Problem Solving for CGS Math Analysis Students

Six problems are outlined below.  One  problem must be handed in to your math teacher.  A grading rubric will be used to score your solution.  Please consult this rubric to ensure you are handing in a complete and thoughtful solution.  The honor code is to be followed in completing this assignment.  Here are the problems to choose from:

#1.     Why Didn't It Fit?             

Grandmother Stewart started a family quilt years ago. As each family member becomes sufficiently skilled, he or she is given the task of designing and completing a new square for the quilt. It has become a rite of passage in the Stewart family to have Grandmother approve and add a new quilt square.

Cousins Michael and Jeanne-Marie were busy working on their squares, helping each other prepare the pieces for sewing. Jeanne-Marie told Michael that she needed a burgundy triangle with an angle of 51 degrees, an adjacent side of 4.9 cm, and an opposite side of 4.6 cm.

Since they both liked Geometry and Trigonometry, they knew that most triangles can be determined with three of their six parts. Thus, Michael did a little calculating and then cut Jeanne-Marie's triangle, remembering to add enough for the seam allowance.

Unfortunately, the triangle Michael cut did not fit Jeanne-Marie's design. Why not?

©The Math Forum

 

#2    In the country of Puevigi, the population consists of Soothsayers, who never lie, Dissemblers, who always lie, and Diplomats, who alternately lie and tell the truth. If you meet a citizen of Puevigi, how with just two questions can you determine to which group he belongs?  

 

#3   How many colors are necessary to color the squares of a chess board in such a way that the King cannot move from one square to another of the same color? (The case of the King castling should not be considered.)

#4   Find two numbers whose sum and product are equal and whose quotient and difference are also equal.

#5  In ∆ABC, what is the ordered pair of real numbers (x,y) for which sinA:sinB:sinC = 4:5:6 but cosA:cosB:cosC = x:y:2?    

©Mathematics Leagues, Inc.

#6   Two cylindrical cans have the same volume.  The height of one can is triple the height of the other.  If the radius of the narrower can is 12 units, how many units are in the length of the radius of the wider can?  Express your answer in simplest radical form. 

©NCTM