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: mpatter1@cc.swarthmore.edu

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.