The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.

Students Can (Evidence Outcomes):

HS.G-GMD.A. Geometric Measurement and Dimension: Explain volume formulas and use them to solve problems. 

• Give an informal argument for the formulas for the volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. (CCSS: HS.G-GMD.A.1) 

• Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.⭑ (CCSS: HS.G-GMD.A.3)

HS.G-GMD.B. Geometric Measurement and Dimension: Visualize relationships between two-dimensional and three-dimensional objects.

• Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. (CCSS: HS.G-GMD.B.4) 

HS.G-MG.A. Modeling with Geometry: Apply geometric concepts in modeling situations. 

• Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).⭑ (CCSS: HS.G-MG.A.1)

• Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).⭑ (CCSS: HS.G-MG.A.2)

• Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).⭑ (CCSS: HS.G-MG.A.3)

A star symbol (⭑) represents grade level expectations and evidence outcomes that make up a mathematical modeling standards category.

Assessments:

• Chapter 12 Assessment (PDF)

• Geometry Mastery Assessment (PDF), Geometry Mastery Assessment (Optional Part 2) (PDF)

• SAT Suite Educator Question Bank (Content Domain: Geometry and Trigonometry)

• Additional Assessment Tasks

Instructional Resources & Notes:

• Big Ideas Geometry Chapter 12

• Supplemental Lesson Resources for Chapter 12

• Additional Modeling Tasks

  • Beau-coup Beans, Country Boy Gas, Let's Go Camping!, Fearless Frames, Bestsize Cans, Propane Tanks, Funsize Cans, Kiln-Baked Pisa, A New Container, The Garden Wall (References: Completing the Modeling Cycle, Advice on Modeling)

• Notes: 

  • Students do not need to use Cavalieri’s Principle for deriving the formulas for the volume of a sphere and other solid figures.

  • Volumes of Prisms and Cylinders (Lesson 12.2), volumes of cones (Lesson 12.4), and volume of spheres (Lesson 12.5) review prior knowledge from middle school. Condense and combine these lessons to focus on the new concepts in Chapter 12.

  • Students do not need to compute surface areas of cones and spheres in Lesson 12.4 (Surface Areas and Volumes of Cones) and Lesson 12.5 (Surface Areas and Volumes of Spheres).

Algebra 1 Review:

In addition to the Review & Refresh exercises included with each Big Ideas Geometry lesson, the following resources can be used for curating frequent, ongoing mixed review exercise sets of key Algebra 1 concepts and skills. These resources focus on linear equations, linear functions, systems of equations & inequalities, exponential functions, quadratic functions, and quadratic equations:

• Big Ideas Algebra 1 Additional Practice

• Using Your Algebra Skills Lessons

• Algebra Warm-Ups for Geometry Teachers (Geoff Krall)

• SAT Suite Educator Question Bank (Content Domains: Algebra, Advanced Math)