HANNAH DURANKO
MATHEMATICS AND COMPUTER SCIENCE TEACHER
LANDER VALLEY HIGH SCHOOL
MATH 1
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 1.
CHECKERBOARD BORDERS
Rather than starting a unit on algebraic modeling by forcing students to memorize predefined function templates, this visual progression task challenges students to systematically extract algebraic rules from geometric growth. The activity begins individually or in small groups as students are presented with an expanding, multi-layered checkerboard pattern sequence surrounding a grid of white tiles. Their objective is to determine a strategy to quickly count and model the total number of colored border squares at any arbitrary stage of the sequence.
The high-leverage learning moment happens as students transition from basic counting to structural analysis. Instead of relying on a teacher-led algorithm, teams experiment with different geometric groupings—such as breaking the border into overlapping corners, identical side lengths, or subtracting an inner square from an outer square. As the geometric complexity scales, students collaborate to bridge the gap between these visual counting strategies and formal symbolic logic, discovering how different visual perspectives result in equivalent explicit and recursive algebraic expressions. This active modeling approach shifts mathematics away from passive calculation and turns it into a transparent, logical system.
CAFETERIA ACTIONS AND REACTIONS
Rather than teaching multi-step algebraic equations through rote, abstract rules like PEMDAS, this context-driven modeling task leverages real-world logic to demystify variable operations. The activity begins as students interpret a narrative scenario detailing a dynamic sequence of events—unloading cartons, distributing items across various serving lines, and tracking remaining inventory. Individually and in small teams, students are challenged to work backward through the chronological timeline to solve the baseline mathematical mystery.
As the mathematical demands scale, the lesson leans into deeper peer collaboration. Instead of following a teacher-led algorithm, students work together to map out the visual mechanics of the problem, translating word-based actions into precise algebraic operations. Through trial, error, and shared problem-solving, teams discover how to reverse a nested sequence of operations, naturally uncovering why inverse operations must occur in the exact opposite order of the original actions. This inquiry-driven approach shifts mathematics away from blind rule-following, giving students the analytical tools to construct, manipulate, and justify multi-step algebraic systems with total clarity.
GIVE ME FIVE
Rather than teaching the key features of functions—such as domain, range, intercepts, and intervals of increase—through dry, isolated lecture slides, this dynamic matching task models mathematics as a highly connected network. The activity begins as an open-ended investigation where students parse through a diverse collection of mathematical representations, including graphs, tables, explicit equations, and contextual descriptions.
As students begin identifying hidden overlaps across different representations, the lesson naturally leans into deeper collaborative strategy. Instead of relying on a teacher-led checklist, small groups work together to cross-examine algebraic structures against visual data, defending their sorting logic to accurately pair equivalent features. Through trial, error, and peer-to-peer critique, students independently discover how shifts in an algebraic expression directly govern the boundaries of its domain and coordinate intercepts. This active, inquiry-driven approach shifts function analysis away from passive memorization, transforming abstract notation into a visible, highly logical system.
GROWING GROWING DOTS
Rather than simply introducing exponential functions and geometric sequences through passive lecture slides, this visual progression task relies on student investigation to unpack non-linear growth patterns. The lesson begins as an intuitive counting puzzle where students track an expanding cluster of geometric dots over a timeline of discrete minute intervals. Their challenge is to look past the static shapes, isolate the changing variables, and project the behavior of the system into the future.
The critical learning leap occurs as students discover that simple linear addition fails to capture the acceleration of the pattern. As the numbers rapidly compound, the lesson naturally leans into collaborative modeling strategy. Working in groups, students cross-examine the visual data stream from multiple perspectives—translating the physical expansion of the dots into numerical tables, coordinate graphs, and symbolic notation. Through trial, error, and peer-to-peer debate, teams independently discover a constant growth multiplier, bridging the gap between tactile patterns and formal explicit and recursive exponential equations. This inquiry-driven approach shifts mathematics away from blind rule-following, transforming abstract exponents into a visible, highly predictable system.