MAT-HS.G-GMD.01
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.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. |
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). |
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). |
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.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
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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. |
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). |
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). |
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.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. |
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). |
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). |
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
Vocabulary
Websites |
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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).
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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-SRT.04
MAT-HS Targeted Standards (G) Concept: Geometry (SRT) Domain: Similarity, Right Triangle, and Trigonometry Cluster: Prove theorems involving similarity
MAT-HS.G-SRT.04 Prove theorems about triangles.
Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. |
Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
- I can use AAA, SAS, SSS similarity theorems to prove triangles are similar.
- I can use triangle similarity to prove other theorems about triangles.
- I can prove a line parallel to one side of a triangle divides the other two proportionally, and it’s converse.
- I can prove the Pythagorean Theorem using triangle similarity.
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.05
MAT-HS Targeted Standards (G) Concept: Geometry (SRT) Domain: Similarity, Right Triangle, and Trigonometry Cluster: Prove theorems involving similarity
MAT-HS.G-SRT.05 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
- I can determine congruence and similarity among geometric objects.
- I can use similarity or congruence to solve for a missing side/angle.
Skills (Performance) Targets
- I can use similarity and congruence criteria to solve real world problems.
- I can use congruence and similarity to prove relationships involving geometric figures.
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.05.a
MAT-HS Targeted Standards (G) Concept: Geometry (SRT) Domain: Similarity, Right Triangle, and Trigonometry Cluster: Prove theorems involving similarity
MAT-HS.G-SRT.05.a Use congruence to solve problems in geometric figures.
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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.
- Error analysis (explain why the reasoning of others is incorrect)
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Explain why the answer is incorrect and give the correct answer.
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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.
- Use congruence to solve problems.
- Use congruence to show relationships in geometric figures (using CPCTC)
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Two door stops have cross sections that are right triangles. They both have a 200 angle and the length of the side between the 900 and the 200 angles are equal. Are the cross sections congruent? Explain.
Solve for x and y:
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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).
- recognizes the congruence criteria for triangles (SAS, ASA, etc.)
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recognize and use specific terminology such as:
Corresponding angles, corresponding sides, congruence statement
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Identity all the pairs of corresponding sides and angles. Then write a congruence statement.
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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.05.b
MAT-HS Targeted Standards (G) Concept: Geometry (SRT) Domain: Similarity, Right Triangle, and Trigonometry Cluster: Prove theorems involving similarity
MAT-HS.G-SRT.05.b Use similarity criteria to solve problems in geometric figures.
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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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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 similarity properties and proportions to solve for missing measurements
- use similarity to prove relationships in geometric figures
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Find the height of the tree.
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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).
- can solve provided proportionality problems
- can recognize vocabulary such as congruence, similarity, scale factor, ratio and proportion
- recognizes the similarity criteria for triangles (SAS, SSS, AA)
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Identify if the given triangles are similar. If they are similar, give the scale factor.
Solve for x.
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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. |
- |
Resources
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