From: Carol.Hooper@f90.n381.z1.fidonet.org (Carol Hooper)
Newsgroups: k12.sys.channel2
Subject: Cycle Three Problems
Date: Sat, 09 Jan 93 16:25:38 PDT
Organization: FidoNet node 1:381/90 - Stallion K12 Net BB, El Paso TX

***** Mathmagic Problem Cycle 3: Level K-2 *****
DOUBLING-These problems all deal with the idea of
doubling **Edna has 9 pennies. Her mom gives her 9
more pennies. This doubles the amount of pennies
that Edna has. How many pennies does Edna now have?
**Tom tells 2 friends a secret. Each of these
friends tells 2 more people the secret.  Including
Tom, How many people know the secret?  **Fold a
piece of paper in half. when you open the paper it
is divided into 2 sections.  If you fold it in half
twice, how many sections will there be?  How many
times must you fold a piece of paper in half to get
16 sections?  **How many seconds does it take you
to say the alphabet? If you take twice as long the
next time, how long will it take?
***** Mathmagic Problem Cycle 3: Level  3-4*****
Monica, Tony, and Ana want to equally share a cake.
How can they do this so that everybody feels that
they got their fair share?
***** Mathmagic Problem Cycle 3: Level 5-6 *****
A palindrome is an expression that reads the same
forwards and backwards. An example of a palindrome
word is "race car." Write it backwards and it still
spells the same thing.  Last year was a palindrome
year, since 1991 is a palindrome number. Answer
these questions concerning palindrome numbers.  A)
Prior to 1991 when was the last palindrome year?
B) When will the next palindrome year occur? (How
old will you be?) C) What is the greatest
palindrome number less than 500?  D) What is the
least 4 digit palindrome number?  E) What kind of
number do you get when you add 2 palindrome numbers
together?
***** Mathmagic Problem Cycle 3: Level 7-8 *****
A triangular number is formed by counting the dots
needed to form a triangular pattern. The first 4
triangular numbers are:
*          **          ***         ****
           *           **          ***
                       *           **
                                   *
1          3           6           10
As you can see, these patterns represent a list of
numbers called
a sequence. Answer the questions below and explain
how you arrive
at each answer.
A) What is the 6th triangular number?
B) What is the 10th triangular number?
C) Describe the type of number you get when you add
two consecutive triangular numbers together.
D) The 100th triangular number is 5050. What is the
101th?
E) Are there more even triangular numbers or odd
triangular numbers?
F) How many triangular numbers are prime?
***** Mathmagic Problem Cycle 3: Level 9-10 *****
The temperature can be measured using a variety of
temperature scales. Two common scales are the
Celsius and Fahrenheit Scales.  Each scale
indicates the warmth using its own scale. For
example, 37 degrees Celsius is the same as 98.6
degrees Fahrenheit, normal body temperature for
humans.  A) What is the formula which can be used
to convert from Fahrenheit to Celsius?  B) What is
the formula which can be used to convert from
Celsius to Fahrenheit?  C) Are there any
temperatures with equal readings on both the
Celsius and Fahrenheit scales? If so, what is the
reading?  D) When meteorologists report the
weather, they almost always round the temperature
to the nearest whole degree. With this in mind, it
is possible to find readings on the Celsius and
Fahrenheit scales for the same temperature such
that the reading on one scale can be found by
reversing the digits of the reading on the other
scale (i.e. 21 becomes 12). Can you find instances
where this occurs.  There may be more than one
solution.
***** Mathmagic Problem Cycle 3: Level 11-12 *****
NOTE: To represent squares such as 5 squared equals
25 we will use the notation 5^2 = 25.  Many
trinomials factor into algebraic factors whose
coefficients are identical to the factorization of
whole numbers. For example: 1y^2 + 6y + 9 = (1y +
3)^2, and
           169      = (13)^2
Does this work for all trinomials?
Does this work for all perfect square trinomials?
Must the coefficient of the squared term be 1?
Explain why this works and its limitations, if any.
Exemplify your responses when desired and state
conclusions in general terms when possible.
           Have fun!  Carol


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