**11 Algebra Stem Lessons from NASA**

These **“Algebra 1 and 2 – Exploring Space Through Math” STEM lessons** are the gateway course to the entire high school mathematics curriculum and is essential for success in high school science courses. The first 8 algebra lessons emphasize linear and quadratic functions. The last 3 lessons give students the opportunity to make connections between algebra and geometry and use one to help solve the other. All of the answers to the algebra problems are shown in the Educator editions. Some of these algebra lessons request students to be familiar with using a calculator, such as the Texas Instruments Nspire.

**SUIT YOURSELF**

**Key Topics:** slope, linear equations, systems of linear equations, x-intercept, y-intercept

Astronauts wear a spacesuit when they leave the pressurized vehicle to perform spacewalks. Some of the key features of the spacesuit are breathable air and heating and cooling control. Students will perform a brainstorming activity to create critical components of a spacesuit. Students will also evaluate the oxygen usage of two astronauts performing a spacewalk using linear equation concepts.

Students will:

- identify slope and the effects of a change in slope, and determine what slope means in a problem situation;
- find the x-intercept, y-intercept, and determine what they represent in a problem situation;
- create linear equations given y-intercept and slope;
- solve linear equations and systems of linear equations using the substitution method and the graphing calculator; and
- work in cooperative learning groups to communicate mathematical ideas in a team environment.

**Lesson Files:**

- Suit Yourself Educator Edition
- Suit Yourself Student Edition
- Video: STS-126 Spacewalkers at Work (10.01 min, 24.4 mb)
- Video: Preparing for a Spacewalk (3.48 min, 20.1 mb)
- Video: Interview with Amy Ross, Spacesuit Engineer (6.19 min, 34.1 mb)

**EXERCISING IN SPACE**

**Key Topic:** Slope, linear equations, direct variation, independent and dependent variables, different representations of a function

Students will identify a direct variation, solve linear equations, and create tables based on the exercise equipment provided for astronauts on long duration missions on the International Space Station (ISS) in order to maintain their fitness to perform mission objectives and to return to Earth without serious health complications.

Students will:

- identify direct variation from ordered pairs by calculating the constant of variation;
- calculate slope from two points using the slope formula;
- determine independent and dependent variables;
- solve linear equations; and
- create tables.

*Prerequisites: Students should have prior knowledge of direct variation, the constant of variation, linear functions, different representations of a linear function, the properties of a linear function, calculating slope, and solving linear equations.*

**Lesson Files:**

**LOST IN SPACE: BONE DENSITY**

**Key Topic:** Linear Equations and Functions

Students will explore slope and y-intercept and solve linear equations while investigating the risks of increased loss of Bone Mineral Density, or BMD, when the human body is in the reduced gravity of space compared to Earth’s 1 *g* environment.

Students will:

- explore slope and the effects of a change of slope;
- recognize slope and y-intercept from key words;
- identify the y-intercept and interpret its meaning in a real world situation;
- write linear equations in slope-intercept form;
- calculate values using percents and proportional relationships;
- solve linear equations; and
- create tables from words.

*Prerequisites: Students should have prior knowledge of functions, different representations of a linear function, properties of a linear function, and slope intercept form.*

**Lesson Files:**

**SPACE SHUTTLE ASCENT: ALTITUDE VS. TIME**

**Key Topic:** Quadratics

Students will be asked to create scatter plots and find quadratic regression equations using mission data on the altitude of the space shuttle during the first two minutes of the ascent phase.

Students will:

- create scatter plots from a data table;
- determine correlation and interpret its meaning;
- find quadratic regression equations; and
- use a function to find the altitude for times not shown in the table.

*Note: This problem is related to the Algebra 1 problem in this series, Space Shuttle Ascent: Mass vs. Time.*

**Lesson Files:**

- Space Shuttle Ascent – Altitude vs. Time Educator Edition
- Space Shuttle Ascent – Altitude vs. Time Student Edition
- Video: STS-121 Shuttle Launch
- Google Earth Ascent-Trajectory Tour (KMZ)
*(Note: This file requires Google Earth to be installed on the users computer. The application is available for download at earth.google.com.)*

**ASCENT: 50 SECONDS TO MECO**

**Key Topic:** Domain and range, independent and dependent variables, characteristics of a function

Students will interpret velocity and acceleration graphs from the ascent phase of a space shuttle flight (8.5 minutes), and focus on the last 50 seconds before Main Engine Cut-Off, or MECO, to identify a linear function.

Students will:

- determine independent and dependent variables;
- identify domain and range;
- interpret graphs and tables;
- identify functions; and
- use tables to determine the function rule.

*Prerequisites: Students should have prior knowledge of the characteristics of functions and be able to identify functions from tables and graphs.*

**Lesson Files:**

**SPACEWALKING**

**Key Topics:** slope, linear regression, linear equations, y-intercept

Aspects of spacewalks performed on the International Space Station are monitored by an Extra-Vehicular Activities officer. The pressurized spacesuit worn by astronauts during a spacewalk is officially known as an Extra-vehicular Mobility Unit, or EMU. One of the key components on the EMU is breathable air. Students will use previous oxygen usage data from two astronauts to predict if these astronauts can complete an upcoming spacewalk.

