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"Bits and Bytes" -- February '99
Table of Contents
- Pearls of URLs
This monthly item will highlight Internet web sites which are considered
"gems" by educators.
- Notes and Quotes
This regular column provides information on a potpourri of technological
"tidbits".
- The "magic" of spreadsheets: A
step by step approach
This classroom spreadsheet activity provides teachers with a series
of questions that they may use to encourage problem solving. This step-by-step approach
can foster creative thinking, analysis and collaboration in a classroom as students
attempt to design a 3 x 3 magic square.
- "Let's Get Connected" - Linking the Internet to
curriculum
Educators wishing to facilitate a curriculum-driven, Internet-using
activity as part of the province-wide "Let's Get Connected" event culminating
during the week of May 10-14, 1999 can submit their activities on-line. This year,
facilitators can qualify for a SchoolNet grant of $300, $600 or $900 and the first 30
activities submitted will receive the excellent Internet resource book entitled "Spinnin'
the Web: Designing & Developing Web Projects" by Dr. Annette Lamb.
- Food for Thought: The paradox of our time
This article, forwarded to me from a friend in India, compares our "advances" of
today with the past.
- Three Canadian explorers attempt to cross the Empty Quarter
on foot
Although this trek started in late January, you might want to visit this
web site to experience the possibilities for connecting the real-world experiences with
students in classrooms around the world.
- Pan Am Games Activity - Comparing Search Strategies
Bob Angst shares two activities that he developed for a staff workshop.
Participants compared and contrasted the procedure for acquiring information on the
up-coming Pan Am Games from both the Information Finder CD ROM and the Internet.
- Freebie Request Page
This month's freebies include the following two Windows '95 programs
for younger students: "Penny Penguin's Math Bingo 3.1" and "Mathematics
Worksheet Factory Lite 1.05".
Pearls of URLs
 The Road to Freedom: Using
the WWW to Teach About Slavery at:
http://www.education-world.com/a_lesson/lesson101.shtml
The Well Connected Educator -
ThinkQuest Award Narratives at:
http://www.gsh.org/wce/tq/tquest.htm
Brian Metcalfe - Editor - "Bits and Bytes"
Copyright © 1999 (ISSN 1195-5864)
Last revision date: February 24, 1999
Information has been shared with 
Notes and Quotes
by Brian Metcalfe - Technology Education
Electronic Time Capsule (ETC)
Project at: http://207.161.85.21/metks4/tech/currtech/etc/
On Friday, February 26th, Manitoba Education and Training will
launch their "Let's Get Connected Week" activity on the Kindergarten to Senior 4
Web Site. This activity is called the "Electronic Time Capsule (ETC) Project"
and was designed for all Kindergarten to Senior 4 teachers and students.
The ETC was created to store and share students representations
of positive school experiences with other students around the world. Teachers can complete
this activity with their students by simply asking them some guiding questions and having
them complete the phrase "School RULES in 1999 because ..." This phrase
can be completed by using poems, songs, scripts, art work, etc. and can take as much or as
little class time as teachers/students want to use. You will need access to an email
account, a browser (e.g., Internet Explorer or Netscape) and an Internet connection to
participate. Additional hardware and software may be required depending on the nature of
your submission to the time capsule.
What Do Principals
Do?
"A principal's job responsibilities are endless ... They
involve monitoring and mentoring, planning and policing, evaluating and envisioning. A
principal is a PR person and policy maker, the hirer and firer, a cheerleader and a change
agent."
But what do the students in your school think you do? Students at
Orangewood Elementary School in Phoenix, Arizona share their unique perspectives on what
their principal, Dr. Peggy George, does. Principals may find the student-created pictures
and sentences describing their principal's most important duties to be quite illuminating.
However, all administrators will want to bookmark this Education World website at http://www.education-world.com since it
provides administrators with a wealth of current resources.
French Software Distributors
Jerry LeMay, from Ecole LaVerendrye, provided me with the following two locations from
which he had recently ordered French Software:
- The Learning Company, 1586 Cartier Court, Mississauga, ON L4M
4B3.
