G-GMD - Domain
Geometric Measurement & Dimension
High School Geometry · Common Core State Standards · Common Core 2010
Standard Unwrapping
AI-generated as a starting point — sign in to edit.Vocabulary
volumecircumferenceareacylinderpyramidconespheresolid figuresdissection argumentsCavalieri's principleinformal limit argumentstwo-dimensional cross-sectionsthree-dimensional objectsrotationscross-sections
Skills
- Identify (shapes of two-dimensional cross-sections) #dok1
- Use (volume formulas for basic problems) #dok1
- Explain (informal arguments for volume formulas) #dok2
- Visualize (relationships between 2D and 3D objects) #dok2
- Solve (problems using volume formulas) #dok3
- Prove (volume formulas using informal arguments) #dok3
- Apply (Cavalieri's principle to differentiate and solve complex volume problems) #dok4
- Analyze (how cross-sections relate to three-dimensional structures) #dok4
Learning Targets
- I can identify the shapes of two-dimensional cross-sections of three-dimensional objects. #dok1
- I can use volume formulas for straightforward calculations involving cylinders, pyramids, cones, and spheres. #dok1
- I can explain why an informal argument supports the volume formulas for basic solid figures. #dok2
- I can visualize how a two-dimensional shape can form a three-dimensional object through rotation. #dok2
- I can solve real-world problems by applying the appropriate volume formulas. #dok3
- I can prove volume formulas for simple shapes using informal arguments. #dok3
- I can apply Cavalieri's principle to analyze complex volume-related problems. #dok4
- I can analyze cross-sectional representations to understand and explain the structural integrity of three-dimensional figures. #dok4
Big Ideas
- Volume formulas offer a powerful way to calculate and understand the capacity of three-dimensional objects.
- Understanding the relationship between two-dimensional cross-sections and three-dimensional objects enhances spatial reasoning and problem-solving skills.
Essential Questions
- How can we use informal arguments to understand volume and area formulas?
- What is Cavalieri's principle, and how does it help us with volume measurements?
- How can cross-sections help us understand three-dimensional shapes?
- What are the differences in how two-dimensional and three-dimensional objects are defined and measured?
- In what ways can we apply our understanding of geometry to real-world objects and situations?