Are you smarter than a 5th grader?

[Bret Taylor-2]

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I'm not.  I missed a math question a week or two ago.  The question went something like this:

 

If the denominator of a unit fraction is 5, what is the numerator?

 

I've got a Masters degree in math.  I have taught high school math and community college math most of my adult life.  I have taught college math from developmental (Arithmetic and Pre-Algebgra - two courses) through calculus.  I have also taught Math for Elementary School teachers for several years.  And, I don't think I have ever heard of the term "unit fraction."  I picked what I thought was the only logical answer - 5.  (5/5 = 1, unity.  Or so when my logic.)  And, I was wrong.  I was so shocked that I googled "unit fraction" and found out that I might be the only math teacher in the world who has never heard of a "unit fraction."

 

Is there anybody on this list who has also never heard of a unit fraction?

 

 

Bret Taylor
Eustis, FL

 

John 3:30

[Fred Siegeltuch]

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Bret,

Wouldn't this make a great question to ask on a national teacher's exam? It is easy to ask and grade, and there would probably be a good distribution of scores. We just shouldn't let it worry us if it has virtually nothing to do with competence in doing or teaching math. But seriously, it does make one think about how we often overburden students with non-essential terminology.

Fred Siegeltuch

--- On Thu, 5/1/08, Bret Taylor <bret.taylor@...> wrote:

From: Bret Taylor <bret.taylor@...>
Subject: Are you smarter than a 5th grader?
To: mathedcc@...
Date: Thursday, May 1, 2008, 7:13 PM

I'm not.  I missed a math question a week or two ago.  The question went something like this:

 

If the denominator of a unit fraction is 5, what is the numerator?

 

I've got a Masters degree in math.  I have taught high school math and community college math most of my adult life.  I have taught college math from developmental (Arithmetic and Pre-Algebgra - two courses) through calculus.  I have also taught Math for Elementary School teachers for several years.  And, I don't think I have ever heard of the term "unit fraction."  I picked what I thought was the only logical answer - 5.  (5/5 = 1, unity.  Or so when my logic.)  And, I was wrong.  I was so shocked that I googled "unit fraction" and found out that I might be the only math teacher in the world who has never heard of a "unit fraction."

 

Is there anybody on this list who has also never heard of a unit fraction?

 

 

Bret Taylor
Eustis, FL

 

John 3:30

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[broomell]

I was watching that show when the question was asked and my initial thought was 5/5, but then I remembered a unit that I taught years ago about "Egyptian Fractions."  It became a challenge for my students (an me) to express fractions as the sum of unique unit fractions.  A colleague had an algorithm that worked to find the sum, but I cannot remember it because I have not used it in so long. 
Bev Broomell
Suffolk County Community College
Selden, NY 11784

----- Original Message -----
From: Bret Taylor
Date: Thursday, May 1, 2008 8:17 pm
Subject: Are you smarter than a 5th grader?
To: mathedcc@...

> I'm not. I missed a math question a week or two ago. The
> question went something like this:
>
> If the denominator of a unit fraction is 5, what is the numerator?
>
> I've got a Masters degree in math. I have taught high school
> math and community college math most of my adult life. I have
> taught college math from developmental (Arithmetic and Pre-
> Algebgra - two courses) through calculus. I have also taught
> Math for Elementary School teachers for several years. And, I
> don't think I have ever heard of the term "unit fraction." I
> picked what I thought was the only logical answer - 5. (5/5 =
> 1, unity. Or so when my logic.) And, I was wrong. I was so
> shocked that I googled "unit fraction" and found out that I
> might be the only math teacher in the world who has never heard
> of a "unit fraction."
>
> Is there anybody on this list who has also never heard of a unit
> fraction?
>
>
> Bret Taylor
> Eustis, FL
>
> John 3:30
>

[Jodi Cotten]

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I'm with Bev - I remembered seeing the name and learning some where - it was my 300 level math history course. Have not used it or seen it since, until today.

----- Original Message -----

From: broomell@...

To: bret.taylor@...

Cc: mathedcc@...

Sent: Thursday, May 01, 2008 10:12 PM

Subject: Re: Are you smarter than a 5th grader?

I was watching that show when the question was asked and my initial thought was 5/5, but then I remembered a unit that I taught years ago about "Egyptian Fractions."  It became a challenge for my students (an me) to express fractions as the sum of unique unit fractions.  A colleague had an algorithm that worked to find the sum, but I cannot remember it because I have not used it in so long. 
Bev Broomell
Suffolk County Community College
Selden, NY 11784

----- Original Message -----
From: Bret Taylor
Date: Thursday, May 1, 2008 8:17 pm
Subject: Are you smarter than a 5th grader?
To: mathedcc@...

