MAT-HS.G-GMD.01
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MAT-HS Targeted Standards
(G) Concept: Geometry
(GMD) Domain: Geometric Measurement and Dimension
Cluster: Explain volume formulas and use them to solve problems.
MAT-HS.G-GMD.01 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
- I can explain the formulas for circumference of a circle and area of a circle by determining the meaning of each term.
- I can explain the formulas for volume of a cylinder, pyramid and cone by determining the meaning of each term.
Skills (Performance) Targets
Product Targets
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Proficiency Scale
| Score |
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Description |
Sample Activity
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| 4.0 |
In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. |
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3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
| 3.0 |
“The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. |
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2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
| 2.0 |
The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). |
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1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
| 1.0 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). |
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0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
| 0.0 |
Even with help, the student demonstrates no understanding or skill. |
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Resources
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MAT-HS.G-GMD.02 |
MAT-HS Targeted Standards
(G) Concept: Geometry
(GMD) Domain: Geometric Measurement and Dimension
Cluster: Explain volume formulas and use them to solve problems.
MAT-HS.G-GMD.02 Calculate the surface area for prisms, cylinders, pyramids, cones, and spheres to solve problems.
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
Product Targets
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Proficiency Scale
| Score |
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Description |
Sample Activity
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Advanced
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In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations.
- Create a solid of revolution by rotating a 2 dimensional figure about a line and find the surface area of that solid.
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A geometric figure is created when bounded by the lines y=¾ x-3, y=0, x=0. Draw a picture of the region being revolved about the x-axis. Determine the surface area of the geometric solid. |
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3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
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Proficient
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“The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations.
- Calculate the surface area formulas for cylinders, pyramids, cones, and spheres to solve problems
- Solve for various heights and lengths for use in the surface area formulas using inductive reasoning, pythagorean theorem, and trigonometry.
- Label the answer using the correct units based on the context of the problem.
- Give either the approximate or exact answer, given the context of the problem.
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Find the surface area of the figure:
  
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2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
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Progressing | The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content).
- Select the appropriate formula for finding the surface area of a solid
- Students can solve for surface area of given shapes when given all necessary measurements
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Find the surface area of the figure:
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1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
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Beginning
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With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content).
- can solve for surface area with help
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0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
| 0.0 |
Even with help, the student demonstrates no understanding or skill. |
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Resources
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MAT-HS.G-GMD.03 |
MAT-HS Targeted Standards
(G) Concept: Geometry
(GMD) Domain: Geometric Measurement and Dimension
Cluster: Explain volume formulas and use them to solve problems
MAT-HS.G-GMD.03 Know and apply volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems.
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Student Learning Targets:
Knowledge Targets
- I can choose the appropriate formula from a list.
Reasoning Targets
- I can, given formulas, compute the surface area and volume of a right prism, right cylinder, right pyramid, right cone, and sphere.
Skills (Performance) Targets
Product Targets
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Proficiency Scale
| Score |
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Description |
Sample Activity
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Advanced
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In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations.
- Create a solid of revolution by rotating a 2 dimensional figure about a line and find the volume of that solid.
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A geometric figure is created when bounded by the lines y=¾ x-3, y=0, x=0. Draw a picture of the region being revolved about the x-axis. Determine the volume of the geometric solid. |
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3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
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Proficient
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“The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations.
- Know and use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
- Solve for various heights and lengths for use in the volume formulas using inductive reasoning, pythagorean theorem, and trigonometry.
- Label the answer using the correct units based on the context of the problem.
- Give either the approximate or exact answer, given the context of the problem.
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Find the volume of the figure:
  
Find the value of x.
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2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
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Progressing
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The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content).
- Select the appropriate formula for finding the volume of a solid.
- Students can solve for volume of given shapes when given all necessary measurements
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Find the volume of the figure:
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1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
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Beginning
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With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content).
- Students can solve for volume with help.
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0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
| 0.0 |
Even with help, the student demonstrates no understanding or skill. |
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Resources
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MAT-HS.G-GMD.04
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MAT-HS Targeted Standards
(G) Concept: Geometry
(GMD) Domain: Geometric Measurement and Dimension
Cluster: Visualize relationships between two-dimensional and three-dimensional objects
MAT-HS.G-GMD.04 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
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Student Learning Targets:
Knowledge Targets
- I can identify the properties and attributes of two and three-dimensional objects that distinguish one from another; e.g., a square is a parallelogram with four congruent sides and four right angles; a cylinder has two parallel circular bases.
- I can identify two dimensional cross sections of three dimensional objects.
- I can identify three dimensional objects created by rotating two dimensional objects.
Reasoning Targets
Skills (Performance) Targets
Product Targets
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Proficiency Scale
| Score |
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Description |
Sample Activity
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| 4.0 |
In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. |
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3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
| 3.0 |
“The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. |
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2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
| 2.0 |
The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). |
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1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
| 1.0 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). |
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0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
| 0.0 |
Even with help, the student demonstrates no understanding or skill. |
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Resources
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