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(Math) Word Problems

 
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adedios
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Joined: 06 Jul 2005
Posts: 5060
Location: Angel C. de Dios

PostPosted: Fri Mar 31, 2006 9:10 am    Post subject: (Math) Word Problems Reply with quote






Problems to Sharpen the Young

By Ivars Peterson

Muse, March 2006, p. 42.

One of the oldest collections of mathematical problems we know of is Problems to Sharpen the Young. No one knows who wrote the book, but some scholars say that the author might have been someone named Alcuin, who lived from about 732 to the year 804 (three-digit years!). Alcuin was born near the city of York in England and was a student, then a teacher, and then head of the Cathedral School at York.

Here's a problem from the book you might find interesting:

A staircase has 100 steps. On the first step stands a pigeon; on the second, two pigeons; on the third, three; on the fourth, four; on the fifth, five; and so on, on every step up to the hundredth. How many pigeons are there altogether?

Can you find a quick way to solve the problem that doesn't require you to add all the numbers from 1 to 100? You'll find the answer at the end of this article.

Problem 5 in the collection is one of six variations in the book on what was known as the "hundred fowls" problem, so-called after a 5th-century version that features 100 birds (cocks, hens, and chicks):

A merchant wanted to buy 100 pigs for 100 pence. For a boar, he would pay 10 pence, for a sow, 5 pence; while he would pay 1 penny for a couple of piglets. How many boars, sows, and piglets must there have been for him to have paid exactly 100 pence for 100 animals?

Problem 52 in the collection has survived in various forms to this day:

A certain head of household ordered that 90 modia of grain be taken from one of his houses to another 30 leagues away. Given that this load of grain can be carried by a camel in three trips (not necessarily all the way) and that the camel eats one modium per league but only eats when he is carrying a load, how many modia were left over at the end of the journey?

Forget about the modia. The units are irrelevant. Modern versions are sometimes called jeep problems because they describe a jeep in the desert with n cans of fuel and a distant destination.

Here's a really sneaky one:

A man has 300 pigs and orders that they are to be killed in three days, an odd number each day. What odd number of pigs must be killed each day?

There's no answer. According to the book, this problem was composed to show up smart-alecky or misbehaving schoolchildren. Wonder how long it took students to figure out that this was a trick question and that three odd numbers can never add up to an even number.

It seems that some things about school haven't changed much—even over hundreds of years.


--------------------------------------------------------------------------------

ANSWER: Alcuin's clever solution to the staircase problem is to count the pigeons in pairs, starting with the one on the first step and the 99 on the 99th step. That makes 100. The two on the second step and the 98 on the 98th step also make 100. Remember the 50th step and the 100th step have no pairs. The grand total? 5050 pigeons, which is a lot of feathers.


--------------------------------------------------------------------------------

If you want to try other problems in the collection, go to logica.ugent.be/albrecht/alcuin.pdf


Science News for Kids is made possible by the Willis Harlow Shapley Education Fund.

*************************************************************

Here are other sites that provide math word problems as well as strategies:

What are math word problems?

http://www.college.ucla.edu/up.....hword.html

Word problem solving strategies

http://library.thinkquest.org/4471/learn.htm
http://www.how-to-study.com/So.....oblems.htm
http://www.cliffsnotes.com/Wil.....31110.html

Paying attention to the English in word problems

http://www.purplemath.com/modules/translat.htm

Word problems and algebra

http://www.algebrahelp.com/les...../index.htm

Constructing equations from word problems

http://astro.temple.edu/~dhill.....emeqn.html

"Age" word problems

http://purplemath.com/modules/ageprobs.htm

Geometric word problems

http://purplemath.com/modules/perimetr.htm

"Coin" word problems

http://purplemath.com/modules/coinprob.htm

"Distance" word problems

http://purplemath.com/modules/distance.htm

"Savings" or "Investment" word problems

http://purplemath.com/modules/investmt.htm

"Mixture" word problems

http://purplemath.com/modules/mixture.htm

"Number" word problems

http://purplemath.com/modules/numbprob.htm

"Percent" word problems

http://purplemath.com/modules/percntof.htm

"Work" problems

http://purplemath.com/modules/workprob.htm

Math word problems and physics

http://www.ncsu.edu/felder-pub.....icist.html

Florida's Department of Education - Math Word Problems for Elementary Schools

http://www.manatee.k12.fl.us/S.....sindex.htm

Math Word Problems from Canada

http://www.cdli.ca/CITE/math_problems.htm

Weekly math word problems

http://www.eduplace.com/math/brain/

More than 1000 math problems solved

http://www.webmath.com/AnswerStore/

Word Problems for Addition and Subtraction

http://www.actionmath.com/Katie1/Katiewp1.html

Word Problems for Multiplication and Division

http://www.actionmath.com/GSM2/GSM2wp1.html

Math Word Problems in Video

http://www.actionmath.com/TuneIn_1.html

GAMES

http://www.mathplayground.com/logicgames.html
http://www.mathplayground.com/games.html
http://www.dositey.com/math/mistery2.html


