CONFERENCE MATH
MATERIALS
by Dave Mitchell
143 White Pine Cr., Waterloo, ON N2V 1B3, 5198855700
email: mitchell@arithmecode.com
MATH SONGS / RAPS
/ COMMERCIALS / PUPPET SKITS
THE
FRACTION RAP
( Generate rap
noise in the background.)
A Fraction is a division,
so you don't have to make a decision.
You just take the numerator and divide by the denominator,
And then sooner or later, you get a repeater or terminator.
'Cause a fraction is a division, so you don't have to make a
decision.
That's a rap  2  3  4 . That's a rap.
MATHEMATICAL PI
( To the tune of American
Pie )
A long, long time ago,
I can still remember when those numbers used to make me cry.
But I knew if I had my chance, I could make those figures dance and
in math class,
I'd be happy for a while.
But studying just made me quiver, and each math fact would send a shiver
__
Bad news on my math test, it sent me on a new quest.
I still recall with greatest pride, the day my mind was opened wide.
Math's importance got inside, the day I really tried.
And now I'm singing, "Why, why don't you learn about Pi
? "
Get ecstatic 'bout quadratics and let calculus fly.
Take a swig of trig and you will be on a high, singing,
"This'll be the day that I try ! "
BEDMAS
( To the tune of the Hokey  Pokey )
You do the brackets first,
exponents then take flight,
Next you divide and multiply in order left to right.
You add 'em and subtract 'em as you go and then you shout,
That's what BEDMAS is all about.
You work in BEDMAS order, you work in BEDMAS order,
You work in B  E  D  M  A  S order, work in BEDMAS order.
You work in B  E  D  M  A  S order, that's what BEDMAS is all
about.
CIRCLE SONG
or VERSE
Here is a
circle, it knows how to get around.
It has a radius from centre to rim.
And its diameter's a line that goes from side to side
while passing through the centre.
Now isn't that sim  ple?
Pi R squared sounds like area to me, when I need a circumference I'll
just use Pi D.
Pi R squared sounds like area to me, when I need a circumference I'll
just use Pi D.
ZERO SONG
( Author unknown. To the tune of Rudolph )
Zero, that funny number,
has a shape that looks like oh.
And if you want to use it, there are things you need to know.
Never divide by zero. If you do you will be sad,
Getting a crazy answer, making your report look bad.
But treat zero as your friend, use it carefully.
Safe to multiply or add, that's the rule for zero lads and lasses.
Zero, that funny number, wants to be a comrade true,
But never divide by zero, or you'll be getting zero too.
SPEAKING OF
PI
See, I have
a rhyme assisting my feeble brain its tasks oft'times resisting.
(Count the number of letters in each word in the sentence above to get
Pi to
12 decimal places)
113355  (first three odd natural numbers, each one duplicated)
Turn it into a division: 113 into 355, in other words, 355 ÷
113. Try it.
EXCELLENT
Words
A 
B 
C 
D 
E 
F 
G 
H 
I 
J 
K 
L 
M 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
N 
O 
P 
Q 
R 
S 
T 
U 
V 
W 
X 
Y 
Z 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
The value of a word is the sum of the values of its letters. A word is
excellent if its
value is exactly 100. Find the value of each of the following words: EXCELLENT,
ATTITUDE, PERCENTS, EDMONTON, ANALYSIS. What excellent words can
your students find?
MATH and MOZART (The
Mozart Effect)
Researchers at the University
of Southern California have found that students do
better on arithmetic calculations if Mozart is being played in the background
while
they work. You can test this theory by having students do arithmetic without
Mozart
and then doing questions of comparable difficulty while Mozart is being
played. A
Mozart CD should be easy to find. You might extend this by testing other
types of
music. (Students might search for the Mozart Effect on the internet.)
1997 PROBLEM
Using all four and
only the four digits 1,9,9,7 each time, form expressions for
all the numbers from 1 to 100. You may use + ,  , x , ÷ , ( )
, ! , radicals and
exponents as appropriate if they involve only 1,9,9,7.
Examples: 99  17 = 82, 9 ÷ 9 + 7  1 = 7, 97  9^{1}
= 89, etc.
Post a chart at the back of the room. Make it an ongoing class project
to get
expressions for all the numbers from 1 to 100. Each time a student
posts a correct
expression, he/she initials it.
ALPHABITS
CEREAL ACTIVITY
 one cup
of cereal on a paper towel on each desk
 students count and tally the number of each letter (  discount the
broken pieces )
 calculate the percent of their own pieces which are As, Bs, Cs, ...
Zs
 add up all student totals to get the total number
of As, Bs, Cs, ... Zs in the box
 suppose there are 2000 pieces in the box and Betty found that 5 %
of her pieces
are As. Based on this, she might predict that 5 % of the
2000 pieces or 100 As
should be found in the box. How does this compare with
the actual total number
of As in the box ?
 repeat for the other letters
 would the students in Betty's row make better predictions if they
used the totals
for their row converted to percents rather than just their own
individual totals ?
 students eat the cereal and will then ask to be excused to get a drink
of water
 have one of the students call the 1  800 number on the box to ask
why there are
not approximately the same number of each letter
in a box (report back)
BAD
MATH COST MAN CONDO ON FLORIDA'S GULF COAST
In the 1980s,
Canada trust had a contest. For each $50 you deposited, you got a
ballot. All ballots from branches across Ontario were collected
when the contest
ended. From the big drum of ballots, one was drawn and the person
whose name
was selected was asked to report to test his skill in order to win the
condominium
prize which, at the time, was worth $80 000 U.S. He was given
a pencil, paper and
fifteen minutes. No calculator was allowed. Here is the question he
was given :
1. multiply 228 by 21
2. add 10 824
3. divide by 12
4. subtract 1 121 
He got the wrong answer and was, of course, terribly
disappointed. Another name was drawn and this time
the contestant was successful in obtaining the correct
answer, along with the condo in the sunny south !

