Grade 11 - Claim 1 - Target E
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Claim 1
Concepts and Procedures
Standards
SSE-3
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
SSE-3a
Factor a quadratic expression to reveal the zeros of the function it defines.
SSE-3b
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
SSE-3c
Use the properties of exponents to transform expressions for exponential functions. For example the expression $1.15^{t}$ can be rewritten as $(1.15^{frac{1}{12}})^{12t}$ ≈ $1.012^{12t}$ to reveal the approximate equivalent monthly interest rate if the annual rate is...
Clarifications
Tasks for this target will require students to choose or produce an equivalent form of an expression, including factoring a quadratic expression, completing the square, and using properties of exponents. Some of these tasks...
Range Achievement Level Descriptors
Evidence Required
1
The student understands that the factored form of a quadratic expression reveals the zeros of the function it defines.
2
The student understands that completing the square for a quadratic expression reveals the maximum or minimum value of the function it defines.
3
The student uses the properties of exponents to transform exponential expressions.
Item Guidelines
Depth of Knowledge
M-DOK1
Recall includes the recall of information such as fact, definition, term, or a simple procedure, as well as performing a simple algorithm or applying a formula. That is, in mathematics a one-step, well-defined, and straight algorithmic procedure should be...
M-DOK2
Skill/Concept includes the engagement of some mental processing beyond a habitual response. A Level 2 assessment item requires students to make some decisions as to how to approach the problem or activity, whereas Level 1 requires students to demonstrate a...
Allowable Item Types
- Hot Spot
- Multiple Choice, single correct response
- Equation/Numeric
Allowable Stimulus Materials
quadratic expressions (in expanded form), exponential expressions
Key/Construct Relevant Vocabulary
monomial, binomial, trinomial, polynomial, maximum value, minimum value, zero (of a function)
Allowable Tools
calculator (varies by task model)
Target-Specific Attributes
None
Accessibility
Item writers should consider the following Language and Visual Element/Design guidelines [1] when developing items. Language Key Considerations: Use simple, clear, and easy-to-understand language needed to assess the construct or aid in the understanding of the...
Development Notes
None
Task Models
Task Model 1a
Item Types
Hot SpotDepth of Knowledge
M-DOK2Standards
SSE-3a
Target Evidence Statement
The student understands that the factored form of a quadratic expression reveals the zeros of the function it defines.
Allowable Tools
None
Accessibility Note
Hot Spot items are not currently able to be Brailled. Minimize the number of items developed...
Task Description
Prompt Features: The student identifies the factored form of a quadratic expression that represents f(x) as best for revealing zeros and chooses the zeros. Stimulus Guidelines: Equivalent forms of quadratic equations are given in different forms. Difficulty...
Stimulus
The student is presented with equivalent quadratic equations for f(x).
Example 1
Example Stem:
Part A: Three equations that all represent the same function f are shown. Select the equation that includes the zeros of f(x) as numbers that appear in the equation.
Part B: Select all values of x for which f(x) = 0.
Rubric:
(1 point) The student selects the correct equation for f(x) and selects the correct zeros.
