Applying the National Aeronautics and Space Administration NASA ConceptsMission to Americas Grade Si

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• Applying the National Aeronautics and Space
  Administration (NASA) Concepts/Mission to
  Americas Grade Six Mathematics Standards
  Traveling Back to the Moon
• With NASAs Digital Learning Network (DLN)

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Abstract
The primary focus of this research was to
develop a new NASA Digital Learning Network
module that was mathematically based and tied to
NASA concepts. This world of interactive learning
with NASAs DLN was available to teachers and
students to enhance learning about our home
planet. Objectives of this module applied Six
Grade Mathematics Standards of ratio and
proportions, scaling, area, and volume to NASAs
space vehicle transportation systems that will
return to the moon by 2020. The module educated
six grade students on how America will send a new
generation of explorers to the moon aboard NASAs
Orion crew exploration vehicle. The mathematics
team reviewed results of faculty and student
research projects to identify sources used in the
mathematics preparation of children at the six
grade level.  Educational lessons were produced
that incorporated mathematical concepts from the
data collected. Thus, this project was designed
to build on the curiosity and enthusiasm of
children as related to the study of mathematics. 
Appropriate mathematical experiences were
designed to challenge young children to explore
ideas related to data analysis and probability,
measurement, mathematical connections, algebraic
concepts, and numerical operations.  The success
of this research produced results that allowed
six grade students to experience learning linked
to NASA exploration in future years. The students
also used age-appropriate mathematical
calculations to fully understand related
processes. Participants in this newly-developed
DLN activity aided NASA in calculating the
surface areas, obtaining measurements of models,
and using proportions to discover how why NASA
scientists have constructed the Orion, Ares I,
and Ares V vehicles.  
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The History of Space Exploration
Apollo 11 was the first manned mission to land
on the Moon and return safely. The Saturn V
rocket launched, July 16, 1969 carrying Neil
Armstrong, Michael Collins, Edwin Buzz Aldrin,
Jr. They arrived there in a lunar lander, which
had been propelled into orbit around the Moon as
part of the Apollo 11 space flight.
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The History of Space Exploration
On July 20, commander Neil Armstrong stepped out
of the lunar module and took one small step in
the Sea of Tranquility, calling it a giant leap
for mankind. Innovation and improvisation were
necessary, but there were five more missions that
went on to land on the moon.
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The History of Traveling Back to the Moon
The Moon 1st men on the Moon
Apollo Command Module Apollo Mission Patch
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The 1st Manned Mission on the Moon
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• Now its time to go back to the Moon

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Future Space Exploration

• NASA now has plans to return humans to the Moon
  and eventually to Mars.
• NASA's Constellation Program is developing a
  space transportation system that is designed to
  return humans to the moon by 2020.

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Components for Future Exploration

• The program components to be developed
• include the Orion crew exploration vehicle,
• the Ares I crew launch vehicle, the Ares V
• cargo launch vehicle, the Altair lunar lander
• and other cargo systems.

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Why go back to the Moon?

• Want to colonize (develop Moon colonies)
• To live
• Survive on the moon based upon the found results
  of the history and possible descendants of Mars.

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Ares I

• Ares I is an in-line, two-stage rocket
  configuration topped by the Orion crew vehicle
  and its launch abort system.
• The Ares I will carry crews of four to six
  astronauts
• and it may also use its 25-ton payload capacity
  to
• deliver resources and supplies.
• The versatile system will be used to carry cargo
• and the components into orbit needed to go to
  the
• moon and later to Mars.

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Ares V

• The Ares V can lift more than 286,000 pounds to
  low Earth orbit and stands approximately 360 feet
  tall.
• The versatile system will be used to carry cargo
  and the components into orbit needed to go to the
  moon and later to Mars.

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Ares I and Ares V
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Proportional Reasoning

• The concept of ratio is directly related to the
  ideas of rational numbers, percents, and
  proportions.
• All of these concepts are fundamental to the
  development of mathematics and various
  applications in real-life situations.

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Connection to the NCTM Principles and
Standards

• Noted in the National Council of Teachers of
  Mathematics Principles and Standards,
  proportional reasoning is fundamental to much of
  middle school mathematics. Proportional
  reasoning permeates the middle grades curriculum
  and connects a great variety of topics. The
  study of proportional reasoning in the middle
  grades should enable students to
• Work flexibly withpercents to solve problems
• Understand and use ratios and proportions to
  represent quantitative relationships and
• Develop, analyze, and explain methods for solving
  problems involving proportions, such as scaling
  and finding equivalent ratios.
• Reasoning and solving problems involving
  proportions play a central role in the
  mathematical processes emphasized in the NCTM
  Principles and Standards. The concept of ratio
  is fundamental to being able to reason
  proportionality.
• In grades 6-8 students investigate proportional
  reasoning and properties of proportions. They
  learn the concept of percent and its connection
  to ratio. They solve problems involving percents
  and different types of interest problems.

