# Mathematics Content Assessed by PAWS

Wyoming Content Standard 3.
Measurement |
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Skill 1. Understand measurable
attributes of objects and the units, systems, and processes of
measurement. |
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Benchmark |
Context |
Content Limits: |

06.3.1Students apply estimation and measurement of length to content problems and express the results in metric units (centimeters and meters). |
Problem solving
situations will include the use of appropriate methods, tools, and units to solve problems involving estimation and measure of length, weight and capacity using metric units; and conversion of measurements of length within the metric system and weight and capacity in the U.S. customary system. |
• Items involving length,
weight, and capacity should involve the metric system of measurement. • Items may require students to solve real-world problems, including distance, using a scale drawing. • Measurements may be in either metric or customary units. • All conversions of units must be within the same system of measurement (metric or customary). • Items may involve up to three-unit conversions. • Items should involve interpreting and applying various scales, including those based on models and maps. • Scales must use only whole number increments and measures • Items should be set in a real-world context. • Graphics should be used in most of these items, as appropriate. |

06.3.2Students apply estimation and measurement of weight to content problems and express the results in U.S. customary units (ounces, pounds, and tons). |
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06.3.3Students apply estimation and measurement of capacity to content problems and express the results in U.S. customary units (teaspoons, tablespoons, cups, pints, quarts, gallons). |
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06.3.4Students demonstrate relationships within the U.S. customary units for weight and capacity and within the metric system (centimeters to meters) in problem-solving situations. |
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Skill 2. Apply appropriate
techniques, tools, and formulas to determine perimeter, area or volume. |
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Benchmark |
Context |
Content Limits: |

06.3.5Students determine the area and perimeter of regular polygons and the area of parallelograms, with and without models. |
Problem solving situations will include calculating the perimeter of regular polygons with no more than 8 sides and the area of parallelograms with and without models. |
• Items involving area should be
limited to triangles, rectangles, and parallelograms. • The number of two-dimensional figures assessed in an item cannot exceed two. • Items should use numbers that are easy to compute with so that meaning rather than computation is the major focus. • Items may assess the relationship between the area or perimeter of an original figure and that of a newly created figure, or how perimeter or area is affected by changes in the dimensions of the figure. • The changes in dimensions of a figure that are increases should use scale factors that are whole numbers. • The changes in dimensions of a figure that are decreases should use scale factors that are common - unit fractions with denominators of 2, 3, or 4. • Items may present two - or three-dimensional figures. • Graphics should be used in most of these items, as appropriate. • Items requiring three-dimensional graphics must be realistic and must include verbal descriptions. • Items should be set in either a real-world or mathematical context |

Wyoming Content Standard 4.
Algebra |
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Skill 1. Understand patterns,
relations, and functions. |
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Benchmark |
Context |
Content Limits: |

06.4.1Students recognize, describe, extend, create, and generalize patterns, such as numeric sequences , by using manipulatives, numbers, graphic representations, including charts and graphs . |
Problem solving
situations will require the use of sound reasoning to recognize, describe, and extend numeric patterns in a problem solving situation. |
• Items will assess
numerical and graphic patterns. • Items may use pictures and graphics to present one- step linear equations. • Items should not use more than two variables or include more than one operation. • Items will use words, tables, symbols, variables, and graphs expressing equations or patterns. • Items are limited to non- negative values . • Operations in patterns such as function tables may include the effects of the four basic operations on whole numbers to solve problems • Items may include graphic representations of a pattern, sequence, relationship, or function. • Items may be set in either a real-world or mathematical context. • Graphics should be used in most of these items, as appropriate. |

06.4.2Students apply their knowledge of patterns to describe a constant rate of change when solving problems. |
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Skill 2. Use mathematical
models to represent and understand quantitative relationships. |
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Benchmark |
Context |
Content Limits: |

06.3.3Students represent the idea of a variable as an unknown quantity, a letter, or a symbol within any whole number operation. |
Problem solving situations will require using symbolic reasoning to represent the concepts of a variable as an unknown quantity, letter, or symbol within any one-step whole number operation. |
• Items may include only one variable
limited to whole numbers. • Problem situations involving multiplication should represent the operation as 5 · n or 5n or 5 x n. • Problem situations involving division should represent the operation using the symbol “÷” or “/” (e.g., 5 ÷ n or 5/n). • Items involving graphing functions should be from the first quadrant and limited to plotting points with whole number coordinates. • Items should rely primarily on translating among written descriptions, expressions, and graphic representations. • Items may be assessed in either a real-world (including money) or mathematical context. • Graphics should be used in most of these items, as appropriate |

Wyoming Content Standard 5.
Data Analysis and Probability |
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Skill 1. Collect, organize,
and display relevant data to answer questions and use appropriate
statistical methods to analyze the data. |
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Benchmark |
Context |
Content Limits: |

06.5.1Students systematically collect, organize, and describe/represent numeric data using line graphs. |
Problem solving situations will require finding and interpreting mean and mode for data sets of no more than 10 pieces of data in real- world situations; and collecting, organizing, describing, and representing data using a variety of data displays including line graphs. |
• Items may include pictographs,
charts, stem-and-leaf plots, bar graphs, and single-line graphs, and
Venn diagrams. • Histograms will not be assessed. • The data presented should represent eight or fewer categories and a sum that can easily be divided without a remainder. • Items will assess finding the range, mean or mode of a set of data presented in a chart, list, table, graph, or plot (e.g., stem-and-leaf plot or line plot). • Items that assess understanding of these concepts may ask students to draw conclusions from an analysis of range and/or central tendency measures. • No more than 10 pieces of data should be used for calculations of the mean and mode. • No more than eight categories of information should be used in data sets. • Data contained in these items need not be ordered . • Items will assess: • interpreting and comparing information from bar graphs, single-line graphs, stem-and- leaf plots, or Venn diagrams; • recognizing appropriate displays for different kinds of data; • using and recognizing appropriate scale increments; • choosing reasonable titles, labels, scales, and intervals for data on pictographs and bar or line graphs; • generating questions, collecting responses, and displaying data on graphs; and • analyzing and explaining in writing the implications of graphed data. • Graphics should be used in most of these items, as appropriate. • Items should be set in a real-world context. |

Skill 2. Develop and evaluate
inferences and predictions that are based on data.. |
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Benchmark |
Context |
Content Limits: |

06.5.2Students, given a scenario, recognize and communicate the likelihood of events using concepts from probability (i.e., impossible, equally likely, certain) appropriate to grade level. |
Problem solving situations with simple probability and will require communicating the likelihood of events from experiments or simulations of 2 independent events using the language: certain, most likely, equally likely, least likely , and impossible. |
• Items may include probabilities for
independent and dependent events. • In items involving the determination of all possible outcomes, the number of outcomes should not exceed 24. • Mathematical expectations of probabilities will be assessed using simple empirical data or theoretical probabilities. • Most items developed for this context should assess simple events. • Probabilities should be based on whole numbers. • Items will assess the likelihood or probability of an outcome occurring. • Probabilities may be expressed as certain, most likely, equally likely, least likely, and impossible. • Items should be set in a real-world context. • Students may be presented with word problems and/or tables. • Graphics should be used in most of these items, as appropriate. |

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