Fourth Grade Grab Bag
Date: Mon, Nov 7, 1994 6:02 PM From: "Gary Stephen Quiring" Subject: Re: Ask Dr. Math: on-line math problem solvers Dr. Math, Here are some questions from my 4th grade class. For your information, these students are all designated as Limited English Proficient and are currently reading at the 1st to 3rd grade level. 1. Do you need to study a lot of math to be a scientist? (Houa) 2. What does it mean when you multiply two numbers together? (Nidia) 3. How would you measure the distance around the moon? (Lorena) 4. What was Albert Einstein's greatest contribution to mathematics? (Miguel) 5. Who first made up math? (Maikau) 6. My teacher says you can't divide a number by zero. Why? (Gary) 7. Where do centimeters come from? (Sandy) We hope our questions are not too hard. Mr. Stiffler's Class Gary Quiring Technology Resource Teacher for Susan B. Anthony Elementary, FUSD
Date: Tue, 8 Nov 1994 09:50:49 +0900 X-Sender: firstname.lastname@example.org Hi everyone- These are great questions. All of us Math Doctors have been thinking about them, and are really glad that you wrote to us. We haven't answered all of them yet, but here is what we have. We will definitely write back to you with the rest. >Dr. Math, > >1. Do you need to study a lot of math to be a scientist? (Houa) Well, this is a tough question. It depends on what kind of scientist you want to be. To be a mathematician, you certainly need to study of a lot of math. For other kinds of sciences, math is important too, but I think this is a good thing. Math is a lot of fun, and you can use it to help learn other things, like physics and chemistry, but also things which you might not think of as sciences, like political science, economics, and philosophy. Have you heard of _Alice in Wonderland_? Lewis Carrol is the author of that book. It is a great story, and there is a lot of math and philosophy (called logic) in the story. Ask your teacher to find this book for you, and tell us what you think of it. -Margaret >2. What does it mean when you multiply two numbers together? (Nidia) Nidia, multiplying two numbers is just like adding them a bunch of times. What if we want to know what 2+2+2+2 equals. Well, we can add them and get 8. That doesn't take too long, but what if we want to add 15 two's together. That might take longer, so we write it like this: 2 x 15. (To say this out loud, you say, two times fifteen.) This is multiplication. Once you practice the smaller numbers, like 2 x 4 = 8, then you can move on to bigger numbers and it is easy to see that 2 x 15 = 30. -Margaret >3. How would you measure the distance around the moon? (Lorena) Lorena- What a good question! We will have to think a little bit more about this one. Do you have any ideas? -Margaret > >4. What was Albert Einstein's greatest contribution to mathematics? (Miguel) Miguel- I don't know the answer to this one. Einstein's most famous work is called the General Theory of Relativity and it certainly has a lot to do with math, but people usually think of it as being physics. I hope another math doctor has some ideas on this one. We'll get back to you. -Margaret > >5. Who first made up math? (Maikau) Maikau, Math has been around for a long time. The problem with asking "who first made up math" is that there are lots of kinds of math! There is the adding and subtracting math, there is geometry, and many other kinds of math that would be very hard to explain to you right now. Basic math began with counting things and adding things. If a man had one dog and added another dog, he would have two dogs. But in the beginning, this wasn't always obvious that two dogs was the same things as two cows. When people began to realize that any two things was the same number as any other two things, math was born. Then people began learning about other numbers. There were many different ways to count. We count only using the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, but other groups of people used different symbols for their numbers. Gary asked why you couldn't divide a number by zero. In fact, zero wasn't invented until a long time after people began counting things. But when zero was created, it made math a lot easier and created other problems like trying to divide numbers by zero. After counting came adding and subtracting numbers. Since then, math has continued to have more and more things in it. There is a lot to math and one person can't possibly understand all of it! But that is why it's so fun. -- Melissa > >6. My teacher says you can't divide a number by zero. Why? (Gary) Gary- Let's look at some examples of dividing other numbers. 10 -- = 5 This means that if you had ten blocks, you could separate them into five 2 groups of two. 9 -- = 3 This means that if you had nine blocks, you could separate them into 3 three groups of three 5 -- = 5 Five blocks could be separated into five groups of one 1 5 -- = ? How many groups of zero could you separate five blocks? 0 It doesn't matter how many groups of zero you have, because they would never add up to five since 0+0+0+0+0+0=0. you could even have one million groups of zero blocks, and they would still add up to zero. So, it doesn't make sense to divide by zero since there is not a good answer. If you know a little bit about mulitplication, then you could look at it this way: 10 -- = 5 This means that 5 x 2 = 10 2 9 -- = 3 This means that 3 x 3 = 9 3 5 -- = 5 This means that 5 x 1 = 5 1 5 -- = ? This would mean that the answer x 0 = 5, but anything times 0 is always 0 zero. So there isn't an answer. I hope this makes sense. Let us know if you don't understand. >7. Where do centimeters come from? (Sandy) Sandy, Do you know what a meter is? A meter is a certain length that never changes. Since it never changes, we can use it to measure the length of other things, and when we say the length, like "this table is 3 meters long," then everyone else will know what we mean. A meter is little bit longer than three feet. A centimeter is smaller than a meter. In fact 100 centimeters is the same as one meter. When this is true, we say that a centimeter is one hundredth of one meter. The first part of the word, centi, means 100. You can add other words to meter to mean different lengths, but they always are in comparison to one meter. So, a millimeter is even smaller than a centimeter, because there are 1000 millimeters in a meter. Can you figure out how many millimeters are in a centimeter? In almost every other country in the world, they use this type of measurement. It is called the metric system. In the United States, we still use an older system that uses inches, feet, yards, and miles. There are 12 inches in a foot and three feet in a yard and a little over 1,700 yards in a mile. All of these numbers can be hard to remember. With the metric system, everything is in terms of ten. There are ten millimeters in a centimeter, ten centimeters in a decimeter, ten decimeters in a meter, etc. Maybe your teacher can show you some ways to use the metric system. -Margaret >We hope our questions are not too hard. They are great questions and we are glad to answer them. We would love to hear what you think about our answers. Please tell us if you don't understand them.
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