HANNAH DURANKO
MATHEMATICS AND COMPUTER SCIENCE TEACHER
LANDER VALLEY HIGH SCHOOL
MATH 2
Explore a variety of engaging projects and lessons that highlight my teaching methods and classroom activities. Each one showcases unique skills and creativity in Math 2.
MUSCLE MARCH
Rather than simply introducing quadratic functions and non-linear equations through passive lectures, this introductory modeling task utilizes collaborative discovery to let students experience changing rates of change firsthand. The activity begins with a seemingly simple pattern: modeling a student's daily increase in physical exercise. Working in collaborative teams at the vertical whiteboards, students quickly map out a linear progression for the daily repetitions, building confidence as they construct baseline explicit and recursive equations.
The cognitive challenge escalates when the task shifts focus to tracking the cumulative sum of those daily repetitions for a charity fundraiser. As teams scramble to calculate the total over time, their initial linear models break down. Using the vertical whiteboards as a shared sandbox, students map out physical diagrams and tables to track the compounding growth. Through active experimentation, trial, and peer collaboration, teams discover the transition from a constant rate of change to a linear rate of change—unveiling the underlying architecture of a quadratic function. This method transforms a standard textbook problem into a visible, tactile system where students learn to navigate complex mathematical structures and collectively justify their algebraic reasoning.
BUILDING THE PERFECT SQUARE
Rather than teaching the algebraic process of "completing the square" through rote memorization and abstract algorithms, this geometric modeling task uses visual experimentation to build deep conceptual understanding. Standing at the vertical whiteboards in collaborative teams, students are challenged to represent quadratic area expressions—modeled after customizable quilt block designs—using concrete geometric layouts.
The cognitive leap happens when teams receive "scrambled" block orders that do not form a perfect square. Instead of following a teacher-led formula, students use the whiteboards as a dynamic workspace to physically arrange the area models, manually distributing the linear $x$-blocks to balance the dimensions. Through trial, error, and peer debate, they discover what a missing constant piece represents and how to mathematically adjust the expression to force a perfect square. This inquiry-driven method transforms a notoriously difficult algebraic procedure into a visible, logical progression where students self-correct and justify their structural reasoning.
DISCOVER TRIG RELATIONSHIPS
Rather than simply handing students pre-programmed trigonometric definitions like sine, cosine, and tangent to memorize, this introductory right-triangle task relies on collective measurement and shared data to spark geometric discovery. Working in collaborative groups at the vertical whiteboards, students are assigned distinct, varying sizes of right triangles containing an acute angle of exactly 60 degrees. Teams must manually construct the triangles, measure the side lengths, and calculate the ratios of the opposite-to-hypotenuse, adjacent-to-hypotenuse, and opposite-to-adjacent sides.
The high-leverage learning moment happens during a class-wide Gallery Walk. As students analyze the data points calculated by other teams, they make an unexpected realization: despite the triangles being completely different sizes, the corresponding side ratios are practically identical across the room. Standing at the whiteboards, students use Angle-Angle (AA) similarity to prove why these ratios remain constant, uncovering the underlying logic of trigonometry. This inquiry-driven simulation transforms abstract trigonometric ratios into a predictable, visible system, giving students the structural tools to justify their geometric reasoning with absolute clarity.
DISCOVER SIMILAR FIGURES
Rather than simply lecturing on definitions of geometric similarity or providing pre-made scale factors, this inquiry-driven task forces students to confront, test, and debate the mathematical rules of geometric transformations. Working in collaborative teams at the vertical whiteboards, students are handed a series of geometric conjectures—such as "all rectangles are similar" or "all rhombuses are similar"—and are tasked with proving or disproving them through mathematical modeling.
The whiteboards serve as a dynamic testing ground where student misconceptions are made visible. Using tools like GeoGebra alongside manual coordinate tracking, teams manipulate side lengths and internal angles to search for counterexamples. Through trial, error, and peer-to-peer argumentation, students independently discover that equivalent scale factors across side lengths are meaningless if corresponding internal angles are not preserved. This active, proof-based approach transforms abstract geometric proportions into a concrete logical framework, teaching students how to systematically construct mathematical arguments and justify their structural reasoning with total clarity.