MAT-HS.A-REI.07
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MAT-HS Targeted Standards
(A) Concept: Algebra
(REI) Domain: Reasoning with Equations and Inequalities
Cluster: Solve systems of equations
MAT-HS.A-REI.07 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
For example, find the points of intersection between the line y = –3x and the circle x²+ y² = 3. |
Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
- I can solve for (isolate) a specific variable.
- I can perform transformations that produce equivalent equations (e.g., adding the same amount to both sides of the equation, etc.).
- I can check the solution.
- I can set a polynomial equal to zero and solve by factoring, quadratic formula, graphing, linear combinations, and substitution.
- I can solve for (isolate) a specific variable.
- I can write a linear system.
- I can perform transformations that produce equivalent equations (e.g., adding the same amount to both sides of the equation, etc.)
- I can check the solution.
- I can solve a quadratic.
- I can multiply and factor polynomials.
- I can solve a linear inequality.
- I can graph a linear inequality.
- I can solve a system of linear inequalities.
- I can graph a system of linear inequalities.
- I can check the solution of the system.
- I can solve a linear system (substitution, linear combination, graphically).
- I can write a linear system.
- I can identify the number of solutions of a linear system.
- I can identify the most efficient method to solve a system.
- I can check the solution of the system.
- I can solve a system containing a linear equation and a quadratic equation in two variables algebraically and graphically.
Product Targets
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Proficiency Scale
| Score |
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Description |
Sample Activity
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| 4.0 |
In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. |
- |
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3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
| 3.0 |
“The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. |
- |
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2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
| 2.0 |
The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). |
- |
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1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
| 1.0 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). |
- |
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0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
| 0.0 |
Even with help, the student demonstrates no understanding or skill. |
- |
Resources
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MAT-HS.A-REI.08
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MAT-HS Targeted Standards
(A) Concept: Algebra
(REI) Domain: Reasoning with Equations and Inequalities
Cluster: Solve systems of equations
MAT-HS.A-REI.08 Represent a system of linear equations as a single matrix equation in a vector variable.
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
Product Targets
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Proficiency Scale
| Score |
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Description |
Sample Activity
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| 4.0 |
In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. |
- |
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3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
| 3.0 |
“The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. |
- |
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2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
| 2.0 |
The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). |
- |
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1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
| 1.0 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). |
- |
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0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
| 0.0 |
Even with help, the student demonstrates no understanding or skill. |
- |
Resources
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MAT-HS.A-REI.09
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MAT-HS Targeted Standards
(A) Concept: Algebra
(REI) Domain: Reasoning with Equations and Inequalities
Cluster: Solve systems of equations
MAT-HS.A-REI.09 Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
Product Targets
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Proficiency Scale
| Score |
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Description |
Sample Activity
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| 4.0 |
In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. |
- |
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3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
| 3.0 |
“The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. |
- |
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2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
| 2.0 |
The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). |
- |
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1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
| 1.0 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). |
- |
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0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
| 0.0 |
Even with help, the student demonstrates no understanding or skill. |
- |
Resources
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MAT-HS.A-REI.10
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MAT-HS Targeted Standards
(A) Concept: Algebra
(REI) Domain: Reasoning with Equations and Inequalities
Cluster: Represent and solve equations and inequalities graphically
MAT-HS.A-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
- I can find any solution to an equation in two variables from the graph of that equation.
- I can graph the solution(s) of any linear or exponential function.
- I can verify an ordered pair is a solution to the equation.
Product Targets
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Proficiency Scale
| Score |
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Description |
Sample Activity
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| 4.0 |
In addition to achieving level 3.0 content, the student makes in-depth inferences and applications that go beyond what was taught |
Given a quadratic function, identify two solutions.
Given more than one function on a graph, determine the solution of the system.
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3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
| 3.0 |
The student can:
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Find any solution to an equation in two variables from the graph of that equation.
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Graph the solution(s) of any linear or exponential function.
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Verify an ordered pair is a solution to the equation.
The student exhibits no major errors or omissions. |
Given the following function: y=3x+2, create a graph on a coordinate plane to show all solutions of the function.
