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)

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.

 

Abstract

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 men on the MoonApollo Command Module

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 landerand 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 IAres 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 StandardsNoted 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 RatioThe concept of ratio is fundamental to

understanding how two quantities vary proportionally.

A Ratio as a ComparisonOne 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 KnowWhat 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 ExampleExample

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 ExampleNikita 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

What are proportions?

An equation stating that two ratios are equivalent.

Term to Know

4 girls

2 boys

x

100 %

2 boys x 400% girls

2 boys 2 boys

x

=

=

= 200 % more girls than boys

Example of Proportion

=

Apply What You Have Learned:

You have 4 space vehicles and 1 famous landmark. FIND THEIR RATIOS

NASA’s Exploration Launch ArchitectureNASA’s Exploration Launch Architecture

364ft

184 ft

321 ft 305 ft358 ft

Apollo Saturn V

Ares I

Space Shuttle

Ares V

Statue of Liberty

Ratios RatiosSaturn V to 364:305 364/305Statue of LibertyShuttle to 184:305 184/305Statue of LibertyAres I to 321:305 321/305Statue of LibertyAres V to 358:305 358/305Statue of Liberty

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 IncreaseOriginal 184New Amount 321 Increase 137Fraction 137/184Decimal Number 0.74Percent 74 %

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

Finding Percent DecreaseOriginal 358New Amount 184 Increase 174Fraction 174/358Decimal Number 0.49Percent 49 %

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

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

Term to Know

Formula to find the area of a circle?

A = πrA=area r =radius

π = 3.14

2

12.795 feet

Apollo Command Module

Area of Apollo Command Module

12.795 feet

A= πr

A= π(6.5 ft)

A= π42.25 ft

A= 133 ft

2

2

2

2

Orion Crew Module(NASA Concept)

Orion Crew Module(NASA Concept)

16.404 feet

16.404 feet

Area of Orion Crew Module

A= πr

A= π(8 ft)

A= π64 ft

A= 201 ft

2

2

2

2

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 20

New Amount 32

Increase 12

Fraction 12/32

Decimal Number 0.38

Percent 38%

WE’RE GOING BACK TO THE MOON!!

Langley Research Center

NASA’s Vision/Goals

Will you be the next NASA astronaut, engineer,

or scientist?

ConclusionThe 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?