Contact person: Robert Martellacci, Canadian
Regional Sales - Phone: (905) 542-9417, FAX: (905) 542-2387 The Learning
Company will fax a list of available products.
- The Centre Franco-Ontarien,
290, rue Dupuis, Vanier, ON K1L 1A2 - Phone (613) 747-1553, FAX: (613) 747-0866
Check out their web site at: http://www.cforp.on.ca
"Riding the Wave of Change" Conference - May 14 &
14, 1999
Once again Evergreen School Division is planning their National Conference to be
held in the Country Resort in Gimli. The conference will involve keynote speakers,
hands-on workshops, interactive sessions, displays of modern technology concurrently
scheduled with cutting-edge video conferencing and technology sessions. The cost of this
2-day conference is $250.00 or $150.00 for each single day. To be placed on the mailing
list to receive information describing all available sessions in detail, contact: Lloyd
Roche, Evergreen School Division, Box 1200, Gimli, MB R0C 1B0, Phone: 204-642-6270),
FAX: 204-642-7273, e-mail: lroche@minet.gov.mb.ca or web site at: http://www.esd.mb.ca
Quote of the Month
"I expect to pass through life but once. If, therefore, there be any
kindness I can show, or any good thing I can do to any fellow-being, let me do it now, and
not defer or neglect it, as I shall not pass this way again." -- William Penn
[Table of Contents]
The "magic" of spreadsheets: A step by step approach
by Brian Metcalfe - Technology Education
Over 20 years ago I introduced the concepts of "magic squares" to my students
as an exercise in programming. Recently I spoke with Richard Burkett, Computer Consultant
for the River East School Division, who was extremely excited by the problem solving
opportunities that existed when educators used the magic square concept to introduce
spreadsheets. This article will be presented as a series of questions which educators
might use to challenge their students as they investigate the "magic" of
mathematics and problem solve to create a magic square using a spreadsheet to test various
hypotheses.
What is a magic square?
A magic square is an arrangement of the numbers from 1 to n^2
(n-squared) in an n x n matrix, with each number
occurring exactly once such that the sum of the entries of any row, any column, or any
main diagonal is the same.
The simplest magic square is the 1 x 1 magic square whose only entry is the number 1.
The next simplest is the 3 x 3 magic square which we will use the spreadsheet tool to
explore. In fact the main focus of this article will be to have students arrange the
numbers 1 through 9 in a 3 x 3 array such that it makes a magic square in which the sum of
any row, column, or the two main diagonals is the same?
How can I use a spreadsheet to help me construct a magic square?
Use the spreadsheet component of Works (or any other spreadsheet tool) to construct a 3 x
3 square which has the numbers from 1 to 9 positioned in sequence in the cells as shown
below:
In order for a square to be designated as "magic", the sum of
all rows, all columns, and the two main diagonals must be the same. In this case we will
begin with a simple 3 x 3 matrix of 9 cells and we will use the spreadsheet's features to
calculate the sum of certain cells so that we can "guess and test" our theories
as to where the numbers from 1 to 9 should be placed. Begin by placing the number 1 in
cell B2 and work across the row. Start the second row of the square with the value 4 in
cell B3 and finish up with the 9 in the third row of the square in location D4.
How can I determine if I have created a magic square?
- Position the cursor in cell E2 and use the AutoSum button to select the three adjacent
cells B2, C2 and D2. Since 6 is the total of these three adjacent cells in the second row
of the spreadsheet, the sum is automatically displayed in location E2.
- Using the AutoSum button repeat the process to find the sums of the third and fourth
rows of the spreadsheet above and position the respective sums in cells E3 and E4.
- Next position the cursor in cell B5 and use the AutoSum button to select the three
adjacent cells B2, B3 & B4. The sum of this column is 12 so this value should be
displayed in cell B5 when the total is calculated.
- Repeat the same process to find the sums of the C and D column and place the results in
cells C5 and D5 respectfully.
- To determine the sum of the diagonal cells one must enter the formula by hand. For
example, if the cursor is positioned in location A5, the user should enter the formula
"=B4+C3+D2" (without quotes) to calculate the sum of the three cells in the main
diagonal rising to the right.
