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Mathematics Content Assessed by PAWS

Wyoming Content Standard 1. Number Operations and Concepts
Skill 1. Understand the meaning of arithmetic operations and make reasonable estimates.
Benchmark Context Content Limits:
06.1.4
Students explain their choice of
estimation and problem solving strategies
and justify results when performing
number operations with fractions and
decimals in problem -solving situations.
Problem solving situations will
include conversion and
simplification of proper and
improper fractions and mixed
numbers; rounding decimal
places to 10ths, 100ths, and
wholes; and estimation of
whole numbers and decimals
(tenths, hundredths, and
thousandths) greater than zero.
• The data presented to students may be either precise
values, a range of values, or a combination of precise
values and estimates of other values.

• Items involving estimation should be limited to use
of whole numbers and decimals (tenths, hundredths,
and thousandths) greater than zero only.

• Item situations should require estimation to find the
solution and should not lend themselves to the
calculation of an exact amount.

• Items may assess the effects of the four basic
operations on whole numbers, fractions, mixed
numbers, and decimals, and the use of properties of
real numbers (commutative and associative) to solve
problems.

• Items will not include whole numbers with more
than three digits, positive fractions with more than
two-digit numerators and denominators , and/or
decimals greater than thousandths.

• Items should not assess abstract constructs.

• Items should be set in either a real-world or a
mathematical context

Graphics should be used in most of these items, as
appropriate
06.1.6
Students demonstrate an understanding of fractions and decimals by:
• representing fractions as division of
whole
numbers;
converting between mixed numbers
and improper fractions;
• simplifying fractions and mixed
numbers;
• writing fractions in equivalent forms;
• using parts of a set;
• rounding decimal numbers to 10ths,
100ths, and whole numbers (units)
place; and
• converting between decimals (from
.01 to .99), fractions and representing percentages.
Skill 2. Understand ways to represent numbers, relationships among numbers, and number systems.
Benchmark Context Content Limits:
06.1.1
Students use the concept of place value to
read and write decimals (to 1000ths) in
words, standard, and expanded form .
Problem solving situations will
include the use of place value
to read and write decimals (to
thousandths) in words and
standard form; ordering, and
comparison of whole numbers
and decimals (tenths,
hundredths, and thousandths)
greater than zero; and
representation of whole
numbers and fractions greater
than zero on the number line.
• Items may compare whole numbers and decimals
(tenths, hundredths, and thousandths) greater than
zero and include ordering numbers on a number line.

• Items may compare smaller or larger numbers, or
compare the order of magnitude between numbers.

• Words, number lines, drawings, numerals, or
symbols (<,>, =,≤,≥) may be used.

• An item may utilize one format or a variety of
formats, such as fractions or decimals.

• Items may include the relationships among whole
numbers and decimals given a real-world context.

• The place values of the fractional part of decimal
numbers should range from tenths through
thousandths.

• Items may contain multiple forms of a given value.

• Items will not include repeating decimals.

• Some items should include word names as well as
numerals.

• Items should be set in either a real-world or
mathematical context.

• Graphics should be used in some of these items, as
appropriate.
06.1.3
Students represent the number line using
integers.
06.1.6
Students demonstrate an understanding of fractions and decimals by:
• representing fractions as division of
 whole numbers;
• converting between mixed numbers
and improper fractions;
• simplifying fractions and mixed
numbers;
• writing fractions in equivalent forms;
• using parts of a set;
• rounding decimal numbers to 10ths,
100ths, and whole numbers (units)
place; and
• converting between decimals (from
.01 to .99), fractions and representing percentages.
Skill 3. Develop the connection between conceptual understanding and computational proficiency.
Benchmark Context Content Limits:
06.1.2
Students multiply decimals (10ths &
100ths) and divide whole numbers by 2-
digit divisors and divide decimals by
 whole numbers.
Problem solving situations will
include computational fluency
 with addition and subtraction
of decimals, multiplication of
whole numbers, and division
of two-digit whole numbers
greater than zero.
• Items will assess the effects of the four basic
operations on whole numbers; addition and
subtraction of decimals , multiplication and division
of two-digit whole numbers greater than zero to
solve problems (decimals may be used in the context
of money only).

• Items will not include a divisor more than two digits .

• Items will not include whole numbers with more
than three digits, positive fractions with more than
two-digit numerators and denominators, and/or
decimals greater than thousandths.

• Items should not involve division by a fraction.

• Items should be set in either a real-world or a
mathematical context.

• Graphics should be used in some of these items, as
appropriate.
Wyoming Content Standard 2. Geometry
Skill 1. Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
Benchmark Context Content Limits:
06.2.1
Students classify, describe, compare, and
draw representations of 1- and 2-
dimensional objects and angles.
Problem solving situations will
include identifying,
classifying, and drawing lines
(parallel, perpendicular, and
intersecting) and angles (acute,
right, and obtuse).
• Items will assess identifying basic properties of lines
and various types of angles.

• Objects or points on the coordinate grid should be
placed on the points of intersection of the grid lines.

• Items may assess understanding and application of
perpendicularity and parallelism.

• Items should utilize only a single figure, with no
comparisons to other figures or transformations.

• Items should assess only geometric concepts of two-
dimensional figures.

• Items may use coordinate planes.

• Items should be set in either a real-world or
mathematical context.

• Graphics should be used in most of these items, as
appropriate.
Skill 2. Analyze characteristics and properties of two- and three-dimensional geometric shapes.
Benchmark Context Content Limits:
06.2.1
Students classify, describe, compare, and
draw representations of 1- and 2-
dimensional objects and angles
Problem solving situations will
include geometrical attributes
of circles and regular polygons
to allow students to use spatial
reasoning and geometric
modeling.
• Items will assess identifying basic properties and
attributes of regular polygons, such as
parallelograms, trapezoids, pentagons, hexagons,
triangles, and quadrilaterals.

• Items assessing three-dimensional figures will use
rectangular prisms or right circular cylinders.

• Items assessing three-dimensional figures will use
various types of drawings and perspectives (e.g., flat
patterns/nets, isometric drawings).

• Items may use coordinate planes.

• Items should be set in either a real-world or
mathematical context.

• Graphics should be used in most of these items, as
appropriate.
Skill 3. Apply transformations and use symmetry to analyze mathematical situations.
Benchmark Context Content Limits:
06.2.2
Students identify and classify congruent
objects by properties appropriate to grade
level.
Problem solving situations will
include communicating with
mathematical language to
identify and classify congruent
objects when properties
of shapes are provided.
• Items may assess properties and relationships
pertaining to regular two-dimensional shapes, and
the concepts of symmetry, reflections, and
congruency.

• Items may assess understanding and application of
symmetry, and congruency.

• Items will not assess three-dimensional figures.

• Items should assess only geometric concepts of two-
dimensional figures.

• Items may present a coordinate plane to locate
and/or describe objects.

• Items may be set in either a real-world or
mathematical context.

• Graphics should be used in most of these items, as
appropriate.
06.2.3
Students communicate the reasoning used
in identifying geometric relationships in
problem-solving situations appropriate to
grade level.
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