Transcript Slide 1

Applying the National Aeronautics and
Space Administration (NASA)
Concepts/Mission to America’s Grade
Six Mathematics Standards: Traveling
Back to the Moon
With NASA’s Digital Learning Network (DLN)
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 NASA’s
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 NASA’s 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
NASA’s 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.
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.
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.
The History of Traveling Back to the
Moon
The Moon
1st
Apollo Command Module
men on the Moon
Apollo Mission Patch
The 1st Manned Mission on the Moon
Now it’s time to go back to the
Moon…
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.
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.

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.
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.
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.
Ares I and Ares V
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.
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 with…percents 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.
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.
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.
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.
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.
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, x:y, x
y (y≠0)
2 to 3, 2/3, 2:3, 2
3 (y≠0)
Ratio Example

Example
If you have a classroom with 4 girls
and 2 boys:
The ratio of girls to boys is: 4/2 or 4:2.
The ratio of boys to girls is 2/4 or 2:4.
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.
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 3:2.
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.
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:
(a) Part to part:
Nurses to doctors, 6/2; or doctors to
nurses, 2/6
(b) Part to whole:
Nurses to staff, 6/8; or doctors to
staff, 2/8
(c) Whole to part:
Staff to nurses, 8/6, or staff to doctors,
8/2
Term to Know
What are proportions?
An equation stating that two
ratios are equivalent.
Example of Proportion
4 girls
=
x
=
2 boys
100 %
2 boys x
400% girls
2 boys
=
2 boys
x = 200 % more girls than boys
Apply What You Have Learned:
You have 4 space vehicles and 1 famous landmark.
FIND THEIR RATIOS
364ft
358 ft
321 ft
NASA’s Exploration Launch Architecture
305 ft
Apollo
Saturn V
Ares V
184 ft
Ares I
Space
Shuttle
Statue of
Liberty
Saturn V to
Statue of Liberty
Shuttle to
Statue of Liberty
Ares I to
Statue of Liberty
Ares V to
Statue of Liberty
Ratios
364:305
Ratios
364/305
184:305
184/305
321:305
321/305
358:305
358/305
Term to Know

What is a percent?
A percent (%) is a ratio with a
denominator of 100.
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.
Scale Factor is the Percent (%) of increase or
decrease
The number that is multiplied to another to
equate two things.
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 %
Steps for an decrease from the
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 %
Ares
Term to Know

What is Diameter?
Diameter
A straight line joining two points on the
circumference of a circle that passes
through the center of that circle.
Term to Know

What is radius?
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)
Formula to find the area of a circle?
A = πr
A=area
2
r =radius
π = 3.14
Apollo Command Module
12.795 feet
Area of Apollo Command Module
2
A= πr
2
A= π(6.5 ft)
2
12.795 feet
A= π42.25 ft
2
A= 133 ft
Orion Crew Module
(NASA Concept)
16.404 feet
Area of Orion Crew
Module
2
A= πr
2
A= π(8 ft)
16.404 feet
A= π64 ft
2
2
A= 201 ft
Lunar Excursion
Module
(Apollo)
20.013
feet
Lunar Surface Access Module
(NASA Concept)
32.152
feet
Ratio of Apollo Lunar Excursion
Module to Ares Access Module
Ratio
20:32 or
32 Ares
20 Apollo
Scale Factor of Apollo Lunar Excursion
Module to Ares Access Module
Finding Percent of Increase
Original
New Amount
Increase
Fraction
Decimal Number
Percent
20
32
12
12/32
0.38
38%
Langley Research Center
NASA’s Vision/Goals
WE’RE GOING BACK TO THE MOON!!
Will you be the next
NASA astronaut, engineer,
or scientist?
Conclusion
The implementation of the NASA Digital Learning Network™ provided
an interactive element of learning. It gave insight into NASA’s 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.
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.
Questions?