- Likewise if the formula "=B2+C3+D4" (without quotes) is entered into the cell
location E5, the sum of the three cells in the main diagonal rising to the left will be
calculated.
- If the version of your spreadsheet supports borders you might choose to highlight the
nine cells in the actual 3 x 3 matrix and place a border around the perimeter by selecting
the Format and Border menu items. This provides a border which separates the cells of the
square from the totals of the three rows, three columns and two main diagonal sums.
- Review your matrix to ensure that the numbers from 1 to 9 inside the border are located
in the same cells as indicated above. Furthermore make certain that your summation
functions work properly and that the sums of all three rows, three columns and two main
diagonals correspond exactly with the above illustration.
Does the arrangement of the sequential values from 1 to 9 in the matrix above
constitute a magic square?
Undoubtedly the variation of the sums of the rows (6, 15 & 24), columns (12,
15, & 18) and main diagonals (15 & 15) of the above layout do not qualify the
present layout as a 3 x 3 magic square. At this point, I would recommend that the students
delete the contents of the 9 cells within the border and then begin entering the numbers 1
through 9 into the nine squares in a different arrangement to see if they can use the
"guess and test" method to position the nine values so that all rows, columns
and main diagonals add up to the same value. After exploring this "trial and
error" process, most students will be more willing to explore a more systematic
approach. If some students are lucky enough to create a 3 x 3 magic square using this
"hit or miss" process, ask them to see if they can create another magic square
in which the number 1 is located in a different cell.
Based on the current sums of the rows, columns and diagonals illustrated in the
matrix above, what value might seem like a possible target sum?
Of the eight sums surrounding the matrix (15, 12, 15, 18, 15, 24, 16 & 6), 15
appears most. Let us hypothesize that 15 is the "magic sum" of this 3 x 3 array
and attempt to position the numbers 1 through 9 in such a way that the sum of each row,
column and main diagonal is 15. Armed with this fact, students should delete all entries
within the 3 x 3 boundary and attempt to position the numbers from 1 to 9 in the 9 cells
so that 15 is the sum. After more "guessing and testing", the teacher might ask
students to analyze the relative importance of the position of any of the nine cells in
the square.
Which cell is most critical or influences the most sums of rows, columns or
diagonals? Is it one of the four perimeter corners (currently with values 1, 3, 7 &
9), or one of the four middle cells on the perimeter (currently containing 2, 6, 8 &
4) or the exact centre (currently containing the 5)?
Through discussion, students should agree on the following order of significance:
- Exact centre is part of four sums (two main diagonals, one row & one column)
- Perimeter corner is part of three sums (one row, one column & one main diagonal)
- Perimeter middle is part of two sums (one row, & one column)
Thus it would appear that the exact center cell (currently containing the 5) is the key
position since it is a portion of four different totals.
If the centre cell influences the most number of sums, what would be a good
choice of number to be positioned in this cell?
Teachers may find it beneficial to write the numbers on the chalkboard from 1 to
9 as illustrated below to help guide students through this choice.
1 2
3
4
5
6
7
8
9
Why would 9 be a poor selection for the key middle position? Would 8 be
any better? Is 1 a good choice? Why or why not? After discussion, many students will
select the middle-most value to be placed in the centre of the matrix. Now
have the students return to their spreadsheet model, delete all the entries inside the
boundary and start guessing and testing using the two bits of information (the total is
probably 15 and the exact centre value should probably be 5).
If the exact centre is 5, what two values (from 1 to 9 - excluding
5 ) can be selected to complete a row, column, or main diagonal so that the sum is 15?
For example, let us assume that we are attempting to fill in the "C column" in
the spreadsheet. If we assume that 5 is in the middle and we pick a lower number like 3 to
enter in the C2 cell, then a higher number like 7 must be placed in the C4 cell to
maintain "balance" between the lower and higher numbers that pivot about the 5
and still contribute to a columnar total of 15. Have your students continue to "guess
and test" using this newly acquired information.
Which number appears hardest to fit into the matrix and still
maintain the 15 total?