Last edited by adedios on Sat Jan 27, 2007 3:08 pm; edited 1 time in total
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aca72



Joined: 24 Nov 2005
Posts: 22
Location: Arlene Cagayat Alegre

PostPosted: Mon Jul 17, 2006 8:01 pm    Post subject: arlene alegre Reply with quote

Hi Prof.

My pupils in grade 4 Venus and 4 Earth really love and enjoy the math games under the math word problems...like speedy sum, race of the wangdoodles etc. talagang active na active sila pagdating dito sa computer lab.

Thanks po
________
arlene
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adedios
SuperPoster


Joined: 06 Jul 2005
Posts: 5060
Location: Angel C. de Dios

PostPosted: Mon Jul 17, 2006 8:06 pm    Post subject: Re: arlene alegre Reply with quote

aca72 wrote:
Hi Prof.

My pupils in grade 4 Venus and 4 Earth really love and enjoy the math games under the math word problems...like speedy sum, race of the wangdoodles etc. talagang active na active sila pagdating dito sa computer lab.

Thanks po
________
arlene


Arlene:

That is great news. Is this the same class that I saw one morning? Keep up the good work. And thanks.

-Angel
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adedios
SuperPoster


Joined: 06 Jul 2005
Posts: 5060
Location: Angel C. de Dios

PostPosted: Tue Jul 10, 2007 9:06 am    Post subject: Mobile math lab for cell phones Reply with quote

University of Haifa
10 July 2007

Mobile math lab for cell phones

Can kids finally get the answer to the perennial question: What do we need to study math for" The latest development of Prof. Michal Yerushalmy, of the Institute for Alternatives in Education of the Faculty of Education at the University of Haifa, may indeed have the answer to this question, through a medium that today's youth understand very well –their cellular telephones.

The applications that Prof. Yerushalmy developed, in cooperation with Arik Weizman and Zohar Shavit of the University of Haifa Computer Science Department with support from Eurocom Israel, can be installed on most cellular phones on the market today. When installed, they enable cellular phones to function like computers which, among other things, are able to perform mathematical functions at different levels – from elementary school geometry to high school level calculus. The applications were developed specifically for the educational system, and they can be used like any application installed on a cell phone. The availability of the medium means that students are no longer reliant on computer classrooms in the school and that educational opportunities are as mobile as students are.

"I believe that mathematics needs to be learned in creative ways, and not by memorization and repetition. Just as physics and biology labs teach through experimentation, I believe that there should also be math labs, where learning is experiential," said Prof. Yerushalmy. According to Prof. Yerushalmy, computerized math labs like these have been developed in the past, but the cost of computers and the limited availability of computer classrooms limited their use. Cellular phone applications are accessible to both teachers and students on the school campus, on the way home or just about anywhere else.

Using cellular telephones provides another advantage: enabling creation of a community of learners. The applications enable users to send graphs and formulas to one another as short text messages (SMS), allowing them to work together to solve problems and involve any number of people to share in the learning process.

A pilot research project, recently completed in the University of Haifa Faculty of Education, evaluated students' use of the applications. As part of the research, participants recorded simple occurrences such as the speed of a dripping faucet, buses pulling away from a bus stop and a number of other events with the video cameras on their cell phones. They were then instructed by Dr. Galit Botzer, who conducted the research, to turn their video clip into a mathematical model using the applications available on their cell phone.

"It was important for us to see whether or not the students actually do use their phone as a medium for communication to help solve the problem. We found that they did indeed use text messaging to send one another information, questions and comments at different times and from different places. Our next step is to engage in more intensive research, and to develop additional, unique applications for cellular phones," said Dr. Botzer.


###
More information can be found on the website: www.math4mobile.com . The program can be downloaded and further explanations and ideas for its use are available on the site. Once the program has been downloaded, it can be shared with others by sending a text message with a link to the site. Download the program and you, too, will carry a math lab in your pocket.
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