Welcome to Corning, New York!  Our little city is nestled within the rolling hills of the Finger Lakes Region.  Corning has a population of about 11,000 people and is home to the famous Corning Museum of Glass.  Here you can see amazing glass shows and watch the “master glassblower gather, shape, blow, and transform molten glass into a sparkling vase or fanciful fish.”  The City of Corning is also home to Corning Inc. a Fortune 500 Company that invented fiber optics.

Where or where can math be found in our little City of Corning?

First Stop on the Trail (Time is 6:51 A.M.)

Our journey should not begin until we have the most important meal of the day, Breakfast

at Crystal City Bakers

Question:  Besides counting each doughnut individually what is another way to determine just how many doughnuts there are on this tray?

The table below illustrates what Crystal City Bakers utilizes to make a batch of their fresh baked bread.

If the bakers use all of the contents listed in the table above, how many loaves of bread can they make if each loaf weighs 1pound and 5 ounces?

(Hint: You may need to find out what one loaf of bread weighs in Ounces.)

We sure did enjoy our fresh baked doughnuts, cold milk, and hot coffee before we got back on the Math Trail.

Special thanks to Greg and the very friendly

staff at Crystal City Bakers for letting us

come through their kitchen

Hey, if we arrived at Crystal City Bakers at 6:51am and left at 7:46am, what was our elapsed time at Stop #1?

Second Stop on the Trail:  Little Joe (7:57am)

    Does anybody know where I can meet 

A.  If I am 4 feet and 9 inches tall, how many ME’S will it take to reach the top of Little Joe?

B.  What is the perimeter of the base of Little Joe if the length of one side is 3.5

           ME’S?

   C.  What would I have to do to find the exact perimeter of the base of Little Joe?

  Hey, if we arrived at Little Joe’s at 7:57am and left at 8:12am, what was our elapsed time at Stop #2?

Third stop on the Math Trail: Corning Headquarters (8:14am)

A.  What would I have to do to find the line of symmetry in the structure above?   (Hint:  Look very closely at what I am pointing to on the ground.)     B.  Does the line of symmetry in this art work     travel horizontally or vertically?  How do you know?

Let’s keep looking around here

at Corning Headquarters and see what else we can find.

Interesting, but what is it?

Oh, a Time Capsule

C.   If I am 12 years old now, how old will I be when this Time Capsule will be opened?

I wonder what is inside.

I am now leaving the very symmetrical Corning Headquarters at 8:53 am.  If I arrived at 8:14am what was my elapsed time at Stop #3

 Fourth stop on the Trail was at the Corning Museum of Glass  (Time is 8:20am)

A.  If my arm is 2.5 feet long and it is equal to the radius of the larger circle then what is the circumference of the circle?

B.  Looking at the smaller center circle only, if the diameter is 15.7 inches long, then what is the area and circumference of this circle?

We spent a wonderful morning exploring in the CMOG (Corning Museum of Glass).

We arrived at 8:20am and left at 11:36am what was our elapsed time at stop #4?

Solutions to problem 1:

 A.       Elapsed Time:                  7:46 am            46   minutes after 7:00                                                                                          6:51 am            +9   minutes to round up to 7:00

 55 Minutes is the Total Elapsed Time

B.      If the bakers use all of the contents listed in the table above, how many loaves of bread can they make if each loaf weighs 1pound and 5 ounces?

Solutions to Problem 2:

1. If I am 4 feet and 9 inches tall, how many ME’S will it take to reach the top of Little Joe?

ME     4 feet = 48 inches                                Little Joe     185 feet

           + 9 inches                                                      x  12 inches

             57 inches total                                            2220 inches total

2220 ÷ 57 = 38.94

     About 39 ME’S

    B.   What is the perimeter of the base of Little Joe if the length of one side is 3.5 ME’S?

                              3.5 x 4 = 14 ME’S

C.  Elapsed Time:                   7:57 am     + 3 minutes to round up to 8:00

                                             8:12 am    +12 minutes after 8:00

                                           15 Minutes

Solutions to Problem 3:

     A.       Elapsed Time:         8:53 am

            −      8:14 am

                       39 Minutes

            B.       To find the line of symmetry of the structure, focus on the squares on the ground and notice    that there is a line that goes directly down the center of this structure and each half is an exact mirror reflection of each other.

C.       The line of symmetry of this figure has to vertical because of the illustration of the vase in the center.

D.       If the capsule is opened in 2051 and I am 12 years old now I will be 59 years old when it is opened.

2051    

         −2004

     47 years + 12 = 59 years young

Solutions to Problem 4:

A.  2.5 ft. = Radius       Diameter then will be 2.5 x 2 = 5 feet

Circumference = Diameter x π             C = 5 x 3.14

                                                                   15.7 feet

B.  Area = r² x π                                                       Circumference = D x π

      Diameter ÷ 2 = Radius                                                   C = 15.7 inches x 3.14

     15.7 ÷ 2 = 7.85 inches                                                  Circumference = 49.29 inches

    7.85² x 3.14 = 24.33 in.²

            Area = 24.33 inches ²

C.       Elapsed Time:

                                   11:36 am

                                   −8:20 am

                                        3 hours and 16 minutes of fun at CMOG

New York State Standards that were met for this little walk through Corning.

Mathematics STANDARD 3

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

Key Idea: Students use MATHEMATICAL REASONING to analyze mathematical situations, make conjectures, gather evidence, and construct an argument.

Key Idea: Students use NUMBER SENSE AND NUMERATION to develop an understanding of multiple uses of numbers in the real world, use of numbers to communicate mathematically, and use of numbers in the development of mathematical ideas.

Key Idea: Students use MATHEMATICAL OPERATIONS and RELATIONSHIPS among them
to understand mathematics.

Key Idea: Students use MATHEMATICAL MODELING/MULTIPLE REPRESENTATION to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.

Key Idea: Students use MEASUREMENT in both metric and English measure to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data.

Key Idea: Students use PATTERNS and FUNCTIONS to develop mathematical power, appreciate the true beauty of mathematics, and construct generalizations that describe patterns simply and efficiently.