After struggling in this "guess and test" process, most students will
find that the 9 is the value that always get left over and is hardest to position. If the
9 is the most difficult value to position, perhaps you might ask students where it can be
placed so that it influences the fewest totals. If students review three bulleted items
above, they will consider placing the 9 in one of the perimeter middle cells since it will
only be part of two sums (one row, & one column). With the 9 positioned now positioned
in a perimeter middle cell and the 5 in the center, the 1 must be at the other end of this
row or column. Now begin placing;acing the other "balancing numbers" in pairs
around the center 5 value.
Do you notice any patterns that appear in the matrix? For example,
will all the perimeter middle cells be even or odd? Will all the corners have even or odd
numbers?
Have students return to spreadsheet matrix and attempt to enter "balancing
numbers" in adjacent cells to the center 5 value and still maintain a row, column,
and main diagonal of 15.
If you successfully create a 3 x 3 magic square, can you rearrange
the numbers to produce more than one solution?
Provide students with an opportunity to see if they can construct a magic square
which is simply a "rotation" of their original.
Is there a systematic way in which a 3 x 3 magic square can be created?
A mathematician by the name of De La Louder developed a method which will work
for odd sized magic squares.
- Place the 1 in the center cell of the top row as shown below
- Continue placing the values 2 through 9 by moving diagonally upwards to the right. In
other words, move one cell up and one cell over to the right. In the process of moving,
should you proceed off the edge, wrap around to the cell at the other end of the row or
column. Continue this cycle of moving diagonally up to the right until the next cell is
already occupied as shown.
- If the next cell in the progression is already occupied, place the next number in the
cell directly below the pervious cell as shown.
- Continue placing the subsequent values moving diagonally up to the right as illustrated
following the conditions specified above. Eventually, the square will be filled with the 9
values in sequence and the total of all rows, columns and main diagonals will be 15 which
will qualify as a true 3 x 3 magic square.
The following questions might challenge some your students:
- Are there other arrangements which would qualify as a 3 x 3 magic square?
- If you multiply each value in each cell by a constant (say 5) will the magic square
properties still exist?
- If you add a constant to each of the nine values (say 4) so that the numbers become 5,
6, 7, ... 13 will these values form a magic square?
- Can you use the above process to enter the 1 - 25 entries in a 5 x 5 magic square?
- Who will be the first student to create a 4 x 4 magic square?
Possible extensions, for both staff and students, might involve visiting the following
web sites:
I trust that this activity, together with the probing questions, will help students to
problem solve and to appreciate the "magic" in mathematics.
[Table of Contents]
"Let's Get Connected" - Linking the Internet to curriculum
by Brian Metcalfe - Technology Education
The Internet holds enormous potential for classroom teachers. At the same time, there
is the challenge of identifying Internet activities designed for classrooms.
Once again, plans are well underway to provide a wide variety of
curricular-driven, classroom activities that utilize the potential of the Internet. Many
educators, throughout the province, are starting to plan Internet-based activities that
will culminate during the week of May 10-14, 1999. In fact during the last two years,
Internet utilization has peaked in Manitoba classrooms during the month of May as students
and staff ‘connected’ in a variety of classroom activities that were enhanced by
Internet use.
This year, to assist educators contemplating creating a "Let's Get
Connected" activity, several innovations and incentives have been created through
partnerships with other agencies.
Innovations include:
Incentives include:
One copy of the excellent Internet resource entitled "Spinnin'
the Web: Designing & Developing Web Projects" by Dr. Annette Lamb will be
distributed to one facilitator from each of the first 30 "Let's Get Connected"
activities that are submitted through the on-line registration process at: http://www.cecm.winnipeg.mb.ca/
Facilitators who develop a K-12 "Let's Get Connected"
activity may also apply on-line as part of the "GrassRoots Program"
at: http://www.schoolnet.ca/grassroots/e/info.centre/index.html
Through a partnership with Canada's SchoolNet, "Let's Get Connected"
activity facilitators may also qualify for a grant of $300, $600 or $900 if they meet the
"GrassRoots" evaluation
criteria illustrated at: http://www.schoolnet.ca/grassroots/e/project.centre/toolkit/build2/evaluation.html
Regardless of whether you wish to facilitate a "Let's Get
Connected" activity or participate with your students in one or more activities,
point your web browser and bookmark this site:
http://www.cecm.winnipeg.mb.ca/lgc/
[Table of Contents]
Food for Thought: The paradox of our time ...
forwarded by Roger Braden
The paradox of our time in history is that we have taller buildings, but shorter tempers;
wider freeways, but narrower viewpoints; we spend more, but have less; we buy more,
but enjoy it less.
