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MAT-HS.G-CO.09

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

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

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

  • I can
  • I can

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

Web
Vocab

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.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

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.

  • Error analysis (find errors in a given proof, fix the error and explain why it was incorrect)

Concepts:

Vertical Angles

Angles created by parallel lines and a transversal

Perpendicular Bisector theorems

 -
  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

  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
  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

Web
Vocab

MAT-HS.G-CO.09.b

MAT-HS Targeted Standards
(G) Concept: Geometry
(CO) Domain: Congruence
Cluster: Prove geometric theorems

MAT-HS.G-CO.09.b 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. (Focus is on applying the theorems for C-CO.9B)

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

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.

Concepts:

Vertical Angles

Angles created by parallel lines and a transversal

Perpendicular Bisector theorems

 

 

Solve for x and y.
  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 the relevant information
  • Apply geometric relationships to create an algebraic model for the situation
  • Solve and answer the given question (Ex. Solve for the given variable, Find the angle measurement)

Concepts:

Vertical Angles

Angles created by parallel lines and a transversal

Perpendicular Bisector theorem

 

Solve for x.

Solve for x and y.
  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 recognize and recall angle pairs
  • can apply postulates, definitions, properties, and theorems to identify angle measurements

Concepts:

Vertical Angles

Angles created by parallel lines and a transversal

Perpendicular Bisector theorems

Example 2
  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

Web
Vocab

MAT-HS.G-CO.10

MAT-HS Targeted Standards
(G) Concept: Geometry
(CO) Domain: Congruence
Cluster: Prove geometric theorems

MAT-HS.G-CO.10 Prove and apply theorems about triangles.

Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can prove theorems about triangles.
  • I can prove the measures of interior angles of a triangle have a sum of 180°.
  • I can prove base angles of isosceles triangles are congruent.
  • I can prove the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length.
  • I can prove the medians of a triangle meet at a point.

Product Targets

  • I can
  • I can

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

Web
Vocab

MAT-HS.G-CO.10.a

MAT-HS Targeted Standards
(G) Concept: Geometry
(CO) Domain: Congruence
Cluster: Prove geometric theorems

MAT-HS.G-CO.10.a Prove theorems about triangles.

(Theorems include but are not limited to: Measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.)

(Focus on proving for this proficiency scale)

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

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.

  • Analyze a proof with errors and make corrections
 -
  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.)

Midsegment of a Triangle Proof

Triangle Interior Angle Proof

Prove a Triangle is Isosceles

 
  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
 Given a statement, the student can fill out the justification.  (skeleton proof)
  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

Web
Vocab

MAT-HS.G-CO.10.b

MAT-HS Targeted Standards
(G) Concept: Geometry
(CO) Domain: Congruence
Cluster: Prove geometric theorems

MAT-HS.G-CO.10.b Apply theorems about triangles.

(Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

(Focus on Applying)

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

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.

  • Analyze a solution and correct the errors
  • Investigate and provide multiple methods for finding a solution to a given problem

Find the measures of these angles in two different ways. Explain the steps you took for each method.
  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.

  • Apply theorems (postulates, definitions, etc.) about triangles to solve problems
  • Justify how to set up a problem using theorems (postulates, definitions, etc.) about triangles

 
  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).

 

  • Identify or relate the theorem used to set up the problem
  • Define the vocabulary associated with triangle theorems
  • Can identify the components of triangles

 

 

 

 -
  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

Web
Vocab

MAT-HS.G-CO.11

MAT-HS Targeted Standards
(G) Concept: Geometry
(CO) Domain: Congruence
Cluster: Prove geometric theorems

MAT-HS.G-CO.11 Prove and apply theorems about parallelograms.

Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can prove theorems about parallelograms.
  • I can prove opposite sides are congruent.
  • I can prove opposite angles are congruent.
  • I can prove the diagonals of a parallelogram bisect each other.
  • I can prove rectangles are parallelograms with congruent diagonals.

Product Targets

  • I can
  • I can

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

Web
Vocab

MAT-HS.G-CO.11.a

MAT-HS Targeted Standards
(G) Concept: Geometry
(CO) Domain: Congruence
Cluster: Prove geometric theorems

MAT-HS.G-CO.11.b Prove theorems about parallelograms.

(Focus on Prove for G-CO.11)

(Theorems include but are not limited to: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.)

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

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.

  • Analyze a proof with errors and make corrections
 -
  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 can perform all the actions for each concept listed below:

  • Identify relevant information

  • Arrange reasoning in a logical sequence

  • Support reasoning using appropriate justifications (theorems, postulates, definitions, etc.)

  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

 

 -
  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

Web
Vocab

MAT-HS.G-CO.11.b

MAT-HS Targeted Standards
(G) Concept: Geometry
(CO) Domain: Congruence
Cluster: Prove geometric theorems

MAT-HS.G-CO.11.b Apply theorems about parallelograms.

Theorems include but are not limited to: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

(Focus is on Application for G-CO.11B)

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

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.

  • Apply theorems (postulates, definitions, etc.) about parallelograms to solve problems
  • Justify how to set up a problem using theorems (postulates, definitions, etc.) about parallelograms

     

Solve for x and y.
  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).

  • Identify the theorem, postulate, or definition used to set up and solve a problem
  • Able to recognize and recall important vocabulary such as:

                    opposite sides

                    opposite angles

                    diagonals

                    congruent triangles

                     perpendicular

                    CPCTC

  • Students are able to find the missing measurements  in a parallelogram given some basic information

  • Can determine if a given figure is a parallelogram

 

Identify if the given figure is a parallelogram.
  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

Web
Vocab

MAT-HS.G-CO.12

MAT-HS Targeted Standards
(G) Concept: Geometry
(CO) Domain: Congruence
Cluster: Make geometric constructions

MAT-HS.G-CO.12 Make basic geometric constructions with a variety of tools and methods.

Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.  Tools may include compass and straightedge, string, reflective devices, paper folding or dynamic geometric software.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can use a variety of methods and tools to:
    • copy a segment
    • copy an angle
    • bisect a segment
    • bisect an angle
    • construct perpendicular
    • lines, including the perpendicular bisector of a line segment
    • construct a line parallel to a given line through a point not on the line

Product Targets

  • I can
  • I can

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.

  • Explain how to construct a geometric figure

Explain the type of construction and the next step in completing the construction, giving specific steps.
  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.

  • Construct a geometric figure using various tools and/or methods  (Ex: compass and straightedge, Geogebra)

 

 

 

(a) copy a given line segment  

(b) copy an angle.

(c) bisect a line segment.

(d) bisect an angle.

(e) construct a line perpendicular to a given line through a point on that line.

(f) construct a line perpendicular to a given line through a point not on that line.

(g) construct the perpendicular bisector of a line segment.

(h) construct a line parallel to a given line through a point not on the line.

Identify and complete the construction.
  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 recognize and recall terminology to answer questions
  •  identify the type of construction given an example
  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

Web
Vocab

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.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

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

  • I can
  • I can

Product Targets

  • I can
  • I can

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

Web
Vocab

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.

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

  • I can
  • I can

Product Targets

  • I can
  • I can

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.

  • Create a solid of revolution by rotating a 2 dimensional figure about a line and find the volume of that solid.
 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.
  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.

  • 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.

Find the volume of the figure:

Find the value of x.
  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).

  • Select the appropriate formula for finding the volume of a solid.
  • Students can solve for volume of given shapes when given all necessary measurements

Find the volume of the figure:

 

 

 

 
  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).

  • Students can solve for volume with help.

 
  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

Web
Vocab

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

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can use coordinate geometry to prove geometric theorems algebraically.

Product Targets

  • I can
  • I can

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

Web
Vocab

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

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

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

  • I can
  • I can

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

Web
Vocab

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

  • I can
  • I can

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

  • I can
  • I can

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

  • I can
  • I can

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

Web
Vocab

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

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

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

  • I can
  • I can

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

Web
Vocab

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.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

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

  • I can
  • I can

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

Web
Vocab

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.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

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.

  • Error analysis (explain why the reasoning of others is incorrect)

Explain why the answer is incorrect and give the correct answer.
  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)

 

 

 

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:

 
  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.)

  • recognize and use specific terminology such as:

    Corresponding angles, corresponding sides, congruence statement

     

Identity all the pairs of corresponding sides and angles. Then write a congruence statement.
  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

Web
Vocab

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.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

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 similarity properties and proportions to solve for missing measurements
  • use similarity to prove relationships in geometric figures   

Find the height of the tree.
  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)

Identify if the given triangles are similar. If they are similar, give the scale factor.

Solve for x.

 
  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

Web
Vocab

MAT-HS.G-SRT.05.c

MAT-HS Targeted Standards
(G) Concept: Geometry
(SRT) Domain: Similarity, Right Triangle, and Trigonometry
Cluster: Prove theorems involving similarity

MAT-HS.G-SRT.05.c Use similarity criteria to prove relationships in geometric figures.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

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 AA, SSS, and SAS Similarity Theorems to prove triangles similar
  • Justify conclusions using valid mathematical arguments.

Sketch the triangles using the given description. Explain/Justify whether the two triangles can be similar.

  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).

  • recognize vocabulary such as similarity, corresponding sides, and proportional

  • recognizes the similarity criteria for triangles (SAS, AA, SSS) 

Are the triangles similar? If so, state the similarity and the postulate or theorem that justifies your answer.
  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

Web
Vocab

MAT-HS.G-SRT.08

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 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Student Learning Targets:

Knowledge Targets

  • I can identify the hypotenuse and legs of a right triangle.
  • I can choose the correct trigonometric ratio given a right triangle.
  • I can identify the appropriate special right triangle.

Reasoning Targets

  • I can identify the hypotenuse and legs of a right triangle.
  • I can choose the correct trigonometric ratio given a right triangle.
  • I can identify the appropriate special right triangle.

Skills (Performance) Targets

  • I can apply trigonometric ratios and the Pythagorean Theorem to solve real world problems involving right triangles.

Product Targets

  • I can
  • I can

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

Web
Vocab

MAT-HS.G-SRT.08.a

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.a 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.)

 

 

 

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

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 solve complex, multi step trigonometry and Pythagorean Theorem problems in applied situations.

  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 solve application problems involving trigonometry and Pythagorean Theorem.

The bottom of a ladder must be placed 3 feet from a wall.  The ladder is 12 feet long.  How far above the ground does the ladder touch the wall?

 
  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

       ·  Angle of elevation

       · Angle of depression

       · Hypotenuse and legs of a right triangle

  • The student can set up trigonometric ratios and solve a basic trigonometry problem.
  • The student can correctly draw and label a diagram modeling the situation  

Solve for x:
  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

Web
Vocab

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.)

 

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

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.

  • The student will know and apply special right triangle relationships and use them to solve application problems.
 The length of a diagonal of a square is 18 cm.  Find the exact perimeter of the square.
  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

    • Special right triangle (30-60-90, 45-45-90)

    • Exact value

    • Short leg

    • Long leg

    • Hypotenuse

    • Isosceles

    • Leg

 

  • The student can simplify radical expressions

 

In each diagram, find the length of AC:
  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

Web
Vocab

MAT-HS.G-SRT.09

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.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

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

  • I can
  • I can

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

Web
Vocab

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