MAT-HS.G-GPE.01
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MAT-HS Targeted Standards
(G) Concept: Geometry
(GPE) Domain: Expressing Geometric Properties with Equations
Cluster: Translate between the geometric description and the equation for a conic section
MAT-HS.G-GPE.01 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
- I can use the Pythagorean Theorem to derive the equation of a circle, given the center and radius. I can given an equation of a circle, complete the square to find the center and radius.
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-GPE.02
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MAT-HS Targeted Standards
(G) Concept: Geometry
(GPE) Domain: Expressing Geometric Properties with Equations
Cluster: Translate between the geometric description and the equation for a conic section
MAT-HS.G-GPE.02 Derive the equation of a parabola given a focus and directrix.
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Student Learning Targets:
Knowledge Targets
- I can, given a parabola, identify the vertex, focus, directrix, and axis of symmetry, noting that every point on the parabola is equidistant from the focus and the directrix.
Reasoning Targets
Skills (Performance) Targets
- I can, given a focus and directrix, derive the equation of a parabola.
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-GPE.03
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MAT-HS Targeted Standards
(G) Concept: Geometry
(GPE) Domain: Expressing Geometric Properties with Equations
Cluster: Translate between the geometric description and the equation for a conic section.
MAT-HS.G-GPE.03 Derive the equations of ellipses and hyperbol as given foci, using the fact that the sum or difference of distances from the foci is constant.
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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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| 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-GPE.04
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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.04 Use coordinates to prove simple geometric theorems algebraically.
For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). |
Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
- I can use coordinate geometry to prove geometric theorems algebraically.
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-GPE.05 |
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.05 Develop and verify the slope criteria for parallel and perpendicular lines.
Apply the slope criteria for parallel and perpendicular lines to solve geometric problems using algebra. (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
- I can use slope to prove that lines are parallel or perpendicular.
- I can solve geometric problems using slope of parallel and perpendicular lines.
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. |
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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.
- Use coordinates to find the slope of lines and determine if they are parallel, perpendicular or neither.
- Write the equation of a line parallel to a given line through a given point.
- Write the equation of a line perpendicular to a given line through a given point.
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Given the points (4, -2) (7, 8) for line 1 and the points (-5, 3) (4, 6) for line 2, determine whether the given lines are parallel, perpendicular or neither.
Write the equation of a line parallel to 2x+3y=9 that passes through the point (-3,4).
Write the equation of a line perpendicular to 3x-4y=16, that passes through the point (2,3).
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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 recall basic terminology and facts such as:
- Parallel
- Perpendicular
- Slope formula
- Opposite reciprocal
- Equation of a line
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Identify whether the lines are parallel or perpendicular.
y=2x-4
y=-½ x +3
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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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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.06
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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.06 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
- I can find the point on a directed line segment between the two given points that divides the segment into a given ratio.
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-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. |
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Resources
Vocabulary
Websites |
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