In this High School Geometry instructional guide, students apply their knowledge and skills related to applying volume formulas through three tasks connected to real-world contexts in architecture, product design, and creative design challenges.

• Instructional Task 1 (45 min) — Students choose between two projects to enhance a mall's entrance lobby: calculating the volumes of scaled-down miniature models of the Great Pyramids of Egypt, or calculating the volumes of composite architectural pieces made of a sphere placed on top of a cylinder

• Instructional Task 2 (45 min) — Students propose dimensions for four differently shaped candles — a rectangular prism, cone, cylinder, and sphere — each with given proportional constraints, then calculate the volume of wax needed for each

• End-of-Unit Performance Task (90 min or 2 class periods) — Students select from different design options and apply their knowledge of volume formulas to create an original design challenge, using diagrams, equations, and calculations to demonstrate their mathematical reasoning

Standards: G.G.MD.1, G.G.MD.2, G.G.MD.3, K-12.MP.1-6

Curriculum Connections: Illustrative Math, Hawaiʻi DOE Geometry Curriculum, CK-12 Basic Geometry Concepts, On Core Mathematics Geometry, Savvas Envision Geometry

In this High School Geometry instructional guide, students apply their knowledge and skills related to similar triangles through three tasks connected to real-world contexts in Hawaiian culture, visual art, and graphic design.

• Instructional Task 1 (40 min) — Students apply a scale ratio to build a proportional model based on a traditional Hawaiian hale, then use reasoning and evidence to prove that the triangles formed by the original and scaled model are similar

• Instructional Task 2 (50 min) — Students examine provided artwork to identify a pair of similar triangles, measure their side lengths and angles, and write a formal proof of their similarity using SSS, SAS, or AA criteria

• End-of-Unit Performance Task (50 min) — Students design an original logo that incorporates at least one prominent triangle, scale it to two different sizes, and mathematically prove that the triangles across all three versions are similar using reasoning and evidence

Standards: G.SRT.B.5, K-12.MP.1-8

Curriculum Connections: Savvas enVision Geometry, Illustrative Mathematics Geometry, CK-12 Basic Geometry Concepts, On Core Mathematics Geometry, Carnegie Learning, HMH Into Geometry, HIDOE, Desmos, ALEKS, Glencoe, McDougal Littell, UH Curriculum