37 NASA STEM & Math Lessons for Advanced High School Students

37 NASA STEM & Math Lessons for Advanced High School Students

These STEM and Math lessons and problems from NASA will challene more advanced high school students and help provide them insight into the limitless array of options in science, technology, engineering and mathematics, or STEM fields. They engage students using real world applications to promote critical thinking and problem-solving on space exploration topics.

These STEM and math problems are for high school students in advanced classes, grades 10-12, and are formatted in a free-response style. Problems are provided for Calculus, Physics, Biology, Chemistry and Statistics. For more STEM, math and advanced lessons and activities, please check out Math, Science and Technology STEM Activities and Lessons from NASA and Mensa For Kids – 83 Lessons, Activities and Guides.

Calculus

Next Generation Spacecraft

Key Topics: Application of Definite Integrals – Determining Volume of a Region (Calculus)

In this real world application, students will use integration to find the volume of the Orion Crew Module – NASA’s newest spacecraft.

Students will:

• use integration to find the volume of a solid generated by a region, R;
• determine the equation of a circle using the standard form and the general form;
• determine the equation of a line using the point-slope form; and
• solve a system of equations with three equations and three unknowns.

Lesson Files:

The Lunar Lander – Ascending From The Moon (Calculus)

Key Topics: Application of Differentiation – Related Rates

In this exploration activity, students will use the application of differentiation – related rates, to solve problems pertaining to the ascent portion of the Lunar Lander.

Students will:

• use the chain rule to find the rates of change of two or more variables that are changing with respect to time; and
• investigate the relationship between the angle of elevation, the rate of change in the angle of elevation and time.

Lesson Files:

Lunar Surface Communications

Key Topic: Differentiation (Calculus)

Future outposts on the moon will require lunar surface equipment to maintain communications with Earth. Students will: use differentiation – chain rule to derive a solution to this space exploration problem.

Students will:

• derive the formula for calculating the line of sight distance to a horizon tangent point;
• derive the distance along a surface to a tangent point; and
• use derivatives to find the rates of change of two or more variables that are changing with respect to distance.

Lesson Files:

Space Shuttle Auxiliary Power Units

Key Topics: Application of Differentiation – Related Rates (Calculus)

This problem focuses on the MMACS flight controller. Students learn about one of his/her duties in monitoring the Auxiliary Power Units of the space shuttle. Students will: apply various calculus concepts including an application of related rates. The focus is on interpretation of the derivative as a rate of change.

Students will:

• analyze graphs to determine the rate of change at specific points; and
• use the chain rule to determine the rate of change of two or more variables that are changing with respect to time.

Lesson Files:

Space Shuttle Guidance, Navigation, And Control Data

Key Topics: Parametric Equations (Calculus)

This problem focuses on the GNC flight controller. Students learn about the state vector that the GNC flight controller monitors and is introduced to the coordinate system that is used in tracking the space shuttle. Students will: analyze a table of data to generate parametric functions.

Students will:

• gain an understanding of the M50 coordinate system;
• write a set of parametric equations based on a table of position coordinates over time; and
• differentiate parametric position functions to determine the velocity and acceleration vectors, as well as the magnitude of the velocity and acceleration.

Lesson Files:

Physics

Lunar Surface Instrumentation

On the lunar surface, environmental sensors and instruments will need to be placed within proximity of a lunar outpost. Students will: work with vector addition to find an answer to this space exploration problem.

Students will:

• add, subtract, and resolve displacement and velocity vectors to determine components of a vector along two specified, mutually perpendicular axes; and
• determine the net displacement of a particle or the location of a particle relative to another.

Lesson Files:

Lunar Surface Instrumentation: Part II

Students will: analyze two different approaches for completing a task based on a number of constraints and will determine the optimal method. Students will: apply vector addition, as well as critical thinking skills.

Students will:

• add, subtract, and resolve displacement using unit-vector notation; and
• evaluate two approaches, apply a set of constraints and choose the best alternative to the problem.

