6 by pengtt

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Grade 6                   Press for Link to                  NS

Item Specs                Grade 6



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      Grade 5
      Grade 4                         Grade 7



                                              6
                                                  NS ME GS PS AS
                                                         NS01 NS02 NS03 NS04 NS05

                                                                                         Next Page
Content Strand 1: Number Sense                                                              NS




   NS01 (Number and Number Theory)
    –   1.1.1 Understand the concept of integers as the set of natural numbers (1, 2, 3 …), their
        opposites (-1, -2, -3 …), and 0.
    –   1.1.2 Understand the relative values of integers and non-negative rational numbers.
    –   1.1.3 Apply properties of addition and multiplication to non-negative rational numbers.
   NS02 (Ratio and Proportion)
    –   1.1.4 Understand the concepts of ratio and percent.
   NS03 (Conceptual Understanding of Operations)
    –   1.1.5 Understand the meaning of multiplication and division on non-negative rational numbers.
   NS04 (Computation)
    –   1.1.6 Apply computational procedures with fluency for addition and subtraction on non-
        negative rational numbers.
   NS05 (Estimation)
    –   1.1.8 Apply estimation strategies to predict or determine the reasonableness of answers in
        situations involving addition and subtraction on non-negative rational numbers.


                                                                  6 NS
                                                                      NS ME GS PS AS
                                               NS01 NS02 NS03 NS04 NS05

Content Strand 1: Number Sense
                                                                    Next Page
                                                                       NS
NS01 (Number and Numeration) Demonstrate
understanding of the concepts and symbolic representations of
mixed numbers, proper and improper fractions, decimals, and
integers as the set of natural numbers (1, 2, 3 …), their opposites
(-1, -2, -3 …), and 0.; demonstrate understanding of the relative
values of integers, non-negative fractions, decimals, and percents;
use properties of addition and multiplication with non negative
rational numbers; demonstrate understanding of the concept of
divisibility including prime and composite numbers, factors and
multiples.(1.1.1, 1.1.2, 1.1.3)

Item Format:
Multiple-Choice and Short-Answer items may be used to test this learning
target.
                                                     6 NS01
                                                         NS ME GS PS AS
                                                NS01 NS02 NS03 NS04 NS05

    Stimulus, Stem, and Prompt Rules:                                    Next Page
                                                                            NS

• Stimulus may include integers, non-negative fractions, decimals, and
  percents presented in symbols, number lines, geometric
  representations, and pictorial models and/or real-world objects.

• Stimulus may include illustrations of thousands blocks, hundreds blocks,
  tens blocks, and ones blocks, sticks, number lines, and other pictorial
  models for whole numbers, fractions, or decimals.

• Stimulus may include numbers from the hundred millions place to the
  thousandths place.

• Stimulus may include fractions with denominators of 2, 3, 4, 5, 6, 8, 10,
  12, 15, 16, 20, 25, 50, and/or 100.

• Items will not require students to name, identify by name, or define
  properties.                                          6 NS01
                                                           NS ME GS PS AS
                                                   NS01 NS02 NS03 NS04 NS05

Mathematical Vocabulary and Terms:
                                                                            Next Page
                                                                               NS


•   Terms that may be used: =, ≠, <, >, ≤, or ≥, decimal, denominator, divisible,
    factor, fraction, greatest common factor, least common multiple, lowest
    terms, multiple, number line, numerator, percent, place value, prime,
    property

•   Terms that may be used with definitions or examples: compare (tell how
    they are alike and/or how they are different), evaluate, quotient, simplify

•   Terms that will not be used: associative, commutative, composite, identity,
    integer, rational number, reduce, relative value, zero property




                                                          6 NS01
                                                              NS ME GS PS AS
                                                               NS01 NS02 NS03 NS04 NS05
     Item Characteristics:
                                                                                            Next Page
•   Items may ask students to explain and/or illustrate the meaning of integer and             NS
    integer values.

•   Items may ask students to explain when a fraction, decimal, or percent of one whole is not
    the same as the same fraction, decimal, or percent of another whole.

•   Items may ask students to convert between fractions, improper fractions, mixed numbers,
    and/or decimals.

•   Items may ask students to compare and/or order integers and non-negative proper and
    improper fractions, mixed numbers, percents, and decimals on a number line, with
    illustrations, or symbolically.

