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# MAFS.912.A-SSE.2.3

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

1. Factor a quadratic expression to reveal the zeros of the function it defines.
2. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
3. Use the properties of exponents to transform expressions for exponential functions. For example the expression  can be rewritten as  ≈  to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
Subject Area: Mathematics
Domain-Subdomain: Algebra: Seeing Structure in Expressions
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Write expressions in equivalent forms to solve problems. (Algebra 1 - Supporting Cluster) (Algebra 2 - Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes

### TEST ITEM SPECIFICATIONS

• Item Type(s): This benchmark may be assessed using: SHT , TI item(s)
• Also assesses:
MAFS.912.A-SSEE.1.1

MAFS.912.A-SSE.1.2

• Assessment Limits :
Items that require the student to transform a quadratic equation to
vertex form, b/a must be an even integer.

For A-SSE.1.1, items should not ask the student to interpret zeros, the
vertex, or axis of symmetry when the quadratic expression is in the
form ax² + bx + c (see F-IF.3.8).

For A-SSE.2.3c and A-SSE.1.1, exponential expressions are limited to
simple growth and decay. If the number e is used then its
approximate value should be given in the stem.

For A-SSE.2.3a and A-SSE.1.1, quadratic expressions should be
univariate.

For A-SSE.2.3b, items should only ask the student to interpret the yvalue of the vertex within a real-world context.

For A-SSE.2.3, items should require the student to choose how to
rewrite the expression.

In items that require the student to write equivalent expressions by
factoring, the given expression may

• have integral common factors
• be a difference of two squares up to a degree of 4
• be a quadratic, ax² + bx + c, where a > 0 and a, b, and c are integers
• be a polynomial of four terms with a leading coefficient of 1 and highest degree of 3.
• Calculator :

Neutral

• Clarification :
Students will use equivalent forms of a quadratic expression to
interpret the expression’s terms, factors, zeros, maximum, minimum,
coefficients, or parts in terms of the real-world situation the
expression represents.
Students will use equivalent forms of an exponential expression to
interpret the expression’s terms, factors, coefficients, or parts in
terms of the real-world situation the expression represents.

Students will rewrite algebraic expressions in different equivalent
forms by recognizing the expression’s structure.

Students will rewrite algebraic expressions in different equivalent
forms using factoring techniques (e.g., common factors, grouping, the
difference of two squares, the sum or difference of two cubes, or a
combination of methods to factor completely) or simplifying
expressions (e.g., combining like terms, using the distributive
property, and other operations with polynomials).

• Stimulus Attributes :
Items assessing A-SSE.2.3 and A-SSE.1.1 must be set in a real-world
context.

Items that require an equivalent expression found by factoring may
be in a real-world or mathematical context.

Items should contain expressions only.

Items may require the student to provide the answer in a specific
form.

• Response Attributes :
Items may require the student to choose an appropriate level of
accuracy.

Items may require the student to choose and interpret units.

For A-SSE.1.1 and A-SSE.2.3, items may require the student to apply
the basic modeling cycle.

### SAMPLE TEST ITEMS (1)

• Test Item #: Sample Item 1
• Question:

Sue removes the plug from a trough to drain the water inside. The volume, in gallons, in the trough after it has been unplugged can be modeled by 4t²-32t+63, where t is time, in minutes.

A. Click on the correct property that will give Sue the amount of time it takes the trough to drain.

B. Click on the expression that will reveal the property.

• Difficulty: N/A
• Type: SHT: Selectable Hot Text