We have bigger houses and smaller families; more conveniences, but less time; we have more
degrees, but less sense; more knowledge, but less judgment; more experts, but more
problems; more medicine, but less wellness.
We drink too much, smoke too much, spend too recklessly, laugh too little, drive too fast,
get too angry too quickly, stay up too late, get up too tired, read too seldom, watch TV
too much, and pray too seldom.
We have multiplied our possessions, but reduced our values. We talk too much, love
too seldom, and hate too often. We've learned how to make a living, but not a
life; We've added years to life, not life to years.
We've been all the way to the moon and back, but have trouble crossing the street to meet
the new neighbor. We've conquered outer space, but not inner space; We've done
larger things, but not better things.
We've cleaned up the air, but polluted the soul; We've split the atom, but not our
prejudice; We write more, but learn less; We plan more, but accomplish less.
We've learned to rush, but not to wait; We have higher incomes, but lower morals; We have
more food, but less appeasement; We build more computers to hold more information to
produce more copies than ever, but have less communication; We've become long on quantity,
but short on quality.
These are the times of fast foods and slow digestion; tall men, and short character; steep
profits, and shallow relationships. These are the times of world peace, but domestic
warfare; more leisure, but less fun; more kinds of food, but less nutrition.
These are days of two incomes, but more divorce; of fancier houses, but broken
homes.
These are days of quick trips, disposable diapers, throw away morality, one-night stands,
overweight bodies, and pills that do everything from cheer to quiet, to kill.
It is a time when there is much in the show window and nothing in the stockroom; a time
when technology can bring this letter to you, and a time when you can choose either to
make a difference, or to just hit delete key ...
[Table of Contents]
Three Canadian explorers attempt to cross the Empty Quarter on foot
by Brian Metcalfe - Technology Education
 The Empty Quarter of
Arabia is the world's largest sand desert. In late January 1999, three Canadian Explorers
will begin a journey, hoping to make a foot crossing of this quarter million square miles
of mystery and desolation. This web site, created in conjunction with the Calgary Board of
Education, will allow children across Canada and around the world to follow the
expedition. Detailed curriculum has been created and is posted on this site for levels K
through 12. The curriculum is designed to provide possibilities for connecting the
real-world experiences of the Empty Quarter Expedition into the educational experiences of
students in the classroom. All teachers, students, and parents are welcome and encouraged
to follow and use this web site free of charge.
Check out this innovative web site and
investigate this "epic desert journey into the unknown" at:
http://www.alwaysadventure.net/intro100.htm
Table of Contents]
Pan Am Games Activity - Comparing Search Strategies
by Bob Angst - Librarian at Garden Grove School
Bob Angst developed the following two activities to help teachers, and ultimately their
students, compare and contrast the research skills needed to acquire information related
to the up-coming Pan Am Games. For this staff workshop, he created the following two
activities which asked educators to retrieve information from two resources, namely the
Information Finder CD ROM encyclopedia and the Internet. In advance of the workshop,
Bob prepared, from a list of the 42 different nations who will compete, sufficient cards
with country names so that each participant could pick a country at random.
Pan Am Games Activity Sheet
World Book Activity
Name of the country you have picked :
____________________________
Using Search: Word / Topic
1. In how many World Book articles does your
country’s name appear?
______________________________________________________
2. What is the population of your country?
______________________________________________________
3. What is the name of your country’s
monetary unit?
______________________________________________________
Using World Book Bookmarks:
- Bookmark the World Book article on your
country.
- Now find the World Book articles on: Chile,
Cuba, Nicaragua, and Paraguay
- Bookmark these articles.