Students will:

- write a regression equation and interpret the meaning of the slope and y-intercepts in the context of the problem;
- make predictions based on the correct mathematical models; and
- solve linear equations.

**Lesson Files:**

*Note: This activity requires using the TI-Nspire calculator.*

- Spacewalking TI-Nspire Educator Edition
- Spacewalking TI-Nspire Student Edition
*Note: The following files are specific for Texas Instrument Nspire calculators*:

**WEIGHTLESS WONDER**

**Key Topic:** Quadratic Functions

Students will investigate the characteristics of quadratic functions to solve real-world problems involving the parabolic flights of NASA’s Weightless Wonder jet.

Students will:

- solve quadratic equations and evaluate and graph quadratic functions;
- find the maximum, the y-intercept, the x-intercepts, and interpret their significance; and
- determine the effects of parameter changes on the graph of an quadratic equation.

*Prerequisites: Students should have prior experience working with quadratic equations and the properties of a parabola.*

**Lesson Files:**

**Files for use with the TI-84 Plus calculator**:

**Files for use with the TI-Nspire calculator:***Note: The following files are specific for Texas Instrument Nspire calculators*:

- Video: NASA Reduced Gravity Student Flight Opportunity (13.42 min, 36.8 mb)

**SPACE SHUTTLE ASCENT: MASS VS. TIME**

**Key Topic:** Modeling data with linear regression equations

Students will be asked to create scatter plots and find linear regression equations using mission data on the mass of the space shuttle during the first two minutes of the ascent phase.

Students will:

- create scatterplots from a data table;
- determine correlation and interpret its meaning;
- find linear regression equations;
- find the slope and y-intercept from a linear equation; and
- communicate the meanings of slope and y-intercept as they relate to a real-world problem.

*Prerequisites: Students should have prior knowledge of scatter plots, types of correlations, linear equations (slope and y-intercept) and linear graphs. Students should also have experience using a graphing calculator or spreadsheet application to create scatter plots and to find linear regression equations.*

*Note: This problem is related to the Algebra 1 problem in this series, Space Shuttle Ascent: Altitude vs. Time.*

**Lesson Files:**

**Files to use with the TI-84 Plus calculator:**

**Files to use with the TI-Nspire calculator:***Note: The following file**are specific for Texas Instrument Nspire calculators*:

- Video: STS-121 Shuttle Launch (3.23 min, 9.4 mb)

**LIGHTS ON THE INTERNATIONAL SPACE STATION**

**Key Topics:** Power functions with negative exponents

The Lighting Environment Test Facility, or LETF, at NASA Johnson Space Center in Houston, Texas, investigates and evaluates proposed lighting systems for use on space vehicles. Lighting systems enhance the crew’s direct and indirect viewing ability during spaceflight. Students will perform a hands-on activity to explore the inverse relationship of illumination to distance. Students will then go on to calculate the number of lights needed in a module on the International Space Station.

Students will:

- analyze data from a simulation;
- model data from a simulation using a graphical and algebraic approach; and
- apply the measure of illumination,
*lux = Candela / m*, to various situations.^{2}

**Lesson Files:**

*Note: This particular activity requires using the TI-Nspire calculator:*

**Files for use with the TI-Nspire calculator:***Note: The following file is specific for Texas Instrument Nspire calculators*:

**NEWTON’S COOL IN THE POOL**

**Key Topics:** Exponential and logarithmic functions, Newton’s Law of Cooling

NASA’s Neutral Buoyancy Laboratory, or NBL, is the largest indoor pool in the world. Astronauts use the NBL for training and refining spacewalks. The pool holds over six million gallons of water at an average temperature of 86°F to minimize the potential effects of hypothermia on astronauts and divers. Students will analyze the temperature change in the pool after a power outage using Newton’s Law of Cooling.

Students will:

- analyze temperature-loss data graphically;
- use Newton’s Law of Cooling to predict temperature loss;
- solve the Newton’s Law of Cooling formula for the exponential constant of cooling (k); and
- determine the time required for tank temperature to equalize with room temperature.

**Lesson Files:**

*Note: This particular activity requires using the TI-Nspire calculator:*

**Files for use with the TI-Nspirre calculator:***Note: The following files are specific for Texas Instrument Nspire calculators*:- Video: Fluid Dynamics – What a Drag!

**COMMUNICATIONS AND THE LUNAR OUTPOST**

**Key Topic:** Pythagorean Theorem, arc length, inverse tangent

Students will apply mathematics formulas to calculate various geometric measures in the relationships between the height of a lunar communication tower and the tower’s communications range.

Students will:

- use algebraic properties to solve equations for a given variable;
- apply formulas to calculate various geometric measures; and
- analyze data to determine a solution to a real life problem.

*Prerequisites: Prior to this activity, students should have had experiences applying formulas. Students should be familiar with using calculators in evaluating formulas and have a basic knowledge of circles, trigonometric functions, and point of tangency.*

**Lesson Files:**

- Communications and the Lunar Outpost Educator Edition
- Communications and the Lunar Outpost Student Edition

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*-love learning -your best ed lessons guide, Scott*

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