Sunday, July 14, 2024, 2:48 AM
Site: Learnbps
Course: BPSS (MAT) Mathematics Standards (S-MAT)
Glossary: MAT-HS: Algebra
M

MAT-HS.A-REI.06

MAT-HS Targeted Standards
(A) Concept: Algebra
(REI) Domain: Reasoning with Equations and Inequalities
Cluster: Solve systems of equations

MAT-HS.A-REI.06 Solve systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can solve systems of equations using graphing (exactly and approximating).
  • I can solve systems of equations using substitution.
  • I can solve systems of equations using linear combination (or elimination).
  • I can explain when there is one solution, no solution, or infinitely many solutions that may arise from a system.

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity

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
  • Solve a  3x3 system of equations

2x-y+5z=16
x-3y+2z=5
x+2y+z=7
  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:

  • solve systems of equations using graphing (exactly and approximating)
  • solve systems of equations using substitution

  • solve systems of equations using linear combination (or elimination)

  • explain when there is one solution, no solution, or infinitely many solutions that may arise from a system.


The student exhibits no major errors or omissions.
  • Solve the following system of equations using your preferred method.

x – 2y = –9

x + 3y = 16

  • Explain when one solution, no solutions, and infinitely many solutions will arise.

 

  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:

  • recognize and recall basic terminology. such as:

    • linear combination (elimination)

    • substitution

    • solution

    • infinitely many solutions

    • no solution

    • system of equations

    • ordered pair

  • determine if an ordered pair is a solution to a system.

  • approximate a solution to a system of linear equations that are graphed.



However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

  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. -
  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

Web

Vocab

  • linear combination
  • elimination method
  • substitution method

MAT-HS.A-REI.07

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

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

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

  • 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.A-REI.08

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.

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
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.A-REI.09

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).

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
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.A-REI.10

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).

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

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

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity
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.  
  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:


  • Find any solution to an equation in two variables from the graph of that equation.

  • Graph the solution(s) of any linear or exponential function.

  • 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.

  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:

  • Recognize and recall basic vocabulary such as:

    • solution

    • ordered pair

    • coordinate plane

  • Graph a function, given a table of solutions or technology.

  • Evaluate using order of operations.

  • Plot ordered pairs on a coordinate plane.



However, the student exhibits major errors or omissions regarding the more complex ideas and processes.
-
  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. -
  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

Web
Vocab

MAT-HS.A-REI.11

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.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

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

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity
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)

                                              

      
  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:

  • 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.

  • use technology and tables to graph the equations and find their points of intersection

  • 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
  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:

  • recognize and recall basic vocabulary, such as:

    • function notation

    • solution

    • x-coordinate

    • linear function

    • exponential function

  • evaluate using function notation and order of operations.

  • 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.

  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. -
  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

Web

Vocab

  • intersection

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.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

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

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity
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


  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:


  • graph the solutions to a linear inequality in two variables, including dashed or solid boundary lines when appropriate.

  • 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.


  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:

  • recognize and recall basic vocabulary, such as:

    • linear inequality.

    • linear equation.

  • understand when to use a solid line vs a dashed line.

  • understand that there is a region of solutions and how to identify it.

  • graph a linear equation as the boundary line.

  • solve for Y in a linear equation or inequality.





However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

  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. -
  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

Web

Vocab

  • half-plane

MAT-HS.A-SSE

Domains are larger groups of related standards. So the Domain Score is a calculation of all the related standards. So click on the standard name below each Domain to access the learning targets and proficiency scales for each Domain's related standards.

Domain (SSE)

Seeing Structure in Expressions

  • Interpret the structure of expressions
  • Write expressions in equivalent forms to solve problems

Domain Description

An expression is a record of a computation with numbers, symbols that represent numbers, arithmetic operations, exponentiation, and, at more advanced levels, the operation of evaluating a function. Conventions about the use of parentheses and the order of operations assure that each expression is unambiguous. Creating an expression that describes a computation involving a general quantity requires the ability to express the computation in general terms, abstracting from specific instances.

Reading an expression with comprehension involves analysis of its underlying structure. This may suggest a different but equivalent way of writing the expression that exhibits some different aspect of its meaning. For example, p + 0.05p can be interpreted as the addition of a 5% tax to a price p. Rewriting p + 0.05p as 1.05p shows that adding a tax is the same as multiplying the price by a constant factor.

Algebraic manipulations are governed by the properties of operations and exponents, and the conventions of algebraic notation. At times, an expression is the result of applying operations to simpler expressions. For example, p + 0.05p is the sum of the simpler expressions p and 0.05p. Viewing an expression as the result of operation on simpler expressions can sometimes clarify its underlying structure.

A spreadsheet or a computer algebra system (CAS) can be used to experiment with algebraic expressions, perform complicated algebraic manipulations, and understand how algebraic manipulations behave.

Standards in this Domain

  • MAT-HS.A-SSE.01 - Interpret expressions that represent a quantity in terms of its context.
  • MAT-HS.A-SSE.02 - Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2).
  • MAT-HS.A-SSE.03 - Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
  • MAT-HS.A-SSE.04 - Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.

 

MAT-HS.A-SSE.01

MAT-HS Targeted Standards
(A) Concept: Algebra
(SSE) Domain: Seeing Structure in Expressions
Cluster: Interpret the structure of expressions

MAT-HS.A-SSE.01 Interpret expressions that represent a quantity in terms of its context.

  • a. Interpret parts of an expression,such as terms, factors, and coefficients.
  • b. Interpret complicated expressions by viewing one or more of their parts as a single entity.
    For example, interpret P(1+r)n as the product of P and a factor not depending on P.

Student Learning Targets:

Knowledge Targets

  • I can identify the different parts of an expression and explain their meaning within the context of a problem.

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can use algebraic expressions, equations or inequalities involving one or two variables to represent geometric relationships.
  • I can interpret expressions that represent a quantity in terms of its context.
  • I can interpret expressions and make sense of the multiple factors and terms by explaining the meaning of the individual parts.

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:

What is a variable?

Vocabulary:

expression term factor coefficient

MAT-HS.A-SSE.02

MAT-HS Targeted Standards
(A) Concept: Algebra
(SSE) Domain: Seeing Structure in Expressions
Cluster: Interpret the structure of expressions

MAT-HS.A-SSE.02 Use the structure of an expression to identify ways to rewrite it.

For example, see x4 – y4 as (x²)² – (y²)², thus recognizing it as a difference of squares that can be factored as (x² – y²)(x² + y²).

Student Learning Targets:

Knowledge Targets

  • I can recall the order of operations.
  • I can understand and identify a power and its parts (base and exponent).
  • I know the properties of exponents (i.e. product of powers, power of a power, power of a product).
  • I can recognize a zero or negative exponent.
  • I can recall the order of operations.
  • I can understand and identify a power and its parts (base and exponent).
  • I know the properties of exponents (i.e. product of powers, power of a power, power of a product).
  • I can recognize a zero or negative exponent.

Reasoning Targets

  • I can analyze an algebraic expression.
  • I can decide what to do next based on my knowledge of the order of operations.
  • I can analyze an algebraic expression.
  • I can decide what to do next based on my knowledge of the order of operations.

Skills (Performance) Targets

  • I can factor algebraic expressions.
  • I can combine like terms to simplify an algebraic expression.
  • I can perform basic operations.
  • I can simplify algebraic expressions.
  • I can apply order of operations.
  • I can simplify an algebraic expression.
  • I can rewrite algebraic expressions in equivalent forms such as factoring or combining like terms.
  • I can use factoring techniques such as common factors, grouping, the difference of two squares, the sum or difference of two cubes, or a combination of methods to factor an expression completely.
  • I can simplify expressions by combining like terms, using the distributive property and using other operations with polynomials.

Product Targets

  • I can

Proficiency Scale

Score   Description Sample Activity
4.0 In addition to achieving level 3.0 content, the student makes in-depth inferences and applications that go beyond what was taught.

Factor the following algebraic expressions.

  • x3+2x2-4x-8

  • 6x3-14x2-12x

  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:

  • uses the structure of an expression to identify ways to rewrite it, using the following techniques to factor:

    • factor by grouping.

    • difference of perfect squares.

    • greatest common factor.

    • factor a trinomial.


The student exhibits no major errors or omissions.

Factor the following algebraic expressions.

  • 4x2-8x+3

  • 2x2-15x+18

  • 3x2-5x-2

  • x3+8x2+6x+48

  • 9x2-49

  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:

  • combines like terms to simplify an expression. (A.SSE.1) & (A.APR.1)

  • uses the following techniques to factor:

    • greatest common factor.

    • factor a trinomial with a leading coefficient of 1.


However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Simplify the following algebraic expressions.

  • 3x2+2x-6x2+4y+6+2x


Factor the following algebraic expressions.

  • 6x2+3x

  • x2+4x+3

  • x2-3x-4

  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. -
  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).

Alg II Equivalent Expressions Proficiency Scale

Score   Description Sample Activity

4.0

(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. Describe the error in each of the following: 
  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:
  • recognize a suitable factoring technique given the structure of the expression.
  • use factoring techniques such as common factors, grouping, the difference of two squares, the sum or difference of two cubes, or a combination of methods to factor an expression completely.
  • rewrite algebraic expressions in equivalent forms such as factoring or combining like terms.  

The student exhibits no major errors or omissions.
 
Factor: x3+3x2-4x-12
Factor and Simplify:
  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:
  • simplify expressions by combining like terms, using the distributive property and using other operation with polynomials.

  • understand that like terms can be combined using the distributive property and using other operations with polynomials.

  • understand factoring techniques such as common factors, grouping, the difference of two squares, the sum or difference of two cubes, or a combination of methods to factor an expression completely.  

  • recognize equivalent forms of the same expression.  

However, the student exhibits major errors or omissions regarding the more complex ideas and processes.


 

Factor: x2+5x-6 

Factor and Simplify:

 

  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, 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