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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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