Lesson Files:

Lunar Landing

Key Topic: Equations of Motion and Force (Physics)

Students will: apply equations of motion and force to solve for unknowns in this real world application about human exploration missions to the Moon.

Students will:

• choose a coordinate system best suited to the problem;
• apply equations of motion and force to solve for unknowns;
• determine magnitude and direction of vectors; and
• calculate a spring constant.

Lesson Files:

Weightless Wonder – Reduced Gravity Flights

Key Topic: Equations of Motion (Physics)

Students will: learn about the parabolic flights of NASA’s C9 jet – the Weightless Wonder, as they use equations of motion to derive a solution to a real life problem.

Students will:

• use trigonometric ratios to find vertical and horizontal components of a velocity vector;
• derive a formula describing height of a parabola in terms of time;
• determine vertical and horizontal displacement of trajectory motion; and
• analyze data to derive a solution to a real life problem.

Lesson Files:

ARED – Resistive Exercise In Space

Key Topic: Mechanics, Torque, Simple Harmonic Motion, Pressure (Physics)

The Advanced Resistive Exercise Device, or ARED, is one of the exercise devices astronauts use aboard the International Space Station. ARED uses vacuum cylinders to simulate free weights for resistive exercise that helps astronauts maintain bone and muscle strength while in space. In this activity, students will analyze different aspects of the mechanics of the ARED device.

Students will:

• apply equations of pressure, force, torque, and harmonic motion to solve for unknowns;
• draw a free-body diagram; and
• analyze the design of exercise equipment used in space.

Lesson Files:

Space Shuttle Orbital Docking System

Key Topic: Springs (Physics)

The space shuttle docks and undocks with the International Space Station with the help of the space shuttle’s orbital docking system. This system uses both torsional and compression springs to damp out the energy as these two vehicles essentially collide in space.

Students will::

• analyze the components of the space shuttle and International Space Station docking system;
• evaluate torque and energy; and
• determine work and separation velocity.

Lesson Files:

Space Shuttle Landing

Key Topics: Equations of Motion, Force, Work and Energy (Physics)

This problem focuses on the MMACS flight controller, who monitors the data associated with the landing and deceleration procedures of the space shuttle. Students will: apply equations of motion, force, work and energy and graphically interpret real data.

Students will:

• apply equations of rotational kinematics and dynamics to solve for unknowns;
• apply equations of motion, force, work and energy to solve for unknowns;
• represent a situation graphically; and
• analyze data to derive a solution to a real life problem.

Lesson Files:

Space Shuttle Short Circuit

Key Topics: DC Circuit, Ohm’s Law (Physics)

This problem focuses on the EGIL flight controller, who monitors the electrical systems, fuel cells and associated cryogenics of NASA’s space shuttle. Using a circuit layout from the space shuttle, students will apply Ohm’s law to solve for unknowns.

Students will:

• apply Ohm’s law to solve for unknowns in a DC circuit; and
• analyze data to derive a solution to a real life problem.

Lesson Files:

Space Shuttle Roll Maneuver

Key Topics: Rotational Motion, Dynamics (Physics)

This problem focuses on the GNC flight controller and on the engines used to control the attitude of the space shuttle. Students will: apply integration techniques to evaluate impulse and angular momentum and will evaluate the rotational kinematics, torque and energy associated with a roll maneuver.

Students will: analyze space shuttle schematics and data to:

• demonstrate graph and schematic interpretation skills;
• apply integration techniques to evaluate impulse and angular momentum; and
• evaluate the rotational kinematics, torque and energy associated with a roll maneuver.

Lesson Files:

Space Shuttle Launch Motion Analysis

Key Topics: Equations of Motion, Graphs of Motion (Physics)

This problem focuses on the FDO flight controller and on the ascent of the space shuttle. Students will: use integration techniques as they analyze an acceleration-time graph to determine velocity and displacement.

