Friday, July 19, 2024, 3:12 AM
Site: Learnbps
Course: BPSS (MAT) Mathematics Standards (S-MAT)
Glossary: MAT-HS: Algebra

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

MAT-HS.A-SSE.03

MAT-HS Targeted Standards
(A) Concept: Algebra
(SSE) Domain: Seeing Structure in Expressions
Cluster: Write expressions in equivalent forms to solve problems

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.

  • a. Factor a quadratic expression to reveal the zeros of the function it defines. See: MAT-HS.A-SSE.03a
  • b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
  • c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

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 can recognize 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 identify a radical.
  • I can identify if a radical expression is in simplest form.
  • I can recognize the properties of radicals, i.e., product, quotient, and sum of radicals.
  • I can identify perfect squares.
  • I can define a logarithm.
  • I can recall properties of logarithms and exponents.
  • I can recognize common logarithms and natural logarithms.
  • I can identify an asymptote.
  • I can recall the change of base formula.

Reasoning Targets

  • I can apply the distributive property.
  • I can analyze what type of factoring technique that should be used for a given expression. (i.e. factor trinomials, factor difference of squares, factor sum and difference of cubes, factor by grouping, factor out the greatest common factor)
  • I can combine like terms in an expression or equation.
  • I can analyze an algebraic expression.
  • I can decide what to do next based on my knowledge of the order of operations.
  • I can distinguish the difference of when to use each property of radicals.
  • I can evaluate the properties of radicals.
  • I can convert from a logarithm to exponential expressions.
  • I can identify an asymptote.
  • I can expand and condense logarithms.
  • I can evaluate logarithms and exponential expressions.
  • I can distinguish between a natural log and common log.

Skills (Performance) Targets

  • I can simplify a polynomial expression.
  • I can multiply polynomials.
  • I can justify the steps taken in manipulating an expression.
  • I can complete all necessary steps in order to simplify the expression.
  • I can distribute and factor an expression.
  • I can simplify an algebraic expression.
  • I can apply factor using perfect square.
  • I can do prime factorization.
  • I can rationalize a denominator.
  • 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 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 apply basic properties of exponents and logarithms to rewrite algebraic expressions.
  • I can graph logarithmic and exponential functions.
  • I can solve logarithmic and exponential equations.
  • I can apply the change of base formula to evaluate a logarithmic expression.
  • I can apply basic properties of exponents and logarithms to rewrite algebraic expressions.
  • I can graph logarithmic and exponential functions.
  • I can solve logarithmic and exponential equations.
  • I can apply the change of base formula to evaluate a logarithmic expression.
  • I can graph and determine the equation of an asymptote.
  • I can choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
  • I can write expressions in equivalent forms by factoring to find the zeros of a quadratic function and explain the meaning of the zeros.
  • I can complete the square in a quadratic expression to convey the vertex form and determine the maximum or minimum value of the quadratic function, and to explain the meaning of the vertex.
  • I can use properties of exponents (such as power of a power, product of powers, power of a product, power of a quotient) to write an equivalent form of an exponential function to reveal and explain specific information about its approximate rate of growth or decay.

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-SSE.03.a

MAT-HS Targeted Standards
(A) Concept: Algebra
(SSE) Domain: Seeing Structure in Expressions
Cluster: Write expressions in equivalent forms to solve problems

MAT-HS.A-SSE.03.a Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

  • a. Factor a quadratic expression to reveal the zeros of the function it defines.

Student Learning Targets:

Knowledge Targets

  • I can

Reasoning Targets

  • I can

Skills (Performance) Targets

  • I can solve a quadratic equation by factoring methods and the zero product property.

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.

Solve the following polynomials by factoring:

  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 solve a quadratic equation by factoring

  • can use the zero product property


The student exhibits no major errors or omissions.

Solve the following polynomials by factoring.

  • x2+8x+7=0

  • 2x2-15x+18=0

  • 3x2+2x+1=7x+3

  • 4x2-8x+3=0

  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:


The student:

  • can solve a quadratic equation using the zero product property


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

Solve the following polynomials by the zero product property.

  • (x+5)(x-3)=0

  • 7x(x-1)=0

  • (3x-5)(x-9)=0

  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-SSE.04

MAT-HS Targeted Standards
(A) Concept: Algebra
(SSE) Domain: Seeing Structure in Expressions
Cluster: Write expressions in equivalent forms to solve problems

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.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can develop the formula for the sum of a finite geometric series when the ratio is not 1.
  • I can use the formula to solve real world problems.

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