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***** 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-> Resume listing: <Y/n>, <c>ontinuous?c (
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.
Good Luck and Have fun.


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