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# Mathematics Content Assessed by PAWS

 Wyoming Content Standard 3. Measurement Skill 1. Understand measurable attributes of objects and the units, systems, and processes of measurement. Benchmark Context Content Limits: 06.3.1 Students 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. 06.3.2 Students apply estimation and measurement of weight to content problems and express the results in U.S. customary units (ounces, pounds, and tons). 06.3.3 Students apply estimation and measurement of capacity to content problems and express the results in U.S. customary units (teaspoons, tablespoons, cups, pints, quarts, gallons). 06.3.4 Students demonstrate relationships within the U.S. customary units for weight and capacity and within the metric system (centimeters to meters) in problem-solving situations. Skill 2. Apply appropriate techniques, tools, and formulas to determine perimeter, area or volume. Benchmark Context Content Limits: 06.3.5 Students 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 Skill 1. Understand patterns, relations, and functions. Benchmark Context Content Limits: 06.4.1 Students 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. 06.4.2 Students apply their knowledge of patterns to describe a constant rate of change when solving problems. Skill 2. Use mathematical models to represent and understand quantitative relationships. Benchmark Context Content Limits: 06.3.3 Students 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 Skill 1. Collect, organize, and display relevant data to answer questions and use appropriate statistical methods to analyze the data. Benchmark Context Content Limits: 06.5.1 Students 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.. Benchmark Context Content Limits: 06.5.2 Students, 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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