that we find is now worth 2x, so we just need to solve for x.
When you don't memorize theorems you don't know what to write in
When you don't know what to write in your proofs you fail your geometry class
When you fail your geometry class you lose all your confidence
When you lose all your confidence you decide to work at a dead-end job
When you decide to work at a dead-end job you get hired to become a low-budget amusement park mascot
And when you get hired to become a low-budget amusement park mascot you get tackled by an immature middle aged man
So don't get tackled by an immature middle aged man, get your theorems memorized and upgrade to a math tutor
When you get straight A's people call you a genius
When you get called a genius you work to make yourself a genius
When you work to make yourself a genius you become the next Albert Einstein
When you become the next Albert Einstein you make theories
When you make theories you want to test Einstein's theories
And when you want to test Einstein's theories you get sucked into a black hole
So don't get sucked into a black hole, ignore people who call you a genius and upgrade to a critic
When you don't do your math homework you don't understand the
When you don't understand the subject you fail the class
When you fail the class you flunk the grade
When you flunk the grade you feel depressed
When you feel depressed you continue to flunk
And when you continue to flunk you become a twenty-five year old man in a fourth-grade class
So don't become a twenty-five year old man in a fourth-grade class, do your homework and upgrade to the next grade level
When you say math isn't your forte Mrs Nguyen gets mad
When Mrs Nguyen gets mad she yells at you
When she yells at you you feel like a loser
When you feel like a loser you don't succeed in life
When you don't succeed in life you can't get a job
And when you can't get a job you work on a smelly old fishing boat
So don't work on a smelly old fishing boat, get rid of saying math isn't your forte and upgrade to loving math
First of all, the equations are coming so much easier to me! I think what helped me is opening up my mind to other methods, and trying out methods that I've seen other people use. I feel that the reason I have trouble with some problems is that in my mind, I make the problem seem so much harder than it actually is. After doing them week after week, everything is coming to me a lot easier than they used to.This week I have learned a lot. I've learned new methods of solving problems and reviewed old ones too. Math Talks have helped me a lot in homework and class work too. God I'm brilliant.
So I have a lot to reflect on because there were a lot of Math Talks. I really liked the shopping problem because, you know, I'm a girl, and I like shopping. Sometimes I don't get anything about a problem or pattern at all, then someone explains it really well and I get it. And I think, "Why didn't I see that?" That happens to me a lot.The next time I think I could think a bit more because this time, now I thought I should have thought about it a little more, seeing all the other people's answers got me to think that I should have done better. Yesterday I wish I raised my hand before some other people because I had it up and other people were saying the same thing as me.To improve I could get more time and after talking to Mrs Nguyen I understand more when she explains it better. The thing I found most difficult is problem solving & solve the patterns because it is hard to finish up mentally.After talking to others it always makes more sense and they help. To improve I could get here earlier.I think I'm getting stronger each day doing mental math and patterns. My favorite math talk this week was the pattern on 2-26-14, I thought it was clever because towards the end it wasn't the rule, it was your rule.I really loved the math talk on last week's Friday. It was the buy one get one free or get 45% off. Because after you told us the answer and it could go either way, I thought to myself like how didn't I figure that out. So there's no right or wrong to the question.I thought the guess-and-check that Cristian did was very helpful and it really helped me learned the strategy.This week of math talks was very fun. I like the problem solving puzzles and equations. After talking to Skylar, she helped me understand the problems more.This week I had better understanding with math talks. The one that really helped me was Janae's; it was different and extravagant.My favorite day this week was "would you rather get 45% off everything or buy one get one free." Although it was simple, it was fun to share our different opinions.One of this week's math talks equation that really helped me understand was Seth's equation from Thursday. It was when you divide money but you ignore the decimal and add it in later. This one helped me a lot.On 2/21/14 math talk I did not get it at all, then when Diego explained how you were supposed to do it, I got it and that was good.I am going to use different kinds of math strategies that everyone was using because some of the strategies help me solve a problem faster....
I feel like geometry is more of a puzzle rather than a chore. Having to find ways of proving something seems more like fun than a class. Learning about shapes and things I thought to be impossible are really cool. I can't wait for what amazing discoveries I'll learn next. [Grade 8]
You've really inspired me and now (more than ever) I want to be a teacher. [Grade 6]
Vice-Principal: Fawn, there was one thing in particular that your former vice-principal had shared about you that stuck with me.Me: Yeah?VP: He said, She was the only teacher who could get our eighth graders to walk perfectly in a straight line and quietly from her room to the gym. How did you do that?M: I just asked them to.VP: You just asked them?M: I mean they know what quiet means and what a straight line is. I told them that we needed to show respect to the other teachers and their students when we pass by their classrooms. We show this respect by walking quietly and orderly so we don't disrupt them.VP: How long did it take to get them to do that?M: First time. Well, we simply didn't move unless they were all quiet and in straight line! I saw pride in them as they walked. At least one teacher would happen to watch them go by and complimented them. When we got back to our room, I always thanked them and told them they made me proud.
I did my best, praying Cranky would approve.Cranky person (comes up from behind me): You! Drop and give me a diagram of this sentence or I'll blow your head off!Me (arms raised in the air to show my English teacher had prepared me for this): Ummm... What's the sentence?Cranky: Try this one, The bored students were considering shooting spit wads.M: May I borrow a pen?C: Will a pencil do?M: That's even better. I might make a mistake.
C: Very nice.M: Oh, thank you very much! My handwriting is normally much better though... Arms are still sore from yesterday's bear crawls that I had to show another assailant.
You don't hate math. You can't. Everything that you love requires math. You must mean you hate school math. And that I believe; and I'm working hard to change your mind. In Edward Frenkel's Love and Math: The Heart of Hidden Reality, he writes:I sometimes think that the best way to change the public attitude to math would be to stick a red label on everything that uses mathematics. "Math inside." There would be a label on every computer... on every airline ticket, every telephone, every car, every airplane, every traffic light, every vegetable...You go to the movies? Do you like the special effects? Star Wars, Lord of the Rings? Mathematics. The first full-length computer-animated movie, Toy Story, led to the publication of about twenty research papers on math...If anything makes use of math, it's the Internet. The main search engine at the moment, Google, was founded on a mathematical method... It's based on matrix algebra, probability theory, and the combinatorics of networks.Modern communications systems simply would not work without a huge quantity of math. Coding theory, Fourier analysis, signal processing...
I want to tell you about all this to expose the sides of mathematics we rarely get to see: inspiration, profound ideas, startling revelations. Mathematics is a way to break the barriers of the conventional, an expression of unbounded imagination in search for truth.Mathematics is as much a part of our cultural heritage as art, literature, and music. As humans, we have a hunger to discover something new, reach new meaning, understand better the universe and our place in it.There is a common fallacy that one has to study mathematics for years to appreciate it. Some people think that most people have an innate learning disability when it comes to math.One of my teachers, the great Israel Gelfand, used to say, "People think they don't understand math, but it's all about how you explain it to them. If you ask a drunkard what number is larger, 2/3 or 3/5, he won't be able to tell you. But if you rephrase the question: what is better, 2 bottles of vodka for 3 people or 3 bottles of vodka for 5 people, he will tell you right away: 2 bottles for 3 people, of course."