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Understanding Ratios

• The Concept of Ratio
• The concept of ratio is fundamental to
  understanding how two quantities vary
  proportionally.
• A Ratio as a Comparison
• One interpretation of ratio is that it compares
  two like quantities.

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Focal Points

• Curriculum Focal Points and Connections for Grade
  6
•  
• The set of three curriculum focal points and
  related connections for mathematics in grade 6
  follow. These topics are the recommended content
  emphases for this grade level. It is essential
  that these focal points be addressed in contexts
  that promote problem solving, reasoning,
  communication, making connections, and designing
  and analyzing representations.
•  
• Grade 6 Curriculum Focal Points
• Number and Operations Developing an
  understanding of and fluency with multiplication
• and division of fractions and decimals
• Students use the meanings of fractions,
  multiplication and division, and the inverse
  relationship
• between multiplication and division to make
  sense of procedures for multiplying and dividing
  fractions and explain why they work. They use the
  relationship between decimals and fractions, as
  well as the relationship between finite decimals
  and whole numbers (i.e., a finite decimal
  multiplied by an appropriate power of 10 is a
  whole number), to understand and explain the
  procedures for multiplying and dividing decimals.
  Students use common procedures to multiply and
  divide fractions and decimals efficiently and
  accurately. They multiply and divide fractions
  and decimals to solve problems, including
  multistep problems and problems involving
  measurement.
•  

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Focal Points cont

• Number and Operations Connecting ratio and rate
  to multiplication and division
• Students use simple reasoning about
  multiplication and division to solve ratio and
  rate problems (e.g., If 5 items cost 3.75 and
  all items are the same price, then I can find the
  cost of 12 items by first dividing 3.75 by 5 to
  find out how much one item costs and then
  multiplying the cost of a single item by 12). By
  viewing equivalent ratios and rates as deriving
  from, and extending, pairs of rows (or columns)
  in the multiplication table, and by analyzing
  simple drawings that indicate the relative sizes
  of quantities, students extend whole number
  multiplication and division to ratios and rates.
  Thus, they expand the repertoire of problems that
  they can solve by using multiplication and
  division, and they build on their understanding
  of fractions to understand ratios. Students solve
  a wide variety of problems involving ratios and
  rates.
•  
• Algebra Writing, interpreting, and using
  mathematical expressions and equations
• Students write mathematical expressions and
  equations that correspond to given situations,
  they
• evaluate expressions, and they use expressions
  and formulas to solve problems. They understand
  that variables represent numbers whose exact
  values are not yet specified, and they use
  variables appropriately. Students understand that
  expressions in different forms can be equivalent,
  and they can rewrite an expression to represent a
  quantity in a different way (e.g., to make it
  more compact or to feature different
  information). Students know that the solutions of
  an equation are the values of the variables that
  make the equation true. They solve simple
  one-step equations by using number sense,
  properties of operations, and the idea of
  maintaining equality on both sides of an
  equation. They construct and analyze tables
  (e.g., to show quantities that are in equivalent
  ratios), and they use equations to describe
  simple relationships (such as 3x y) shown in a
  table.

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Focal Points Cont

• Connections to the Focal Points
•  
• Number and Operations Students work in dividing
  fractions shows them that they can express the
  result of dividing two whole numbers as a
  fraction (viewed as parts of a whole). Students
  then extend their work in grade 5 with division
  of whole numbers to give mixed number and decimal
  solutions to division problems with whole
  numbers. They recognize that ratio tables not
  only derive from rows in the multiplication table
  but also connect with equivalent fractions.
  Students distinguish multiplicative comparisons
  from additive comparisons.
• Algebra Students use the commutative,
  associative, and distributive properties to show
  that two expressions are equivalent. They also
  illustrate properties of operations by showing
  that two expressions are equivalent in a given
  context (e.g., determining the area in two
  different ways for a rectangle whose dimensions
  are x 3 by 5). Sequences, including those that
  arise in the context of finding possible rules
  for patterns of figures or stacks of objects,
  provide opportunities for students to develop
  formulas.
• Measurement and Geometry Problems that involve
  areas and volumes, calling on students to find
  areas or volumes from lengths or to find lengths
  from volumes or areas and lengths, are especially
  appropriate. These problems extend the students
  work in grade 5 on area and volume and provide a
  context for applying new work with equations.

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Term to Know

• What are ratios?
• An ordered pair of numbers used to show
  a comparison between like or unlike quantities
• Written x to y, x/y, xy, x
• y (y?0)
• 2 to 3, 2/3, 23, 2
  
  3 (y?0)

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Ratio Example

• Example
• If you have a classroom with 4 girls and 2
  boys
• The ratio of girls to boys is 4/2 or 42.
• The ratio of boys to girls is 2/4 or 24.

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Term to know

• What are equivalent ratios?
• Two ratios are equivalent ratios if their
  respective fractions are equivalent or if the
  quotients of the respective terms are the same.