Students will::

• interpret and construct graphs of motion based on a space shuttle launch from ascent to orbit; and
• apply integration techniques to evaluate acceleration, speed, and distance along a flight trajectory.

Lesson Files:

Training For A New Spacecraft – Center Of Gravity

Key Topics: Center of Gravity (Physics)

The Water Egress and Survival Trainer (WEST) is a replica of Orion, NASA’s next generation spacecraft. WEST is used in the Neutral Buoyancy Laboratory so astronauts can perform what is called egress training, which provides the skills required to exit a vehicle after landing. In this activity, students will evaluate one of many critical properties that must be understood in order to effectively simulate every possible egress scenario following capsule splashdown in any sea state by using their knowledge of physics and center of gravity.

Students will:

• determine the center of gravity (CG) of the Water Egress and Survival Trainer (WEST);
• construct summation of moment expressions for WEST in static equilibrium; and
• explain the engineering behind the experimental set-up designed to measure the CG of WEST.

Lesson Files:

Training For A New Spacecraft – Moment Of Inertia

Key Topics: Moment of Inertia (Physics)

The Water Egress and Survival Trainer (WEST) is a replica of Orion, NASA’s next generation spacecraft. WEST is used in the Neutral Buoyancy Laboratory so astronauts can perform what is called egress training, which provides the skills required to exit a vehicle after landing. In this activity, students will evaluate one of many critical properties that must be understood in order to effectively simulate every possible egress scenario following capsule splashdown in any sea state by using their knowledge of physics and moment of inertia.

Students will:

• derive an expression to determine the moment of inertia (MOI) of the Water Egress and Survival Trainer (WEST);
• relate the period of a torsional pendulum to rotational inertia; and
• explain the engineering behind the experimental set-up designed to measure the MOI of WEST.

Lesson Files:

Key Topic: Atomic physics (Physics)

Outside of the Earth’s protective atmosphere, the International Space Station (ISS) is exposed to ionizing radiation and electromagnetic radiation. Ionizing radiation has so much energy it can literally knock the electrons out of any atom it strikes – ionizing the atom. In this activity, students will analyze the radiation that could cause problems on the International Space Station.

Students will:

• practice and review atomic physics concepts and equations;
• apply Planck’s constant;
• determine the deBroglie wavelength of a proton; and
• analyze the frequency of photons.

Lesson Files:

Biology

Respiration In Space Flight

Key Topics: Evaluating Cellular Energetics; Synthesis and Application of Lab 5 (Biology)

This problem focuses on the EECOM flight controller, who monitors the gas concentrations and pressures within the space shuttle cabin. Students are introduced to the space shuttle’s CO2 removal process and will analyze respiration rates and metabolic activity from graphical data provided. They will relate gas production/consumption to respiration/metabolism and evaluate the physiological impact of changes in O2/CO2 concentrations to various human systems.

Students will:

• recall materials, procedures, and results of required cellular respiration lab;
• analyze respiration rates and metabolic activity from graphical data;
• relate gas production/consumption to respiration/metabolism;
• evaluate physiological impact of changes in O2/CO2 concentrations on various human systems; and
• propose changes needed to maintain O2/CO2 levels for crew health.

Lesson Files:

Microgravity Effects On Human Physiology: Circulatory System

Key Topics: Physiology of the Circulatory System, Application of Lab 10 (Biology)

This problem focuses on the Flight Surgeon and his role in keeping astronauts healthy before, during, and after flight. Students will: examine the effects of gravity on the evolution of form and function in the human circulatory system and will connect space biology and related medical pathologies on Earth.

Students will::

• analyze the effects of external stimuli on the physiological processes of the body;
• apply the concept of form and function to an unfamiliar situation;
• review and recall specific content knowledge for the circulatory system as it relates to blood pressure and cardiac output;
• examine form and function of the heart as muscle tissue rather than an organ;
• examine the effects of gravity on the evolution of form and function in the human circulatory system;
• find the connection between space biology and related medical pathologies on Earth; and
• recognize the risks and hazards associated with space science and the human body.

