Introduction ||The Golden Greek Face||Colors of M&Ms||Illusions||VT Standards||Resources|| Extensions||Rubric||Worksheets||
Introduction ||The Golden Greek Face||Colors of M&Ms||Illusions||VT Standards||Resources|| Extensions||Rubric||Worksheets||
Our first task is part of A Mathematical Mystery Tour and will beThe Golden Ratio Activity on the web site http://www.markwahl.com/golden-ratio.htm.
The purpose of this activity is to see if your measurements, correct to the nearellimeter (tenth of a centimeter), correspond to the Golden Ratio of 1.618
Process for the Golden Ratio Activity
You will need: calculator, metric ruler (measures to mm), face picture (found in the crate with your folder)
Follow the directions on the "Finding the Gold" activity sheet.
Our second task is going to involve bags of different types of M&Ms.
The web site http://www.baking.m-ms.com/ is the home of "M&M's Network" and it has many tidbits of information about the candies.
Process for M&Ms Activity.
You will need: "M&M's Activity" from the crate
Bag of M&Ms in ziploc bag and be sure to note the variety.
Count the number of different colors of M&Ms in a package and then figure the total count of M&Ms in the bag. Figure the percent of each color. Please be sure to keep the M&Ms in the zip lock bags as you count the different colors so that others will be able to take a successful count.
http://mathforum.com/dr.math/problems/graupn12.15.html to see if your percentages match those expected.
Our final task will involve illusions. Take a look at the following website to see how perceptions can differ. http://www.geocities.com/SiliconValley/Orchard/2704/optical1.html
With the activity for this task we will take a look at how we perceive volume.
Process for Illusions:Two activities are involved with this task.
(Graphic of three successive cylinders each ½ the height and twice the circumference of the previous one.)
1 Cylinders:
The first is to take a standard sized sheet of paper and tape the short edges together to form the lateral surface of a cylinder. Take a second sheet of the same sized paper and cut it in half with a cut parallel to the longer edges. Tape the short ends of both pieces together to form the lateral side of a new cylinder whose height is half that of the previous one and whose circumference is twice as long. Continue by cutting a same sized sheet in fourths parallel to the long edges, then tape the four long pieces together to form the lateral surface of a new cylinder whose height is half of the previous one and whose circumference is double. Set the cylinders on a table and nest them so the tallest one in the center each consecutive one is the next tallest.
(problem was take from : NCTM News Bulletin, February 2000, Volume 36, Issue 7)
Take the worksheet "Cylinders" from the crate and answer the questions about the above cylinders.
2 Circumference
You will need: "The Circumference of a Circle"
Four objects in which you can see and measure circles
Tape measure
Peers
Field of Knowledge
7.7 Geometric and Measurement Concepts
a Solve problems by showing relationships between figures
aa Model situations geometrically to formulate and solve problems
b Examine and compare real objects and abstract figures by one-,
two- and /or three-dimensional features
bb Understand the relationships, properties and measures within and among one-, two-, and three-dimensional geometric objects
e Select and use an appropriate unit (standard or non-standard) with which to measure, according to the properties, size, and use of the quantity to be measured
ee Recognize the differences between measurements of length, area, and volume, and the corresponding uses of units, square units and cubic units
Learning Opportunities
D. Connection
D1 Interdisciplinary Connections
d. Opportunities to make connections among skills, content and concepts within a discipline
D2 Relevance
d. Inclusion of multiple perspectives
1. The University of Chicago Mathematics Project, Transitions Mathematics by
Zalman Usiskin, Cathy Hynes Feldman, Suzanne Davis, Sharon Mallo, Gladys Sanders, David Witonsky, James Flanders, Lydia, Susan Porter, Steven S. Viktora,
