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.