Lesson Files:

Microgravity Effects On Human Physiology: Skeletal System

Key Topics: Feedback Mechanisms; Application of Lab 1 (Biology)

This problem focuses on the Flight Surgeon and his role in keeping astronauts healthy before, during, and after flight. Students will: apply their knowledge of feedback mechanisms and homeostasis and will evaluate the physiological impact of bone mineral loss to various human systems.

Students will:

• recall materials, procedures, and results of required AP Biology lab 1: Diffusion and Osmosis;
• understand feedback mechanisms and how homeostasis is maintained; and
• evaluate the physiological impact of bone density loss to various human systems.

Lesson Files:

Renal Stone Risk To Astronauts

Key Topics: Diffusion, Osmosis, Homeostasis, Human Physiology (Biology)

Renal stones are small rock-like objects made from deposits of calcium and other minerals that form in the kidneys or urinary tract. Because astronauts are at risk to an increase in bone demineralization when exposed to reduced gravity, this also increases the risk of developing renal stones. In this activity, students will utilize their knowledge of biology and the human body to examine this issue.

Students will:

• review the structure and function of the urinary system, and apply the principles of diffusion, osmosis, and homeostasis to electrolyte and plasma fluid levels within the human body;
• examine the physiological impact of increased blood calcium levels and reduced urine output on the formation of renal (kidney) stones in microgravity environments;
• evaluate hydration, diet, and mineral supplements as countermeasures to renal stone formation; and
• understand the biochemical importance of calcium in human physiology with respect to muscle contractions and voltage-charged action potentials.

Lesson Files:

Related Resources:
ARTICLE: Renal Stone Risk During Spaceflight: Assessment and Countermeasure Validation
This is an experiment that was performed on the ISS. The experiment is explained and an overview of the results is given. Published 3-22-12.

ARTICLE: Strong Bones and Fewer Renal Stones for Astronauts
This is a description of an investigation done on the ISS by HRP at JSC and JAXA using Bisphosphonates as countermeasures to spaceflight induced bone loss. If the medicine were to be effective it could mean that astronauts could spend more time on science by saving some of the time now spent exercising. It would also be valuable in case of exercise equipment failure and for injury or illness. Published 2-23-12.

ARTICLE: Twinkle, twinkle kidney stone: With a push you could be gone
This is a news release from NSBRI about ultrasound technology being used to detect and treat kidney stones. The article goes into the details of how this is done and how the technology could be used in other situations as well. Published 1-31-12.

Preventing Decompression Sickness On Spacewalks

Key Topic: Gas solubility in living systems (Biology)

Decompression sickness is a health risk often associated with underwater diving. Astronauts must also take precautions to avoid decompression sickness that could occur when going on spacewalks. The pressurized spacesuits astronauts wear on spacewalks is significantly lower than the ambient pressure of the International Space Station (ISS). For this reason, astronauts go through a denitrogenation process prior to all spacewalks. In this activity, students will apply principles learned about dissolved oxygen in aquatic ecosystems to evaluate nitrogen solubility in the human body.

Students will:

• recall the concepts, data analyses, and conclusions of AP Lab 12: Dissolved Oxygen and Aquatic Primary Productivity;
• correlate gas solubility and function of vertebrate respiratory systems;
• analyze the effect of pressure on gas solubility from experimental data; and
• • predict the physiological consequence with varying nitrogen and oxygen concentrations.

Lesson Files:

Microgravity Effects On Human Physiology: Immune System

Key Topic: Immune Response (Biology)

The effects of microgravity on human physiology are closely studied. The Immunology Laboratory conducts research on the effects on the human immune system. Students will: learn about some of the implications of spaceflight on the immune response and connect it to classroom learning.

Students will:

• review the structure and function of the immune system and its response to infection;
• examine the effects of microgravity on the suppression of the immune system; and
• evaluate implications of discovering how to control T-cell responses and how it could affect cancer tumor treatments.