Have your students try the question to see if they can "win"
the condo.
MATH RALLY ASSIGNMENTS
Students work in groups
to create a map of a fictitious town called Mathton. They
make up a set of questions based on a unit of study and create a rally
directed by
answers to these questions.
Example: Begin at the corner of Triangle Street and Equation Boulevard
and head
north. If the answer to question #1 is x = 5, then turn right at
the first opportunity.
If not, turn left at the first street after Polygon Pizza. etc.
Groups exchange and try the rallies. They also grade the rallies based
on criteria
supplied by you. You collect the rallies and evaluation sheets and add
your own
component to the mark by looking at the quality of the presentations
submitted.
MATHEMATICAL
MIND CONTROL
Take any number
and add 14. Multiply the result by 2. Subtract 8. Divide by 4.
Subtract half the original number. Think of the numberletter association:
1 = A,
2 = B, 3 = C etc. Now think of an animal that starts with the letter
which
corresponds to your answer above. Back up one position in the alphabet
and think
of a country which starts with that letter. ... Are you thinking of
elephants in
Denmark?
If you do the arithmetic properly, no matter what number you start out
with, you
should end up with 5. This will correspond to E and most people think
of Elephant.
The D usually leads people to think of Denmark. (You might get a few
Eagles or
Emus in the Dominican Republic)
Why does it work? It's simple algebra.
Let the number be n. Then you get n + 14. Next you get 2n + 28 followed
by
2n + 28  8 or 2n + 20. When you divide by 4 you get 2n/4 + 5 which
reduces to
n/2 + 5. Now when you take away half of n (i.e. n/2) you get 5.
THE GREAT BEDMAS
CONTROVERSY ( BEIDMAS ? )
What is the
answer to this question? (8)(3) ÷ (2)(4) Do you say
it's 48 or do you
say it's 3? ... BEDMAS would suggest working left to right
on this one because it's
all multiplication and division. However, it is suggested that implied
mutliplication
should be done before multiplication and division notated by
×, ÷. Therefore, you
get 24 ÷ 8 or 3.
GREAT DECODING
PROBLEM :
( Found on an old ditto.)
VZBMXCVBTA VNVBAAHDKB
TVZBGNCXLH TBHJVZBFNY
NXBABXNKSC XVZBABLHXT PHEDTPNEVZ CAYDNSBTNX
CGYHEVNXVE HDBCXVZBNG BECLNXKCLV HESNVVZBTB
LCACKBWNVV DBHJGCTPNS
1. Copy the code on your
paper leaving two blank lines between each line
of letters. (Check)
2. Count the number of As, Bs, Cs, ... , Zs. ( Make a chart. )
3. The most frequently used letter in English is the letter E.
Which letter
in the code represents the letter E? Print an E
underneath each place this
letter appears in the code.
4. The second most frequently used letter is T. Print a
T underneath each place
this letter appears.
5. A very common word is THE. If you can figure out where
the word THE
appears, you now know which letter represents H.
6. This code contains the words UNITED STATES. If you
can find these words
you now know several more letters.
7. Besides E and T, the most frequently used letters in English
are A, O and N.
Look at your chart and you should be able to figure out
which letter
represents O.
8. Solving for the remaining letters is up to you. What is the
message? Try it
on your own first to get the idea and then give it to
your class.
CBC RADIO
Find the call numbers
for your area at www.cbc.ca and turn your students
on to some of these great shows.
 Quirks and Quarks  science show  Saturdays at noon after
the news
 This Morning Tonight  evenings at 8:00 p.m.
 As It Happens  Evenings at 6:30 p.m.
TAKING UP TESTS
 Are you looking at 30
sets of glazed eyes? Try handing
back the tests and posting solutions at a few stations around the room.
Allow a few
minutes for students to check their work, correct their solutions and
negotiate
any mark changes. The ball is now in their court.
SIMPLE MIND
(Like
the game MasterMind but easier. A good way to work
into MasterMind which is available at toy and game stores.)
 the secret code is three
digits made up using 1,2,3,4 with repetition allowed
 score each guess: R means right digit in right place,
W means right digit
in wrong place
 example : if the code is 324 and guess is 332, clue is
RW because the 3 is in the
right place and the 2 is in the wrong place. The middle 3 does
not get a score because
there is only one 3 in the code and it has been accounted for.
NOTE : the order in which the Rs
and Ws are given is of no significance.
Sample Puzzles :
i 
ii 
iii 
121 W
411 W
132 WW
(answer is 243) 
433 R
232 W
131 RWW
(answer is 113) 
322
434 RR
111
(answer is 444) 
 graduate to MasterMind
ArithmeCode
© 1997 by Dave Mitchell
For sample puzzles and information
on booklets, see the main menu of this web site.
Note: Songs and music which accompany many of the ideas I have presented
are available on my CDs, Math, Music and Mayhem, Go Forth and Multiply
and Class Actions. Information on these items can be found
by going to the CD Information Page .
You're a teacher! Your attitude and enthusiasm for math
will make a difference for your students.