Publisher Scott Foresman Addison Wesley 1998
2. Internet
3. Ed Barry
4. NCTM News Bulletin, February 2000, Volume 36, Issue 7
5. Peers - thank you
6. Dittos and materials to accompany the processes.
If time had not been such a limiting factor the original purpose of this web quest was to acquaint students with real life situations and especially professions which use ratios and proportions. I would like to list some of the sites I discovered and recommend:
Two sites by SCORE Mathematics:
Buying My First Car http://score.kings.k12.ca.us/lessons/firstcar.htm
At the Ballpark http://score.kings.k12.ca.us/lessons/ballpark
Indiana University :
Ratio - Wheels in Motion http://www.indiana.edu/~atmat/units/ratio/ratio_s2.htm
Scale Drawings
ArchitectureCreate a Co-op City http://www.co-opcity.com/p10.htm
Measuring the Earth http://ericir.syr.edu/Virtual/Lessons/Mathematics/Geometry/GEOooo4.html
Mathematics Experiences Through Image Processing (METIP)
http://www.cs.washington.edu/research/metip/metip.html
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Getting Started
Access WebQuest
Identify the three tasks/processes and have corresponding materials
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Almost There
Some work done on all of the three tasks/processes
Minimum of 60% accuracy or it is expected that you will correct the work |
Met the Standard
Tables, charts and calculations done for the three tasks/processes
Successful completion requires that all tables, charts and questions be researched and answered With a minimum of 85% accuracy |
Exceeded the Standard
All of the criteria for "Met the Standard" as well as correct units identified and labeled.
Communication on the worksheets is complete and legible
Materials have been used in a courteous and replaced so others can access them
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Name ___________________
Name ________________________________
You will need: "M&M's Activity" from the crate
Bag of M&Ms in ziploc bag and be sure to note the variety.
Count the number of different colors of M&Ms in a package and then figure the total count of M&Ms in the bag. Figure the percent of each color. Please be sure to keep the M&Ms in the zip lock bags as you count the different colors so that others will be able to take a successful count.
Varieties: Baking Bits, Plain, Peanut, Peanut Butter, or Almond
You only need to do a count for one variety.
|
Color |
Count |
Fraction representing amount of M&Ms which are this color |
Percentage representing amount of M&Ms which are this color |
Percentage EXPECTED in an average bag of this variety |
Were your percentages within 5% of what was expected ?
_________________________ Explain .
How are percentages like ratios ?
Name ____________________________
Cylinders:
The first is to take a standard sized sheet of paper and tape the short edges together to form the lateral surface of a cylinder. Take a second sheet of the same sized paper and cut it in half with a cut parallel to the longer edges. Tape the short ends of both pieces together to form the lateral side of a new cylinder whose height is half that of the previous one and whose circumference is twice as long. Continue by cutting a same sized sheet in fourths parallel to the long edges, then tape the four long pieces together to form the lateral surface of a new cylinder whose height is half of the previous one and whose circumference is double. Set the cylinders on a table and nest them so the tallest one in the center each consecutive one is the next tallest.
( This problem was take from : NCTM News Bulletin, February 2000, Volume 36, Issue 7)
(Graphic of three cylinders each successive one being ½ as tall and twice as big around)
Make a prediction as to whether each of these cylinders will hold the same amount.
Why or why not?
When you are filling a 3-D space are you using area or volume?
How do you calculate the volume of a cylinder?
Where in your book can you find the formula?
What is the formula for the area of the base of a cylinder?
Where in your book can you find the formula?
Name _________________________________
Materials: Minimum of four objects in which you can see and measure around circles
Measuring Tape
Groups preferably of two and not more than three
Fill in the table below.
1. List the objects you have chosen.
2. Measure the diameter, longest distance across the circle, to at least two decimal places. Each person should do their own measurements.
(Use page 34 of your book if you need assistance changing fractions to decimals.)
3. Measure the circumference, distance around each circle, to at least two decimal places. Each person should do their own measurements.
4. For each object, then compare them as a group. Calculate the ratio of circumference/diameter and round to the nearest two decimals. Each person should do their own measurements
5. Within your group calculate the average ratio.
6. Fill in the table below
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Object |
Diameter |
Circumference |
Ratio of circumference divided by the diameter |
Average ratio found in your group for this object |
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1 |
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2 |
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3 |
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4 |
7. Average the values that you have in the last column of the above table.
Sum ________________ Average _________________
8. As a group decide which of the following is the correct choice.
As a circle gets larger, the ratio of the circumference to the diameter
a) becomes larger
b) stays about the same
c) becomes smaller
9. If the ratio becomes larger or smaller how much larger or smaller does it become? ______________________________________
10. If the ratio stays the same, about what number does it equal? ___________________________________________
11. Do any of these relate to pi? _____________________________________