AI for Youth Academy Future Scholars Research Initiative
Back to program
Year 1

2D Math + Python Foundations

This year uses a FIRST LEGO Challenge robot car on a map as a living 2D world. Students learn matrix representations of vectors, 2D representations of linear equations, and foundational Python by writing function calls, loops, and if/else logic with the FIRST LEGO Python library.

We ground every concept in navigation: points, vectors, and equations become decisions a robot makes as it drives across a 2D map.

Spring 2026

Course focus

Key themes

  • 2D space, points, vectors, and matrix representations
  • 2D representations of linear equations on a map
  • Python fundamentals: functions, loops, and conditionals

Hands-on moments

  • Program a FIRST LEGO Challenge robot car to navigate a 2D map.
  • Use the FIRST LEGO Python library and function calls to control movement.
  • Practice loops and if/else logic to make navigation reliable.

Outcomes

  • Explain vectors and linear equations with 2D map examples.
  • Write beginner Python programs using functions, loops, and conditionals.
  • Connect robot movement to 2D math representations.

Week-by-week plan

Subject to change based on cohort pace and feedback.

  1. 01

    Course kickoff and 2D maps

    Math

    Coordinate plane, points, and map orientation.

    Reading Material
  2. 02

    Points and distance

    Math

    Reinforce coordinate plane concepts from Week 01 and explore distance between two points.

    Computer Setup

    Install LEGO Education SPIKE App (https://education.lego.com/en-us/downloads/spike-app/software/) or verify browser access to https://spike.legoeducation.com/.

    Python

    LEGO Spike Prime IDE setup and driving SPIKE PRIME using helper functions with the FIRST LEGO Python library.

    Robot

    Drive calibration and distance moves with move_for_degrees to reach map checkpoints.

    Reading Material
  3. 03

    Linear equations and coordinate systems

    Math

    Use systems of two-variable linear equations to understand non-perpendicular ("wacky") coordinate systems and convert between them.

    Reading Material
  4. 04

    Vectors in AI, 3D Space, and Python Basics

    Math

    Word embeddings (king - man + woman = queen), 3D coordinate systems, and locating points in 3D space.

    Python

    Google Colab setup, variable types (int, float, str, list), and NumPy matrix multiplication.

    Reading Material
  5. 05

    Vector addition and scalar multiplication

    Math

    Adding vectors together and multiplying vectors by scalars for movement planning.

    Python

    Introduction to for loops for iterating through vector components.

    Reading Material
  6. 06

    What is intelligence?

    Math

    Introduction to input and output.

    AI

    What makes a task "intelligent"?

    AI

    Google Teachable Machine: training a dogs vs. cats classifier.

    Reading Material
  7. 07

    Finding the best line, one step at a time

    Math

    Absolute error, slope of the error, and the gradient descent update rule.

    Python

    Lists, for loops, functions, and matplotlib scatter/line plots for gradient descent.

    AI

    Gradient descent: start with a random guess and improve step by step.

    AI

    Learning rate: controlling the size of each update step.

    Reading Material
  8. 08

    Review Week — Connecting the Dots

    Math

    Comprehensive review of coordinate systems, vectors, and their applications.

    Python

    Review of variables, lists, for loops, functions, and matplotlib plotting.

    AI

    Connecting all concepts: from abstraction to gradient descent.

    AI

    Comprehensive challenge: implement linear regression from scratch.

    Reading Material
  9. 09

    Bringing Python skills to LEGO Spike

    Math

    Exterior angles of regular polygons (360 ÷ n).

    Python

    Config blocks, custom functions (drive_straight, turn), for loops for repeated patterns, and mission lists for multi-step routes.

    Robot

    Drive polygons, tune config variables, and navigate a multi-waypoint course.

    Reading Material
  10. 10

    To be updated

    Math

    To be updated.

  11. 11

    To be updated

    Math

    To be updated.

  12. 12

    To be updated

    Math

    To be updated.

  13. 13

    To be updated

    Math

    To be updated.

  14. 14

    To be updated

    Math

    To be updated.

  15. 15

    To be updated

    Math

    To be updated.

  16. 16

    To be updated

    Math

    To be updated.

Topics under consideration

The following topics from Weeks 07–16 are under review and will be assigned to specific weeks as the course progresses.

Math

  • y = mx + b and representing lines on the map
  • Solve for the intersection of two lines
  • Break routes into line segments and waypoints
  • Distance targets as conditions
  • Add vectors to track total displacement
  • Combine transforms to plan a route on a grid
  • Tolerance and small error corrections
  • Define points, vectors, and line equations for a custom mission

Python

  • Decomposition: break programs into small functions
  • Lists for route segments and checkpoints
  • Dicts and configs for centralized tuning
  • Modules and multi-file organization
  • Testing with assert and quick A/B checks
  • Micro-UI/menu for selecting runs
  • Logs, notes, and debrief records for repeatability
  • Write a plan and outline modules before coding
  • Implement with the FIRST LEGO Python library and test
  • Refactor functions and clean up code structure

Robot

  • Align then actuate an attachment motor
  • Distance sensor approach and standoff
  • Repeat multi-leg paths using shared tuning
  • Two-mission chain in one launch
  • Turn-in-place vs arc turn comparisons
  • 2:30 run discipline with reset roles
  • Time-boxed rehearsal and checklist habits
  • Sketch the path and assign team roles
  • Run a full mission and capture results
  • Polish the final run for reliability
  • Demo the final mission and reflect on improvements