MAT-HS.G-GPE.03
|
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.
|
Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
Product Targets
|
Proficiency Scale
| Score |
|
Description |
Sample Activity
|
| 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. |
- |
| |
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. |
- |
| |
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). |
- |
| |
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). |
- |
| |
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
|
|
MAT-HS.G-GPE.04
|
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
|
Proficiency Scale
| Score |
|
Description |
Sample Activity
|
| 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. |
- |
| |
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. |
- |
| |
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). |
- |
| |
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). |
- |
| |
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
|
|
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).
|
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
|
Proficiency Scale
| Score |
|
Description |
Sample Activity
|
|
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. |
- |
| |
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.
- 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.
|
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).
|
| |
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 recall basic terminology and facts such as:
- Parallel
- Perpendicular
- Slope formula
- Opposite reciprocal
- Equation of a line
|
Identify whether the lines are parallel or perpendicular.
y=2x-4
y=-½ x +3
|
| |
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
|
|
MAT-HS.G-GPE.06
|
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.
|
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
|
Proficiency Scale
| Score |
|
Description |
Sample Activity
|
| 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. |
- |
| |
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. |
- |
| |
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). |
- |
| |
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). |
- |
| |
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
|
|
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.
|
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 |
|
Description |
Sample Activity
|
|
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.
- The student will be able to use a variety of techniques to determine the area of a shape.
|
|
| |
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 be able to determine the perimeter and area of various shapes on the coordinate grid.
|
Determine the perimeter of the following polygon.
Perimeter = ______ units
|
| |
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 compute the perimeter or area of a figure on a coordinate plane without needing to use the distance formula
|
 |
| |
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
Vocabulary
Websites |
|
MAT-HS.G-MG.01
|
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).
|
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
|
Proficiency Scale
| Score |
|
Description |
Sample Activity
|
| 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. |
- |
| |
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. |
- |
| |
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). |
- |
| |
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). |
- |
| |
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
|
|
MAT-HS.G-MG.02
|
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).
|
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
|
Proficiency Scale
| Score |
|
Description |
Sample Activity
|
| 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. |
- |
| |
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. |
- |
| |
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). |
- |
| |
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). |
- |
| |
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
|
|
MAT-HS.G-MG.03
|
MAT-HS Targeted Standards
(G) Concept: Geometry
(MG) Domain: Modeling with Geometry
Cluster: Apply geometric concepts in modeling situations
MAT-HS.G-MG.03 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).
|
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 solve problems by designing an object or structure that satisfies certain constraints, such as minimizing cost or the enlargement of a picture using a grid, ratios, and proportions.
Product Targets
|
Proficiency Scale
| Score |
|
Description |
Sample Activity
|
| 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. |
- |
| |
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. |
- |
| |
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). |
- |
| |
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). |
- |
| |
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
|
|
MAT-HS.G-SRT.01
|
MAT-HS Targeted Standards
(G) Concept: Geometry
(SRT) Domain: Similarity, Right Triangle, and Trigonometry
Cluster: Understand similarity in terms of similarity transformations
MAT-HS.G-SRT.01 Verify experimentally the properties of dilations given by a center and a scale factor.
- a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
- b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
|
Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
- I can verify experimentally the properties of dilations given by a center and a scale factor.
- I can verify experimentally that a dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
- I can verify experimentally, that when performing dilations of a line segment, the image segment becomes longer or shorter based on the ratio given by the scale factor.
Product Targets
|
Proficiency Scale
| Score |
|
Description |
Sample Activity
|
| 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. |
- |
| |
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. |
- |
| |
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). |
- |
| |
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). |
- |
| |
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
|
|
MAT-HS.G-SRT.02
|
MAT-HS Targeted Standards
(G) Concept: Geometry
(SRT) Domain: Similarity, Right Triangle, and Trigonometry
Cluster: Understand similarity in terms of similarity transformations
MAT-HS.G-SRT.02 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
|
Student Learning Targets:
Knowledge Targets
- I can develop the definition of similarity using the idea of dilation transformations.
Reasoning Targets
- I can determine congruence and similarity among geometric objects.
- I can use similarity or congruence to solve for a missing side/angle.
- I can determine whether two figures are similar.
- I can explain similarity based on the equality of corresponding angles and the proportionality of corresponding sides.
Skills (Performance) Targets
Product Targets
|
Proficiency Scale
| Score |
|
Description |
Sample Activity
|
| 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. |
- |
| |
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. |
- |
| |
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). |
- |
| |
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). |
- |
| |
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
|
|