MAT-HS.G-SRT.08.b |
MAT-HS Targeted Standards
(G) Concept: Geometry
(SRT) Domain: Similarity, Right Triangle, and Trigonometry
Cluster: Define trigonometric ratios and solve problems involving right triangles
MAT-HS.G-SRT.08.b
Use special right triangles (30°-60°-90° and 45°-45°-90°), trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
(Mastery of the Pythagorean Theorem is an 8th grade standard.)
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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 |
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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- |
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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. |
| Proficient |
“The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations.
- The student will know and apply special right triangle relationships and use them to solve application problems.
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The length of a diagonal of a square is 18 cm. Find the exact perimeter of the square. |
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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). |
| 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).
- The student can recognize and recall terminology to answer questions
- The student can simplify radical expressions
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In each diagram, find the length of AC:
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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). |
| Beginning |
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-SRT.09
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MAT-HS Targeted Standards
(G) Concept: Geometry
(SRT) Domain: Similarity, Right Triangle, and Trigonometry
Cluster: Define trigonometric ratios and solve problems involving right triangles.
MAT-HS.G-SRT.09 Derive the formula A = ½ ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
- I can for a triangle that is not a right triangle, draw an auxiliary line from a vertex, perpendicular to the opposite side and derive the formula, A=½ ab sin (C), for the area of a triangle, using the fact that the height of the triangle is, h=a sin(C).
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-SRT.10
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MAT-HS Targeted Standards
(G) Concept: Geometry
(SRT) Domain: Similarity, Right Triangle, and Trigonometry
Cluster: Apply trigonometry to general triangles
MAT-HS.G-SRT.10 Prove the Laws of Sines and Cosines and use them to solve problems.
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
- I can prove the Laws of Sines and Cosines.
- I can use the Laws of Sines and Cosines to solve real world problems.
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-SRT.11
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MAT-HS Targeted Standards
(G) Concept: Geometry
(SRT) Domain: Similarity, Right Triangle, and Trigonometry
Cluster: Apply trigonometry to general triangles.
MAT-HS.G-SRT.11 Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
- I can apply any method to find unknown measurements in right triangles.
- I can apply the Laws of Sines and Cosines to find unknown measurements in non-right triangles.
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.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-GPE.07 |
MAT-HS Targeted Standards
(G) Concept: Geometry
(GPE) Domain: Expressing Geometric Properties with Equations
Cluster: Use coordinates to prove simple geometric theorems algebraically
MAT-HS.G-GPE.07 Use coordinates to compute perimeters of polygons and areas of triangles, parallelograms, trapezoids, and kites.
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Student Learning Targets:
Knowledge Targets
- I can choose the appropriate formula from a list.
Reasoning Targets
- I can compute the area of a regular polygon, given a formula list.
- I can determine relationships between points, lines, and plane figures in the Cartesian coordinate system by using distance, midpoint, and slope.
Skills (Performance) Targets
- I can use coordinate geometry and the distance formula to find the perimeter of polygons and the area of triangles and rectangles.
Product Targets
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.
- The student will be able to use a variety of techniques to determine the area of a shape.
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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.
- The student will be able to determine the perimeter and area of various shapes on the coordinate grid.
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Determine the perimeter of the following polygon.
Perimeter = ______ units
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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).
- The student can recognize and recall terminology to answer questions.
- The student can compute the perimeter or area of a figure on a coordinate plane without needing to use the distance formula
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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).
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- |
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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. |
- |
Resources
Vocabulary
Websites |
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MAT-HS.G-MG.01
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MAT-HS Targeted Standards
(G) Concept: Geometry
(MG) Domain: Modeling with Geometry
Cluster: Apply geometric concepts in modeling situations
MAT-HS.G-MG.01 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
- I can determine an appropriate geometric model that can be used to solve a problem.
- I can use geometric shapes, their measures, and their properties to describe objects.
Skills (Performance) Targets
- I can use geometric models to find solutions to problems in mathematics and other disciplines.
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-MG.02
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MAT-HS Targeted Standards
(G) Concept: Geometry
(MG) Domain: Modeling with Geometry
Cluster: Apply geometric concepts in modeling situations
MAT-HS.G-MG.02 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
- I can determine an appropriate geometric model that can be used to solve a problem.
Skills (Performance) Targets
- I can use geometric models to find solutions to problems in mathematics and other disciplines.
- I can use the concept of density when referring to situations involving area and volume models, such as persons per square mile.
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-CO.09
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MAT-HS Targeted Standards
(G) Concept: Geometry
(CO) Domain: Congruence
Cluster: Prove geometric theorems
MAT-HS.G-CO.09 Prove and apply theorems about lines and angles.
Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. |
Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
- I can prove theorems pertaining to lines and angles.
- I can prove vertical angles are congruent.
- I can prove when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent.
- I can prove points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
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. |
- |
Resources
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MAT-HS.G-CO.09.a |
MAT-HS Targeted Standards
(G) Concept: Geometry
(CO) Domain: Congruence
Cluster: Prove geometric theorems
MAT-HS.G-CO.09.a Prove theorems about lines and angles.
Theorems include but are not limited to: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
Product Targets
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Proficiency Scale
| Score |
|
Description |
Sample Activity
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| Advanced |
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.
Concepts:
Vertical Angles
Angles created by parallel lines and a transversal
Perpendicular Bisector theorems
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- |
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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. |
| Proficient |
“The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations.
- Identify relevant given information
- Arrange reasoning in a logical sequence
- Support reasoning using appropriate justifications (theorems, postulates, definitions, etc.)
Concepts:
Vertical Angles
Angles created by parallel lines and a transversal
Perpendicular Bisector theorems
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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). |
| 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).
- partially prove but reasoning has gaps, steps missing, incorrect reasoning, etc.
- recall theorems, definitions, and postulates
- fill out justification given a statement
Concepts:
Vertical Angles
Angles created by parallel lines and a transversal
Perpendicular Bisector theorems
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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). |
| Beginning |
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). |
- |
| |
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. |
- |
Resources
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