Math in Motion

Robotics & Trigonometric Motion Unit

RoboTrig is an Algebra 2/Trigonometry unit built around a real engineering challenge. Students select an actual user, conduct a real interview, and design a robotic arm solution to meet that user's specific physical needs. Trigonometry is not the backdrop. It is the tool students use to make every design decision.

The unit runs 30 lessons across six engineering design phases: ASK, DEFINE, IDEATE, PROTOTYPE, TEST, and REFLECT. Students advance through five milestones, each requiring documented mathematical evidence before they move forward.

What Students Learn

Students build working knowledge of the trigonometry concepts required in Algebra 2, including the unit circle, radian measure, arc length, right triangle ratios, the Law of Cosines, and trigonometric modeling. They apply these tools to a two-joint robotic arm: calculating reach, predicting tip position from joint angles, and solving for joint angles from a target coordinate.

The math is always in service of a design problem. Students do not calculate angles in the abstract. They calculate angles because their user needs the robot arm to reach a specific position, and they have to prove it works.

How the Unit Is Structured

The six phases follow the engineering design process from problem definition through public presentation. Each phase ends with a milestone that requires students to produce and defend real work.

ASK (L1–L6): Students observe motion, select a user, estimate angles, and conduct a real interview.
DEFINE (L7–L12): Students build the unit circle from robot data, then formalize a problem statement with measurable success criteria.
IDEATE (L13–L16): Students choose a mathematical approach, produce two solution sketches, and justify their tool selection in writing before building anything.
PROTOTYPE (L17–L23): Students work through forward and inverse kinematics, program the robot, debug errors to within 0.5 mm, and defend their solution in a 7-slide presentation with peer review.
TEST (L24–L27): Students run at least two calibration iterations, document design changes, and collect user feedback.
REFLECT (L28–L30): Students present to a public audience with a live robot demonstration, then complete an individual written reflection.

What Makes It Different

Every student works with a real person. The user they identify in Lesson 2 shapes every calculation, every design choice, and every milestone deliverable through Lesson 29. Students do not choose a hypothetical scenario. They interview someone, define that person's constraints, and build a solution they can demonstrate.

Assessment is built into the structure. Students cannot advance past Milestone 4 without passing a Slide Gate review. They cannot complete Milestone 5 without a documented iteration log. The work is visible at every stage.

Our Mission

NYC FIRST inspires and empowers students from diverse communities across New York City to engage with STEM and robotics in meaningful and joyful ways. We create authentic learning experiences that encourage young people to think critically and creatively, and to persevere. NYC FIRST is investing in New York City’s future by preparing the next generation of innovators and leaders.

Our Vision

NYC FIRST is building out a new STEM-based civic infrastructure that broadens resources, delivers opportunity and sets young people on pathways to success academically and professionally through engaging and quality STEM education and robotics programming. This vision is centered on our network of STEM Centers, which level the playing field by centralizing valuable resources – including computing, software, fabrication equipment and expert NYC FIRST staff and mentors – and nurturing a powerful, close, socio-economically integrated community, in a highly cost-effective, scalable structure.

Why we exist

STEM education opens doors to fulfilling learning experiences and careers, but too many of New York City’s youth don’t have access to engaging science, technology, engineering and mathematics resources. Without meaningful opportunities to discover and apply STEM, they don’t pursue it in school or professionally.

Many schools don’t have the resources to offer STEM education that both inspires students to pursue these fields in college and prepares them to meet benchmark qualifications.

To enter and succeed in the STEM job market, young people need to build technical skills and life skills, like working in teams, leadership, respect and empathy.

Women, people of color, and students from low-income communities in the US are under-represented in STEM industries. We create awareness of the opportunities STEM offers and access to support to pursue STEM careers.

Impact

We provide the spark that leads to a lifetime love of STEM. Every student in our programs finds building blocks of confidence and character necessary to succeed in any field and career they choose.

NYC FIRST students across gender, race, and income are three times more likely to be interested in STEM activities, careers, identity, and knowledge.

NYC FIRST alumni are enrolled at top engineering schools, such as MIT, Olin College and Worcester Polytechnic Institute.

Young women in FIRST programs have significant gains in all STEM areas including STEM interest, career interest, activity, knowledge, and identity.

By their fourth year of college, FIRST alumni are more likely to be majoring in STEM fields than comparison group peers.

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