> I'm not. I missed a math question a week or two ago. The
> question went something like this:
>
> If the denominator of a unit fraction is 5, what is the numerator?
>
> I've got a Masters degree in math. I have taught high school
> math and community college math most of my adult life. I have
> taught college math from developmental (Arithmetic and Pre-
> Algebgra - two courses) through calculus. I have also taught
> Math for Elementary School teachers for several years. And, I
> don't think I have ever heard of the term "unit fraction." I
> picked what I thought was the only logical answer - 5. (5/5 =
> 1, unity. Or so when my logic.) And, I was wrong. I was so
> shocked that I googled "unit fraction" and found out that I
> might be the only math teacher in the world who has never heard
> of a "unit fraction."
>
> Is there anybody on this list who has also never heard of a unit
> fraction?
>
>
> Bret Taylor
> Eustis, FL
>
> John 3:30
>

[coolmath2]

In a message dated 5/1/2008 5:13:10 P.M. Pacific Daylight Time, bret.taylor@... writes:

I have also taught Math for Elementary School teachers for several years.  And, I don't think I have ever heard of the term "unit fraction."  I picked what I thought was the only logical answer - 5.  (5/5 = 1, unity.  Or so when my logic.)  And, I was wrong.  I was so shocked that I googled "unit fraction" and found out that I might be the only math teacher in the world who has never heard of a "unit fraction."

Never heard of it!

 

Every ten years they put new terms in the kids math books to confuse the parents.  Boy, I've gotten some really weird questions through Coolmath -- stuff I've never even heard of and I taught Math for Elementary Teachers for years.

 

Karen

Coolmath.com

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[Adam Stinchcombe]

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The easiest algorithm is called the greedy algorithm.  Start with a rational number x, find the smallest n (largest 1/n) so that 1/n<=x, then continue with the new fraction {x-1/n}.  Eventually you get x=sum of unit fractions.  I used this in a liberal arts class to review operations with fractions, and to introduce the idea of algorithm, and to talk about the importance of “does an algorithm terminate?”  You can prove that the greedy algorithm terminates (you prove that the numerators are decreasing).  After one such class one semester, a student remarked, “I never understood what common denominators were good for.  It is nice to see an application.”  I got a chuckle out of that.

 

Adam Stinchcombe

EAC Thatcher AZ

 

---

From: owner-mathedcc@... [mailto:owner-mathedcc@...] On Behalf Of broomell@...
Sent: Thursday, May 01, 2008 7:12 PM
To: Bret Taylor
Cc: mathedcc@...
Subject: Re: Are you smarter than a 5th grader?

 

I was watching that show when the question was asked and my initial thought was 5/5, but then I remembered a unit that I taught years ago about "Egyptian Fractions."  It became a challenge for my students (an me) to express fractions as the sum of unique unit fractions.  A colleague had an algorithm that worked to find the sum, but I cannot remember it because I have not used it in so long. 
Bev Broomell
Suffolk County Community College
Selden, NY 11784

----- Original Message -----
From: Bret Taylor
Date: Thursday, May 1, 2008 8:17 pm
Subject: Are you smarter than a 5th grader?
To: mathedcc@...

> I'm not. I missed a math question a week or two ago. The
> question went something like this:
>
> If the denominator of a unit fraction is 5, what is the numerator?
>
> I've got a Masters degree in math. I have taught high school
> math and community college math most of my adult life. I have
> taught college math from developmental (Arithmetic and Pre-
> Algebgra - two courses) through calculus. I have also taught
> Math for Elementary School teachers for several years. And, I
> don't think I have ever heard of the term "unit fraction." I
> picked what I thought was the only logical answer - 5. (5/5 =
> 1, unity. Or so when my logic.) And, I was wrong. I was so
> shocked that I googled "unit fraction" and found out that I
> might be the only math teacher in the world who has never heard
> of a "unit fraction."
>
> Is there anybody on this list who has also never heard of a unit
> fraction?
>
>
> Bret Taylor
> Eustis, FL
>
> John 3:30
>

[khs2700]

There's more that might be of interest regarding unit or "Egyptian"
fractions. The greedy algorithm Adam mentions is ascribed to ... Fibonacci
in his Liber Abaci! There is an unsolved conjecture posed by Erdos, that
every fraction of the form 4/n can be expressed as the sum of 3 or fewer
unit fractions with positive and distinct denominators. Egyptian fractions
are the subject of one of the most important ancient manuscripts, the
Rhind Papyrus, over which there is a lively historical debate.

And one of the colorful hypotheses as to why the Egyptians might have been
fond of them deals with their possible use in fair division problems, for
example the division of equal unit land areas; perhaps this was to settle
inheritance disputes or to divy up land every year after the Nile waters
receded. If we want to divide 5 separate, same size, same shape parcels
among 6 people, we could give 5 of the people 5/6 of a parcel, and one
person 5 times 1/6 of a parcel. But that latter person might not be too
happy about the many small sized portions.