Determine if the given point (4, ½ ) is a solution to the
function y=212x
Given the following function, identify three solutions.
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2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
| 2.0 |
There are no major errors or omissions regarding the simpler details and processes as the student can:
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Recognize and recall basic vocabulary such as:
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solution
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ordered pair
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coordinate plane
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Graph a function, given a table of solutions or technology.
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Evaluate using order of operations.
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Plot ordered pairs on a coordinate plane.
However, the student exhibits major errors or omissions regarding the more complex ideas and processes. |
- |
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1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
| 1.0 |
With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes. |
- |
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0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
Resources
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MAT-HS.A-REI.11
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MAT-HS Targeted Standards
(A) Concept: Algebra
(REI) Domain: Reasoning with Equations and Inequalities
Cluster: Represent and solve equations and inequalities graphically
MAT-HS.A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Note: In Algebra I, only linear and exponential will be the focus.
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
- I can explain why the intersection of y = f(x) and y = g(x) is the solution of f(x) = g(x) for any combination of linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
Skills (Performance) Targets
- I can use technology to graph the equations and find their points of intersection.
- I can use tables of values or successive approximations to find solutions.
Product Targets
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Proficiency Scale
| Score |
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Description |
Sample Activity
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| 4.0 |
In addition to achieving level 3.0 content, the student makes in-depth inferences and applications that go beyond what was taught |
On the graphs of f(x) and g(x), interpret where f(x)>g(x)or where f(x)<g(x)
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3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
| 3.0 |
The student can:
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explain why the intersection of y = f(x) and y = g(x) is the solution of f(x) = g(x) for any linear or exponential functions.
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use technology and tables to graph the equations and find their points of intersection
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use tables of values or successive approximations to find solutions
The student exhibits no major errors or omissions. |
Use a graphing calculator to find and justify the approximate solution(s) to the system below.
f(x)=x+4 g(x)=4-x
Solutions: x= 0
f(0) = 4 and g(0)=4
Given the following system, for what x value(s), is f(x) = g(x)?
Solutions: x=1
Because f(1) = 5 and g(1) = 5 |
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2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
| 2.0 |
There are no major errors or omissions regarding the simpler details and processes as the student can:
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recognize and recall basic vocabulary, such as:
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function notation
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solution
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x-coordinate
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linear function
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exponential function
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evaluate using function notation and order of operations.
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identify the intersection of two functions.
However, the student exhibits major errors or omissions regarding the more complex ideas and processes. |
Find the value of f(4). if f(x)=3x+7.
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1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
| 1.0 |
With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes. |
- |
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0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
Resources
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MAT-HS.A-REI.12 |
MAT-HS Targeted Standards
(A) Concept: Algebra
(REI) Domain: Reasoning with Equations and Inequalities
Cluster: Represent and solve equations and inequalities graphically
MAT-HS.A-REI.12 Graph the solutions to a linear inequality in two variables as a half-plane. Graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
- I can graph the solutions to a linear inequality in two variables, including dashed or solid boundary lines when appropriate.
- I can graph the solution set to a system of linear inequalities in two variables as their corresponding intersection.
Product Targets
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Proficiency Scale
| Score |
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Description |
Sample Activity
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4.0
(advanced) |
In addition to achieving level 3.0 content, the student makes in-depth inferences and applications that go beyond what was taught |
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3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
3.0
(proficient) |
The student can:
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graph the solutions to a linear inequality in two variables, including dashed or solid boundary lines when appropriate.
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graph the solution set to a system of linear inequalities in two variables as their corresponding intersection.
The student exhibits no major errors or omissions. |
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2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
2.0
(progressing) |
There are no major errors or omissions regarding the simpler details and processes as the student can:
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recognize and recall basic vocabulary, such as:
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linear inequality.
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linear equation.
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understand when to use a solid line vs a dashed line.
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understand that there is a region of solutions and how to identify it.
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graph a linear equation as the boundary line.
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solve for Y in a linear equation or inequality.
However, the student exhibits major errors or omissions regarding the more complex ideas and processes. |
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1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
1.0
(beginning) |
With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes. |
- |
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0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
Resources
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