Mathematics serves as the **foundational language** for science, technology and engineering.
Engineers use and apply mathematical concepts to everyday **problem solving**
and **engineering design** tasks.

Mathematics covers a range of study that includes algebra, geometry, trigonometry, precalculus, calculus, and probability and statistics. Engineers make use of these branches of mathematics to model, analyze and solve complex problems.

For example, mechanical engineers use mathematical equations to determine
the amount of force and energy generated by machines and engines.
They use **algebra** to design suspension systems to keep vehicles running as smoothly as possible.

Civil engineers rely on **trigonometry** to survey various buildings and structures and to calculate
the forces on bridges. They use **geometry** to design and assemble various shapes and incorporate
them into constructing structures such as freeways and tunnels.

Aerospace engineers use **precalculus** to determine rates of change such as velocity or acceleration to
help determine the change in a satellite’s orbit. Electrical engineers rely on **calculus** to model and
analyze dynamic systems and optimization.

Chemical and biomedical engineers use **statistics and probability** to assess experimental data and
processes to ensure quality and consistency. They rely on statistical analysis to help them make
informed decisions on products that must meet given specifications.

TeachEngineering provides lesson plans and activities with math-focused worksheets and assessments to promote mathematical proficiency that is essential to K-12 students. Our resources stress the importance of understanding problems, using models and mathematical concepts to solve problems, and developing feasible arguments based on data.

Our hands-on engineering resources, aligned to Math Standards, encourage students to hone their abstract, spatial reasoning, and critical thinking skills through exploring real-world challenges.

Math Curricula

**
Explore the mathematics-aligned resources featured here, by grade, that support the Common Core Standards for Mathematics.
**

Grades K-2

- Zooming In and Out with Scale and Systems Thinking
**Zooming In and Out with Scale and Systems Thinking**First-grade students are introduced to systems thinking and scale by working in teams to reassemble the separated pages of the Zoom picture book. They experience surprising changes in perspective and learn how engineers work together to examine projects very closely in order to notice details and di...

- Soil from Spoiled: Engineering a Compost Habitat for Worms
**Soil from Spoiled: Engineering a Compost Habitat for Worms**A unique activity for young learners that combines engineering and biology, students design an optimal environment for red wiggler worms in a compost bin.

- How High Can a Super Ball Bounce?
**How High Can a Super Ball Bounce?**Students determine the coefficient of restitution (or the elasticity) for super balls. Working in pairs, they drop balls from a meter height and determine how high they bounce. They measure, record and repeat the process to gather data to calculate average bounce heights and coefficients of elastici...

- Be “Cool” with Popsicle Engineering
**Be “Cool” with Popsicle Engineering**Create popsicles using the engineering design process! In this activity, students work to solve the problems of a local popsicle shop while learning how scientific and engineering concepts play a part in behind-the-scenes design.

- Light Plants and Dark Plants, Wet Plants and Dry Ones
**Light Plants and Dark Plants, Wet Plants and Dry Ones**Students plant sunflower seeds in plastic cups, and once germinated, expose them to varying light or soil moisture conditions. They measure the seedlings' growth every few days using non-standard measurement (inch cubes).

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Grades 3-5

- Falling Water
**Falling Water**Students drop water from different heights to demonstrate the conversion of water's potential energy to kinetic energy. They see how varying the height from which water is dropped affects the splash size. They follow good experiment protocol, take measurements, calculate averages and graph results.

- Engineering a Habitat’s Humidity
**Engineering a Habitat’s Humidity**Students design a temporary habitat for a future classroom pet—a hingeback tortoise. The students investigate hingeback tortoise habitat features as well as the design features of such a habitat. Each group communicates and presents this information to the rest of the class after they research, brai...

- Solar Power
**Solar Power**Students learn how engineers use solar energy to heat buildings by investigating the thermal storage properties of some common materials: sand, salt, water and shredded paper. Students then evaluate the usefulness of each material as a thermal storage material to be used as the thermal mass in a pas...

- Wind Power
**Wind Power**Students develop an understanding of how engineers use wind to generate electricity. Student teams build model anemometers to better understand and measure wind speed.

- Requirements & Constraints: Making Model Parking Garages
**Requirements & Constraints: Making Model Parking Garages**Student teams meet a set of requirements and given constraints as they create small-scale model parking garages. They experience the engineering design process as they design, plan and build their model structures, and then test them for strength to determine their maximum loads.

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Grades 6-8

- Cooler Design Challenge
**Cooler Design Challenge**Students learn about convection, conduction, and radiation in order to solve the challenge of designing and building a small insulated cooler with the goal of keeping an ice cube and a Popsicle from melting. This activity uses the engineering design process to build the cooler as well as to measure ...

- Hot Cans and Cold Cans
**Hot Cans and Cold Cans**Students apply the concepts of conduction, convection and radiation as they work in teams to solve two challenges. One problem requires that they maintain the warm temperature of one soda can filled with water at approximately human body temperature, and the other problem is to cause an identical so...

- Create a Safe Bungee Cord for Washy!
**Create a Safe Bungee Cord for Washy!**Students learn about the role engineers and mathematicians play in developing the perfect bungee cord length by simulating and experimenting with bungee jumping using washers and rubber bands. Working as if they are engineers for a (hypothetical) amusement park, students are challenged to develop a ...

- Swiss Alps Emergency Sled Design
**Swiss Alps Emergency Sled Design**Students act as engineers to solve a hypothetical problem that has occurred in the Swiss Alps due to a natural seismic disaster. Working in groups, they follow the engineering design process steps to create model sleds that meet the requirements to transport materials to people in distress that live...

- Balsa Towers
**Balsa Towers**Students groups use balsa wood and glue to build their own towers using some of the techniques they learned from the associated lesson.

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Grades 9-12

- Engineering Digital Biodegraders for Biological Cleanup
**Engineering Digital Biodegraders for Biological Cleanup**A hypothetical scenario is introduced in which the class is asked to apply their understanding of the forces that drive natural selection to prepare a proposal along with an environmental consulting company to help clean up an area near their school that is contaminated with trichloroethylene (TCE)....

- Exploiting Polarization: Designing More Effective Sunglasses
**Exploiting Polarization: Designing More Effective Sunglasses**Students apply their understanding of light polarization and attenuation to design, fabricate, test and refine their own prototype sunglasses that better reduce glare and lower light intensity compared to available sunglasses, and better protect eyes from UVA and UVB radiation. They meet the project...

- We Have Liftoff
**We Have Liftoff**Building on an introduction to statics, dynamics free-body diagrams, combustion and thermodynamics provided by the associated lesson, students design, construct and test their own rocket engines using sugar and potassium nitrate—an opportunity to apply their knowledge of stoichiometry.

- Volumes of Complex Solids
**Volumes of Complex Solids**Challenged with a hypothetical engineering work situation in which they need to figure out the volume and surface area of a nuclear power plant’s cooling tower (a hyperbolic shape), students learn to calculate the volume of complex solids that can be classified as solids of revolution or solids with...

- Body Motion Vector Visualization
**Body Motion Vector Visualization**Students apply their knowledge of vectors to a project that gathers data on body movements using the (free) ARK Mirror technology. They record their own body movements, such as martial arts or dance, use the computer program to create graphs of position, velocity, and acceleration data, and analyze ...

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