The High School Geometry STEMDay Lab invited participants to explore a variety of concepts in geometry through hands-on activities. Differentiated activities for 1) height and area of triangles, 2) the sum of interior angle measures of a triangle, and 3) relationships between geometric solids and derivation of volume formulas allowed exploration of concepts based on whether students have prior knowledge of the Pythagorean theorem, deductive proof methods, and algebra. A middle school activity guided participants through the derivation of area formulas for various plane figures including parallelograms, triangles, trapezoids, and circles. A high school activity explored multiple methods for determining a general formula for the sum of interior angle measures of a polygon.
Participation in STEMDay 2025 also included a resource kit with materials and tools for implementing these activities in the classroom. Kit includes: Four geometry activities and student worksheets exploring triangles (height, area, and angles), polygons, and volume formulas (including derivation of the formula for volume of a sphere using Cavalieri’s Principle). Tools for these activities and further instructor enrichment include: Pegboards (9” double sided, 2x) with Rubber Bands, Relational Geometrical Solids (17x), Self-Sticking Sand (1x), 6 Quart Bin, Dissectible Sphere (1x), Triangle Angle Activities Flipbook (1 copy), Additional Instructor Resources (online), Flatland Book (1 copy)
GM.5 Be able to represent geometric properties and relationships.
GM.5.2: Identify measurable attributes of figures and objects.
GM.6 Be able to apply appropriate techniques, tools, and formulas to interpret and solve problems.
GM.6.1: Apply coordinate geometry and algebraic formulas to verify characteristics of geometric figures.
GM.6.6: Use formulas to find measurable attributes of figures and objects (i.e. arc, sector, perimeter, area, surface area, volume)
GM.3 Be able to apply mathematical knowledge and skills to a variety of purposes.
GM.3.2: Conduct research (locate, observe/gather, analyze, conclude).
GM.5 Be able to represent geometric properties and relationships.
GM.5.3: Verify similarity and congruence of geometric figures.
GM.6 Be able to apply appropriate techniques, tools, and formulas to interpret and solve problems.
GM.6.3: Construct geometric figures and objects.
GM.7 Be able to analyze results and draw appropriate conclusions.
GM.7.1: Investigate, apply, and prove properties and theorems.
GM.2 Develop abilities in mathematics.
GM.2.3: Develop higher-order thinking skills (analyze, evaluate, reason, classify, predict, generalize, solve, decide, relate, interpret, simplify, model, synthesize).
GM.3 Be able to apply mathematical knowledge and skills to a variety of purposes.
GM.3.1: Use a variety of strategies in the problem-solving process (i.e. patterns, tables, diagrams).
GM.4 Be able to understand terms and symbols of geometry.
GM.4.2: Interpret properties and relationships among figures using inductive and deductive reasoning.
GM.7 Be able to analyze results and draw appropriate conclusions.
GM.7.1: Investigate, apply, and prove properties and theorems.
GM.3 Be able to apply mathematical knowledge and skills to a variety of purposes.
GM.3.2: Conduct research (locate, observe/gather, analyze, conclude).
GM.5 Be able to represent geometric properties and relationships.
GM.5.2: Identify measurable attributes of figures and objects.
GM.6 Be able to apply appropriate techniques, tools, and formulas to interpret and solve problems.
GM.6.1: Apply coordinate geometry and algebraic formulas to verify characteristics of geometric figures.