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Equivalent Ratio Example

• Nikita is planning a party and has to buy soft
  drinks. She estimates that for every 5 people, 3
  will drink diet cola and 2 will drink non-diet
  cola.
• The ratio of diet cola drinkers to non-diet cola
  drinkers is 32.

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Uses of Ratio

• A ratio involving two like quantities permits 3
  types of comparisons (a) part to part, (b) part
  to whole (c) whole to part.

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Examples of Types of Ratios

• If we think in terms of a set of nurses and a set
  of doctors as being the set of medical staff,
  those 3 types of comparisons may be expressed in
  the following ways

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• Part to part
  Nurses to doctors, 6/2 or doctors to nurses, 2/6
  
• Part to whole Nurses to staff, 6/8 or
  doctors to staff, 2/8
• Whole to part
  Staff to nurses, 8/6, or staff to doctors, 8/2

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Term to Know

• What are proportions?
• An equation stating that two ratios are
  equivalent.

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Example of Proportion
4 girls
x


2 boys
100
2 boys x
400 girls

2 boys
2 boys
x

200 more girls than boys
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• Apply What You Have Learned
• You have 4 space vehicles and 1 famous landmark.
  FIND THEIR RATIOS

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364ft
358 ft
321 ft
305 ft
NASAs Exploration Launch Architecture
Apollo Saturn V
Ares V
184 ft
Ares I
Space Shuttle
Statue of Liberty
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• Ratios Ratios
• Saturn V to 364305 364/305
• Statue of Liberty
• Shuttle to 184305 184/305
• Statue of Liberty
• Ares I to 321305 321/305
• Statue of Liberty
• Ares V to 358305 358/305
• Statue of Liberty

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Term to Know

• What is a percent?
• A percent () is a ratio with a denominator of
  100.

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Procedure for finding the Percent Increase or
Decrease

• Step 1 Determine the amount of increase or
  decrease.
• Step 2 Divide this amount by the original
  amount.
• Step 3 Convert this fraction or decimal to a
  percent.

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• Scale Factor is the Percent () of increase or
  decrease
• The number that is multiplied to another to
  equate two things.

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Steps for an increase from
Space Shuttle (184) to Ares I (321)

• Finding Percent Increase
• Original 184
• New Amount 321
• Increase 137
• Fraction 137/184
• Decimal Number 0.74
• Percent 74

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Steps for an decrease from the
Ares V (358) to Space Shuttle (184)

• Finding Percent Decrease
• Original 358
• New Amount 184
• Increase 174
• Fraction 174/358
• Decimal Number 0.49
• Percent 49

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Term to Know

• What is Diameter?
• A straight line joining two points on the
• circumference of a circle that passes through
  the center of that circle.

Diameter
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Term to Know

• What is radius?
• a straight line extending from the center
• of a circle to its edge or from the center
• of a sphere to its surface.
• (1/2 diameter)

Radius
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• Formula to find the area of a circle?
• A pr
• Aarea r radius
• p 3.14

2
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Apollo Command Module
12.795 feet
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Area of Apollo Command Module
2
A pr A p(6.5 ft) A p42.25 ft A 133 ft
2
2
12.795 feet
2
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Orion Crew Module (NASA Concept)
16.404 feet
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Area of Orion Crew Module
2
A pr A p(8 ft) A p64 ft A 201 ft
2
16.404 feet
2
2
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Lunar Excursion Module (Apollo)
20.013 feet
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Lunar Surface Access Module (NASA Concept)
32.152 feet
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Ratio of Apollo Lunar Excursion Module to Ares
Access Module

• Ratio
• 2032 or 32 Ares
• 20 Apollo

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Scale Factor of Apollo Lunar Excursion Module to
Ares Access Module

• Finding Percent of Increase
• Original 20
• New Amount 32
• Increase 12
• Fraction 12/32
• Decimal Number 0.38
• Percent 38

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Langley Research Center
NASAs Vision/Goals
WERE GOING BACK TO THE MOON!!
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• Will you be the next
• NASA astronaut, engineer,
• or scientist?

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Conclusion
The implementation of the NASA Digital Learning
Network provided an interactive element of
learning. It gave insight into NASAs new
mission of placing an individual back on the moon
within the allotted time frame while
simultaneously incorporating the National Council
of Teacher of Mathematics standards or
proportional reasoning within the created lesson.
Both teachers and students alike found it to be
a great way to learn, and applauded it in its
successful incorporation of two very different
elements.
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Future Work
Due to the importance of the new missions, a new
module supporting the newest exploration efforts
had to be developed. Developing an educational
module requires a great deal of research,
knowledge of current NASA missions/explorations,
and the ability to formulate the module to target
various age groups. Suggestions for the future
research of this project are to gear this module
to students in the lower grades, finding the
National Mathematics Standards that are required
for their particular grade level and apply those
mathematical concepts to teach the information
provided in the module. The same method can be
applied for those students in higher-grade levels
to target the mathematical concepts that are
needed and required.
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Questions?