Lesson Files:

Chemistry

Space Shuttle Propulsion System

Key Topics: Thermodynamics, Molecular Structure and Bonding (Chemistry)

This problem focuses on the PROP flight controller and his/her duties in monitoring the propellant for the RCS and OMS engines of the space shuttle. Students will: identify the geometric structure, hybridization, and bonding of molecules and evaluate characteristics of reactions to determine the behavior.

Students will:

• identify the geometric structure, hybridization, and bonding of molecules; and
• evaluate the characteristics of reactions to determine their behavior.

Lesson Files:

Cryogenic Storage

Key Topics: Gas Laws (Chemistry)

This problem focuses on the EGIL flight controller, who monitors the electrical systems, fuel cells and associated cryogenics of NASA’s space shuttle. Students will: find volume of gases using the ideal gas law and will create and interpret a phase diagram to explain a real world problem involving the space shuttle.

Students will::

• find the volume of gases using the Ideal Gas Law; and
• create and interpret a phase diagram to explain a real world problem.

Lesson Files:

Fuel Cell Generation

Key Topics: Stoichiometry, Electrochemistry (Chemistry)

This problem focuses on the EGIL flight controller, who monitors the electrical systems, fuel cells and associated cryogenics of NASA’s space shuttle. Students will: find mass and molar ratios of reactants through stoichiometry and use half reactions to determine standard cell potential.

Students will: analyze space shuttle schematics and data to:

• find mass and molar ratios of reactants through stoichiometry; and
• use half reactions to determine standard cell potential.

Lesson Files:

Carbon Dioxide Removal – Stoichiometry

Key Topics: Stoichiometry; Ideal Gas Law (Chemistry)

This problem focuses on the Electrical, Environmental and Communications, or EECOM, flight controller, who monitors the gas concentrations and pressures with the space shuttle cabin. Students apply the Ideal Gas Law and Stoichiometry to determine the number of canisters and mass of LiOH required to remove the CO2.

Students will::

• find mass and molar ratios through stoichiometry; and
• find moles of gas using the Ideal Gas Law.

Lesson Files:

Carbon Dioxide Removal – Thermodynamics

Key Topics: Thermodynamics (Chemistry)

This problem focuses on the Electrical, Environmental and Communications, or EECOM, flight controller and students are introduced to the space shuttle’s CO2 removal process. They will apply several concepts and equations of thermochemistry as they analyze this situation.

Students will::

• find standard enthalpy change using Hess’s Law;
• determine the standard entropy change for a reaction;
• determine the standard free energy change for a reaction;
• use the sign of the standard free energy change to predict the spontaneity of a reaction; and
• determine the equilibrium constant for a reaction.

Lesson Files:

Dietary Impacts Of Astronauts’ Bones

Key Topics: Stoichiometry, Acid-Base Reaction (Chemistry)

Recently the Nutritional Biochemistry Laboratory has been exploring the amino acids in animal proteins and their affect on the Calcium metabolism. Amino acids containing sulfur can create sulfuric acid in the body, which can cause an increase in calcium metabolism. This activity will have students analyze the chemical reaction that occurs in the bone between sulfuric acid and Calcium carbonate and propose a possible avenue for astronauts to decrease bone mineral loss.

Students will:

• determine mass and volume relationship with an emphasis on mole concepts; and
• write acid-base reactions.

Lesson Files:

Generating Water In Space

Key Topic: Stoichiometry, chemical equilibrium, thermodynamics (Chemistry)

Aboard the International Space Station (ISS), human life exists and must be maintained by a well organized and precise life support system. One part of the life support system generates water to be used by the crew members. In this activity students will analyze the reaction that takes place in this chemical process with hydrogen and carbon dioxide.

Students will:

• write an equilibrium expression for a reaction;
• determine a mass and volume relationship with an emphasis on mole concepts;
• calculate changes in enthalpy, entropy, and free energy;
• calculate reaction quotient; and
• predict the shift in reaction based on Le Chatelier’s principle.