If we use Egyptian unit fractions instead, we express 5/6 = 1/2 + 1/3, and
therefore 5 = 6(1/2 + 1/3). So each of the six people gets a 1/2 parcel
and a 1/3 parcel. Everyone not only gets the same amount, but also the
same shape.

I always use this in my elem. educ. math classes, it ties together histry,
culture, and even an easily understandable unsolved problem, and requires
the students do simple fraction calculations which they must then
coordinate with an interesting geometric decomposition.

Karl Schaffer
De Anza College

> The easiest algorithm is called the greedy algorithm.  Start with a
> rational number x, find the smallest n (largest 1/n) so that 1/n<=x,
> then continue with the new fraction {x-1/n}.  Eventually you get x=sum
> of unit fractions.  I used this in a liberal arts class to review
> operations with fractions, and to introduce the idea of algorithm, and
> to talk about the importance of "does an algorithm terminate?"  You can
> prove that the greedy algorithm terminates (you prove that the
> numerators are decreasing).  After one such class one semester, a
> student remarked, "I never understood what common denominators were good
> for.  It is nice to see an application."  I got a chuckle out of that.
>
>
>
> Adam Stinchcombe
>
> EAC Thatcher AZ
>
>
>
> ________________________________
>
> From: owner-mathedcc@... [mailto:owner-mathedcc@...]
> On Behalf Of broomell@...
> Sent: Thursday, May 01, 2008 7:12 PM
> To: Bret Taylor
> Cc: mathedcc@...
> Subject: Re: Are you smarter than a 5th grader?
>
>
>
> I was watching that show when the question was asked and my initial
> thought was 5/5, but then I remembered a unit that I taught years ago
> about "Egyptian Fractions."  It became a challenge for my students (an
> me) to express fractions as the sum of unique unit fractions.  A
> colleague had an algorithm that worked to find the sum, but I cannot
> remember it because I have not used it in so long.
> Bev Broomell
> Suffolk County Community College
> Selden, NY 11784
>
> ----- Original Message -----
> From: Bret Taylor
> Date: Thursday, May 1, 2008 8:17 pm
> Subject: Are you smarter than a 5th grader?
> To: mathedcc@...
>
>> I'm not. I missed a math question a week or two ago. The
>> question went something like this:
>>
>> If the denominator of a unit fraction is 5, what is the numerator?
>>
>> I've got a Masters degree in math. I have taught high school
>> math and community college math most of my adult life. I have
>> taught college math from developmental (Arithmetic and Pre-
>> Algebgra - two courses) through calculus. I have also taught
>> Math for Elementary School teachers for several years. And, I
>> don't think I have ever heard of the term "unit fraction." I
>> picked what I thought was the only logical answer - 5. (5/5 =
>> 1, unity. Or so when my logic.) And, I was wrong. I was so
>> shocked that I googled "unit fraction" and found out that I
>> might be the only math teacher in the world who has never heard
>> of a "unit fraction."
>>
>> Is there anybody on this list who has also never heard of a unit
>> fraction?
>>
>>
>> Bret Taylor
>> Eustis, FL
>>
>> John 3:30
>>

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[Nic LaHue]

Bret and friends,

I usually just lurk on this list but thought I would drop a note here.  I use The Mathematical Universe by William Dunham for our College Mathematics course at Penn Valley Community College.  This course is basically our version of a liberal arts mathematics course.  This book deals with the topic of unit fractions in the chapter on the Origins of mathematics.  

Ok, back to lurking.

Nic




Nic LaHue
Division Chair - Math-Engineering-
Chemistry-Physics-Computer Science-Business
Penn Valley Community College
nic.lahue@...

>>> "Bret Taylor" <bret.taylor@...> 5/1/2008 7:13 pm >>>
I'm not.  I missed a math question a week or two ago.  The question went something like this:

If the denominator of a unit fraction is 5, what is the numerator?

I've got a Masters degree in math.  I have taught high school math and community college math most of my adult life.  I have taught college math from developmental (Arithmetic and Pre-Algebgra - two courses) through calculus.  I have also taught Math for Elementary School teachers for several years.  And, I don't think I have ever heard of the term "unit fraction."  I picked what I thought was the only logical answer - 5.  (5/5 = 1, unity.  Or so when my logic.)  And, I was wrong.  I was so shocked that I googled "unit fraction" and found out that I might be the only math teacher in the world who has never heard of a "unit fraction."

Is there anybody on this list who has also never heard of a unit fraction?



Bret Taylor
Eustis, FL

John 3:30

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[charmaine condappa]

I have never heard of a unit fraction. I have been teachin mathematics for over 18 years and I did exactly the same thing you did. You are not alone.
Condappa
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[Jodi Cotten]

I'd like to hear from those colleges that have a second semester of Business Calculus.  If you offer it, what topics are covered?

Thanks!