Wednesday, November 6, 2024, 8:55 PM
Site: Learnbps
Course: BPSS (MAT) Mathematics Standards (SMAT)
Glossary: MATHS: Geometry
MATHS.GCO.09
MATHS Targeted Standards (G) Concept: Geometry (CO) Domain: Congruence Cluster: Prove geometric theorems
MATHS.GCO.09 Prove and apply theorems about lines and angles.
Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. 
Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
 I can prove theorems pertaining to lines and angles.
 I can prove vertical angles are congruent.
 I can prove when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent.
 I can prove points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
Product Targets

Proficiency Scale
Score 

Description 
Sample Activity

4.0 
In addition to Score 3.0, the student demonstrates indepth 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 indepth 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


MATHS.GCO.09.a
MATHS Targeted Standards (G) Concept: Geometry (CO) Domain: Congruence Cluster: Prove geometric theorems
MATHS.GCO.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
Reasoning Targets
Skills (Performance) Targets
Product Targets

Proficiency Scale
Score 

Description 
Sample Activity

Advanced 
In addition to Score 3.0, the student demonstrates indepth 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

 

3.5 
In addition to Score 3.0 performance, the student demonstrates indepth 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


MATHS.GCO.09.b
MATHS Targeted Standards (G) Concept: Geometry (CO) Domain: Congruence Cluster: Prove geometric theorems
MATHS.GCO.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 CCO.9B) 
Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
Product Targets

Proficiency Scale
Score 

Description 
Sample Activity

Advanced 
In addition to Score 3.0, the student demonstrates indepth 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 indepth 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


MATHS.GCO.10
MATHS Targeted Standards (G) Concept: Geometry (CO) Domain: Congruence Cluster: Prove geometric theorems
MATHS.GCO.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
Reasoning Targets
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

Proficiency Scale
Score 

Description 
Sample Activity

4.0 
In addition to Score 3.0, the student demonstrates indepth 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 indepth 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


MATHS.GCO.10.a
MATHS Targeted Standards (G) Concept: Geometry (CO) Domain: Congruence Cluster: Prove geometric theorems
MATHS.GCO.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
Reasoning Targets
Skills (Performance) Targets
Product Targets

Proficiency Scale
Score 

Description 
Sample Activity

Advanced 
In addition to Score 3.0, the student demonstrates indepth 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 indepth 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


MATHS.GCO.10.b
MATHS Targeted Standards (G) Concept: Geometry (CO) Domain: Congruence Cluster: Prove geometric theorems
MATHS.GCO.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
Reasoning Targets
Skills (Performance) Targets
Product Targets

Proficiency Scale
Score 

Description 
Sample Activity

Advanced 
In addition to Score 3.0, the student demonstrates indepth 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 indepth 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


MATHS.GCO.11
MATHS Targeted Standards (G) Concept: Geometry (CO) Domain: Congruence Cluster: Prove geometric theorems
MATHS.GCO.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
Reasoning Targets
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

Proficiency Scale
Score 

Description 
Sample Activity

4.0 
In addition to Score 3.0, the student demonstrates indepth 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 indepth 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


MATHS.GCO.11.a
MATHS Targeted Standards (G) Concept: Geometry (CO) Domain: Congruence Cluster: Prove geometric theorems
MATHS.GCO.11.b Prove theorems about parallelograms.
(Focus on Prove for GCO.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
Reasoning Targets
Skills (Performance) Targets
Product Targets

Proficiency Scale
Score 

Description 
Sample Activity

Advanced 
In addition to Score 3.0, the student demonstrates indepth 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 indepth 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


MATHS.GCO.11.b
MATHS Targeted Standards (G) Concept: Geometry (CO) Domain: Congruence Cluster: Prove geometric theorems
MATHS.GCO.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 GCO.11B)

Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
Product Targets

Proficiency Scale
Score 

Description 
Sample Activity

Advanced 
In addition to Score 3.0, the student demonstrates indepth 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 indepth 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 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


MATHS.GCO.12
MATHS Targeted Standards (G) Concept: Geometry (CO) Domain: Congruence Cluster: Make geometric constructions
MATHS.GCO.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
Reasoning Targets
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

Proficiency Scale
Score 

Description 
Sample Activity

Advanced

In addition to Score 3.0, the student demonstrates indepth 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 indepth 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

