HS Mathematics Item Specification C1 TB
HS Math C1 TB
Claim 1: Concepts and Procedures
Students can explain and apply mathematical concepts and interpret and carry out
mathematical procedures with precision and fluency.
Content Domain: Number and Quantity
Target B [m]: Use properties of rational and irrational numbers.
Tasks for this target will require students to demonstrate understanding of operations with
rational and irrational numbers, leading to generalizations about their sums and products.
These will range from providing concrete examples (e.g., give or choose three examples
to show that the sum of two rational numbers is rational) to abstract generalizations (e.g.,
reasoning related to understanding that the sum of any two rational numbers is rational).
Standards: N-RN.3
DOK Target(s): 1, 2, 3
Evidence Required:
1. The student provides examples of addition or multiplication
problems that will have sums or products of a specified type
(either rational or irrational).
2. The student determines if the sum of two numbers is a
rational number or an irrational number.
3. The student determines if the product of two numbers is a
rational number or an irrational number.
4. The student provides an abstract generalization that the sum
or product of any two rational numbers is rational, the sum
of a rational number and an irrational number is irrational,
and the product of a nonzero rational number and an
irrational number is irrational.
Allowable Item Types*: SR, CR
Task Models: 1. CR (DOK 1, 2)
Prompt Features 1: The student is prompted to give example
addition problems that would have a sum that is either a
rational or an irrational number.
Prompt Features 2: The student is prompted to give example
multiplication problems that would have a product that is either
a rational or an irrational number.
Stimulus: The student is presented with a type of number
(rational or irrational) and instructions that will fit studentgenerated example problems into a scorable format.
2. SR (DOK 1)
Prompt Features 1: The student is prompted to identify
whether the resulting sums for the addition problem(s) are
rational or irrational.
Stimulus 1: The student is presented with at least three
addition problems having two addends where at least one
addend is rational.
Stimulus 2: The student is presented with at least three
Version 1.0
HS Mathematics Item Specification C1 TB
addition problems having two addends where at least one
addend is irrational.
Prompt Features 2: The student is prompted to identify which
type of number the other addend will be from a list of possible
number types (e.g., rational, irrational).
Stimulus 1: The student is presented with an addition problem
having two addends and is given that one addend is a rational
number and the sum is a rational number.
Stimulus 2: The student is presented with an addition problem
having two addends and is given that one addend is a rational
number and the sum is an irrational number.
Stimulus 3: The student is presented with an addition problem
having two addends and is given that one addend is an
irrational number and the sum is an irrational number.
3. SR (DOK 1)
Prompt Features 1: The student is prompted to identify
whether the resulting product(s) for the multiplication
problem(s) are rational or irrational.
Stimulus: The student is presented with at least three
multiplication problems having two factors where either both
factors are nonzero rational numbers, or one factor is a
nonzero rational number and one factor is an irrational
number.
Prompt Features 2: The student is prompted to identify which
type of number the other factor will be from a list of possible
number types (e.g., rational, irrational).
Stimulus 1: The student is presented with a multiplication
problem having two factors and is given that one factor is a
nonzero rational number and the product is an irrational
number.
Stimulus 2: The student is presented with a multiplication
problem having two factors and is given that one factor is an
irrational number and the product is an irrational number.
Allowable Stimulus
Materials:
Allowable Disciplinary
Vocabulary:
4. CR (DOK 2)
Prompt Features 1: The student is prompted to explain what
possible sums result by combining any rational number with
either another rational number or an irrational number.
Prompt Features 2: The student is prompted to explain what
possible products result by combining any nonzero rational
number with an irrational number.
Stimulus: The student is presented with two abstract
quantities representing the set of rational numbers or the set
of irrational numbers (e.g., x = rational number, y = irrational
number).
products or sums of rational and irrational numbers, number
type (rational or irrational)
rational number, irrational number, real number
Version 1.0
HS Mathematics Item Specification C1 TB
Allowable Tools:
Target-Specific Only sums and products of two numbers are used.
Attributes:
Nontargeted Constructs:
Accessibility Concerns:
Sample Items:
*SR = selected-response item; CR = constructed-response item; TE = technology-enhanced
item; ER = extended-response item; PT = performance task
Version 1.0