(12/28/97)
(Reminder to *REGISTERED* teams: You can now work with Net Team Partners
(NTPs) that are not registered, just subscribed to the "mathmagic-k-3-
open" list. Feel free to advertize your team name, location and e-mail,
along with the geographical location of the desired partner. To do so,
just send an e-mail to mathmagic-k-3@mathforum.org. PLEASE remember
this only works if you have paid and been included in one of the WELCOMES
regularly posted.)
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MathMagic Cycle 26: Level K-3 Regular
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Box Relations (Make sure you are using Courier or similar font)
Look at the rows of boxes below. Each box in a row is the same as all
others in that row.
+--------+--------+--------+--------+--------+--------+--------+--------+
| 9 | | | | | | | | 72
+--------+--------+--------+--------+--------+--------+--------+--------+
+-------+-------+-------+-------+-------+-------+-------+-------+-------+
| 8 | | | | | | | | | 72
+-------+-------+-------+-------+-------+-------+-------+-------+-------+
+------+------+------+------+------+------+------+------+------+------+
| 7 | | | | | | | | | | 70
+------+------+------+------+------+------+------+------+------+------+
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 6 | | | | | | | | | | | | 72
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
| 5 | | | | | | | | | | | | | | 70
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
| 4 | | | | | | | | | | | | | | | | | | 72
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
|3 | | | | | | | | | | | | | | | | | | | | | | | | 72
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
What is the minimum amount of smaller boxes that you need to match one (or
more) of the big boxes? Make a table like this: [2(9) means 2 nine boxes]
| 8 boxes | 7 boxes | 6 boxes | 5 boxes | 4 boxes | 3 boxes |
+---------+---------+---------+---------+---------+---------+
9 box |9(8)=8(9)|9(7)=7(9)|3(6)=2(9)| | | |
+---------+---------+---------+---------+---------+---------+
8 box | | | | | |
+---------+---------+---------+---------+---------+---------+
7 box | | | | |
+---------+---------+---------+---------+---------+---------+
6 box | | | |
+---------+---------+---------+---------+---------+---------+
5 box | | |
+---------+---------+---------+---------+---------+---------+
4 box | |
+---------+---------+---------+---------+---------+---------+
How many boxes had the same numbers, just reversed?
How many boxes had different numbers?
What do you think are the numbers at the end of each row?
Using only the 3 boxes above (24), how many matches can you make with one or
more of the bigger boxes? Make a table to help your analysis.
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MathMagic Cycle 26: Level K-3 Advanced
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A Bicycle in class???
A bet was made between the Betsy's Red Boxers team and Jorge's Teal
Sardines team regarding bicycles. Betsy's team says that the formula shown
is correct. Jorge's team,
number of teeth on the other hand, insists
wheel revolutions on wheel gear that the right hand side of
----------------- = ---------------- the equation is upside down.
pedal revolutions number of teeth
on pedal gear To help them decide who is
right, your team needs to
bring a bike to class, along with masking tape and a measuring tape. You'll
need to use these items to first compare wheel revolutions and pedal revolu-
tions (do you have enough measurements to predict a constant called GEAR
ADVANTAGE?)
You will want also to see relation between the number of teeth on the wheel
gear and the number of teeth in the pedal gear. The cross product of the
data accumulated will prove Betsy's or Jorge's team correct.
Are the above advantages somewhat more complicated on the multi-speed bikes?
Perhaps you and your NTPs can challenge each other to set up an advantage
table for a five-speed!
Remember to write down your steps and conclusions.
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Good luck and best wishes for 1998
MrH