Lesson Files:

A Breath Of Fresh Air Lab Activity

Key Topic: Electrolysis (Chemistry)

One part of the Environmental Control and Life Support System on the International Space Station is production of breathable oxygen for the crewmembers. In this lab activity Students will: learn about the electrolysis process that is used on the ISS to produce oxygen and will then perform their own electrolysis.

Students will:

• construct an electrolytic cell;
• determine the number of moles and mass of oxygen produced;
• determine the number of electrons transferred; and
• compare their experimental electrolytic cell to the Oxygen Generator System used on the International Space Station.

Lesson Files:

Oxygen Generator System

Key Topic: Oxidation-Reduction, Stoichiometry, Electrochemistry (Chemistry)

Maintaining a permanent human presence on the International Space Station requires a well organized and precise life support system, a part of which is the Oxygen Generator System. Students will: learn about how the OGS produces breathable oxygen for the crew by converting wastewater from the ISS into oxygen and hydrogen through the process of electrolysis.

Students will:

• explain what is meant by the direction, form and strength of the overall pattern of a scatter plot;
• write balanced equations for half reactions;
• predict direction of oxidation-reduction reactions; and
• determine mass and volume relationship with an emphasis on mole concepts.

Lesson Files:

Statistics

Key Topic: Linear Regression (Statistics)

Radar sightings are taken throughout the United States and the world to keep track of the spacecraft like the International Space Station (ISS). The radars used must be calibrated to have a very precise accuracy. In this activity, students will look at data from an uncalibrated radar and a calibrated radar and determine how statistically significant the error is between the two different data sets.

Students will:

• calculate and interpret the meaning of the correlation coefficient, r, and the coefficient of determination, r ²
• write a regression equation, and interpret the meaning of the slope and y-intercept in context to the problem;
• make predictions based on a least squares regression model; and
• plot residuals, and interpret their graphical form.

Lesson Files:

Display Design: A Human Factor Of Spaceflight

Key Topic: Hypothesis Testing (Statistics)

When astronauts view control panels with multiple labels, they may need to pick out a particular label value from a display. An experiment was conducted to compare response times for right vs. left alignment of labels. Students will: evaluate the data compiled from this experiment and perform a hypothesis test to determine whether there is a difference in the response times that would indicate one being preferred over the other.

Students will:

• construct null and alternative hypotheses to analyze the response times for left-aligned vs. right-aligned labels;
• choose an appropriate hypothesis test;
• check assumptions necessary to conduct the hypothesis test;
• perform the hypothesis test; and
• draw the correct conclusion based on the results of the test.

Lesson Files:

SPACEWALK TRAINING

Key Topic: Linear Regression (Statistics)

The Neutral Buoyancy Laboratory allows astronauts an atmosphere resembling zero gravity (weightlessness) in order to train for missions involving spacewalks. In this activity, students will evaluate pressures experienced by astronauts and scuba divers who assist them while training in the NBL.

Students will:

• explain what is meant by the direction, form and strength of the overall pattern of a scatter plot;
• define the correlation coefficient, r, and describe what it measures;
• write a regression equation and interpret the meaning of the slope and y-intercept in context of the problem;
• explain what is meant by extrapolation and interpret a situation where extrapolation occurs;
• make predictions based on the correct mathematical model; and
• plot residuals and interpret their graphical form.

Lesson Files:

Maintaining Bone Mineral Density

Key Topic: Hypothesis Tests (Statistics)

One health concern that arises when shifting from an environment with gravity to microgravity is the loss of bone mass density. Students will: analyze two different exercise countermeasures and construct null and alternative hypotheses to determine their relative effectiveness in maintaining bone mineral density.

Students will:

• construct a null and alternative hypothesis;
• choose an appropriate hypothesis test;
• check assumptions necessary to conduct the hypothesis test;
• perform the hypothesis test; and
• draw the correct conclusion based on the results of the test.

Lesson Files:

-love learning -your best ed lessons guide, Scott

Categories: