MATHS.ASSE.03
MATHS Targeted Standards (A) Concept: Algebra (SSE) Domain: Seeing Structure in Expressions Cluster: Write expressions in equivalent forms to solve problems
MATHS.ASSE.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: MATHS.ASSE.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 (1.15^{1/12})^{12t} ≈ 1.012^{12t} 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

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
