Content Strand 1: Number Sense - Item Specification (8-2005)
NS01 (Number and Numeration) Demonstrate understanding of the concepts and symbolic representations of rational numbers including integers; demonstrate understanding of the relative values of rational numbers including integers; use properties of addition and multiplication with non-negative rational numbers; demonstrate understanding of the additive inverse property with integers (1.1.1, 1.1.2, 1.1.3)
Item Format:
· Multiple-Choice and Short-Answer items may be used to test this learning target.
Stimulus, Stem, and Prompt Rules:
· Stimulus may include numbers from the hundred millions place to the thousandths place.
· Stimulus may include fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 25, 50, 100
· Rational numbers, including integers, may be presented in symbols, number lines, geometric representations, and pictorial models.
· Items will not require students to name, identify by name, or define properties.
Mathematical Vocabulary and Terms:
· Terms that may be used: =, ?, <, >, <=, >=, number line, place value, property
· Terms that may be used with definitions or examples: compare (tell how they are alike and/or how they are different), evaluate, simplify
· Terms that may not be used: associative, commutative, identity, integer, inverse, rational number, reduce, relative value, zero property
Item Characteristics:
a) Items may ask students to show or describe the meaning of a rational number including integers in words or pictures.
b) Items may ask students to explain and/or illustrate the meaning of integers and integer values.
c) Items may ask students to write a rational number based on a picture of a real-world model or a location on a number line.
d) Items may ask students to convert between different representations of rational numbers including integers and mixed numbers.
e) Items may ask students to compare and order rational numbers including integers from the hundred millions place to the thousandths place with illustrations, symbolically, or on a number line.
f) Items may ask students to explain why one integer, fraction, decimal, or percent is greater than, equal to, or less than another integer, fraction, decimal, or percent.
g) Items may ask students to identify, use, illustrate, or evaluate an application of the following addition and multiplication properties with non-negative rational numbers:
h) Items may ask students to use addition and multiplication properties to assist in computations, e.g., 5 x 7 x 6 = 5 x 6 x 7 which is 30 x 7 or 210.
Properties of Addition Commutative Property Associative Property Identity Property Properties of Multiplication Commutative Property Associative Property Identity Property Zero Property
i) Items may ask students to identify, use, or illustrate the inverse property of addition with integers.