Using the World Book Notepad:
- Using the Notepad feature, record the populations
of all 5 of your bookmarked countries. Then rank then below according to population from
largest to smallest.
Country
Population
1.
____________________________ ______________________________
2.
____________________________ ______________________________
3.
____________________________ ______________________________
4.
____________________________ ______________________________
5.
____________________________ ______________________________
Using the World Book Atlas:
Using the Atlas feature in World Book, zoom in on the map of your country until you can
activate the article on your country’s capital city.
1. What is the name of the capital city?
______________________________
2. What is the population of the capital
city? ________________________
Pan Am Games Activity Sheet
Websites and Bookmark Activity
Using Search Engines
Using the search engine Inference,
enter your Query as "Pan Am Games".
Using Links and Back & Forward buttons
Looking at the XIII Pan American Games
Official Website
(http://www.panamgames.org/)
Find:
1. At what location will the archery
competition be held?
______________________________________________________
2. Which event will take place at Le Club La
Vérendrye?
______________________________________________________
3. Approximately how many athletes will
participate in the Winnipeg Pan Am Games?
______________________________________________________
4. Who is Pato, the Pan Am mascot’s,
playmate?
______________________________________________________
Looking at the #1-PanAmGames.Net - The Pan
American Games
Wpg Thomson New Media (http://www.netreader.com/panam/)
Find:
1. Which city other than Winnipeg has hosted
two Pan Am Games?
______________________________________________________
2. What is the length of a Pan Am basketball
game?
______________________________________________________
3. Who opened the 1967 Pan Am Games in
Winnipeg?
______________________________________________________
4. Name the top pop song in Winnipeg during
the opening week of the 1967 games?
______________________________________________________
[Table of Contents]
Freebie Request Page
by Brian Metcalfe - Technology Education
 |
Please duplicate as necessary and
complete form by PRINTING.
NAME: ___________________________________
SCHOOL: _________________________________
PHONE: __________________________________ |
Internet users are encouraged to download these "freebies"
by selecting the appropriate underlined and/or colored link below. Educators in The
Winnipeg School Division No. 1, who do not have Internet connectivity, may still acquire
these "freebies" by sending in this completed form with the appropriate number
of NEW double-sided, HIGH DENSITY 3.5" blank diskette(s) specified in brackets.
Others, outside our Division, are entitled to these "freebies" on the condition
that they download these resources using the Internet.
[ ] "Penny Penguin's Math Bingo 3.1" - FREEWARE for Windows
95/98 or
NT [#291]
(Single
NEW 3.5" high density disk)
This diskette contains a multimedia
game designed to teach children addition,
subtraction, multiplication and
division. With 3D rendered graphics, cute animation
and excellent sound effects, Penny
the Penguin will play "Bingo" with your child,
gentling helping him or her to
choose the correct block on the Bingo card. Instead of
playing with numbers, a
mathematical equation is displayed on the screen. A chip is
placed on the correct answer on the
bingo card. This program can be played between
two students or individuals can
challenge "Penny" to a game.
[ ] "Mathematics Worksheet Factory Lite 1.05" - FREEWARE for
Windows 95/98 or NT [#292]
(This
program MUST be downloaded since it is 1995K and will not fit on a floppy)
Now, with the FREE Mathematics
Worksheet Factory Lite, you can provide students
with the practice they need to
become proficient in the basic mathematical operations.
Easily create instant, customized,
and unlimited worksheets for the practice of
arithmetic facts in addition,
subtraction, multiplication, and division. Features horizontal
or vertical question layout,
intuitive WYSIWYG interface, riddle generator, easy selection
of number of questions from 1 to
100, automatic answer key, customization of title,
comments, date, picture, and font
with easy install and uninstall.
[Editor: A special THANKS is expressed to Bruce Young,
Computer Coordinator for the Seven Oaks
School Division, for sharing the above software sources with me.]
Complete and return to:
"Bits and Bytes" Requests
Room 126 - Administration Building #2
Return to the "Bits and Bytes" Web Page
 Return to The
Winnipeg School Division No. 1 Web Page
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