•   Items may ask students to explain why one integer, fraction, decimal, or percent is greater
    than, equal to, or less than another integer, fraction, decimal, or percent.

•   Items may ask students to identify, use, or illustrate the application of the following addition
    and multiplication properties with non-negative rational numbers:
        Properties of Addition            Properties of Multiplication
        Commutative Property              Commutative Property
        Associative Property              Associative Property
        Identity Property                 Identity Property
                                          Zero Property           6 NS01
                                                                             NS ME GS PS AS
                                                  NS01 NS02 NS03 NS04 NS05

• Items may ask students to use addition and multiplication               Next Page
  properties to assist in computation;                                       NS
  e.g., 5 x 7 x 6 = 5 x 6 x 7 which is 30 x 7 or 210.

• Items may ask students to identify or find numbers that are divisible by a
  given number and/or determine whether one number is divisible by
  another number.

• Items may ask students to demonstrate understanding of divisibility rules
  for the factors of 2, 3, 5, 9, and 10 and/or use rules of divisibility to show
  if a quotient is an integer.

• Items may ask students to identify or find prime or composite numbers
  or explain why a number is prime or composite.

• Items may ask students to determine whether one number is a multiple
  of another number or identify the least common multiple of two numbers.

• Items may ask students to identify or list factors or factor pairs for a
  given number or determine the greatest common factor of two numbers.

                                                         6 NS01
                                                             NS ME GS PS AS
                                               NS01 NS02 NS03 NS04 NS05

                                                                    Next Page
                                                                       NS

Content Strand 1: Number Sense

NS02 (Ratio and Proportion) Demonstrate
understanding of the concepts of ratio and percent
(1.1.4)
Item Format:
Multiple-Choice and Short-Answer items may be used to test this learning
target.




                                                     6 NS02
                                                         NS ME GS PS AS
                                    NS01 NS02 NS03 NS04 NS05

Stimulus, Stem, and Prompt Rules:                      Next Page
                                                          NS


• Stimulus may include numbers, tables, charts, and
  diagrams.

• Stimulus may include whole numbers, ratios, and/or
  percents.




                                        6 NS02
                                            NS ME GS PS AS
                                   NS01 NS02 NS03 NS04 NS05

Mathematical Vocabulary and Terms:                   Next Page
                                                        NS


• Terms that may be used: percent, ratio, scale

• Terms that may be used with definitions or examples:

• Terms that will not be used: rational number




                                        6 NS02
                                            NS ME GS PS AS
                                                        NS01 NS02 NS03 NS04 NS05
     Item Characteristics:
•   Items may ask students to identify or write ratios in part/part and          Next Page
    part/whole relationships using objects, pictures, and symbols                   NS

•   Items may ask students to create a ratio equivalent to a given ratio to determine an
    unknown value for a dimension or a number of events or objects.

•   Items may ask students to identify, demonstrate, or explain percent as 100 equal
    sized parts of a set.

•   Items may ask students to represent equivalent percentages using different objects,
    pictures, and/or symbols.

•   Items may ask students to identify or illustrate the use of percent.

•   Items may ask students to identify or represent equivalent ratios and/or percents.

•   Items may ask students to identify or determine a ratio or percent in a given situation.

•   Items may ask students to explain or show the meaning of a ratio or percent.

•   Items may ask students to give examples of ratio and/or percents in a situation.

•   Items may ask students to identify or determine fraction, decimal, or percent
    equivalents for common percents such as 90%, 75%, 66% 50%, 33%, 25%, and
    10%.                                         6 NS02           NS ME GS PS AS
                                               NS01 NS02 NS03 NS04 NS05

                                                                    Next Page
Content Strand 1: Number Sense                                         NS



NS03 (Conceptual Understanding of Operations)
Demonstrate understanding of the meaning of addition,
subtraction, multiplication, and division of non-negative
decimals and fractions (1.1.5)
Item Format:
Multiple-Choice and Short-Answer items may be used to test this learning
target.




                                                     6 NS03
                                                         NS ME GS PS AS
                                     NS01 NS02 NS03 NS04 NS05
Stimulus, Stem, and Prompt Rules:
                                                        Next Page
                                                           NS


• Stimulus may include words, numbers, mathematical
  expressions, symbols, illustrations, charts, graphs, or
  diagrams.

• Fractions may include denominators of 2, 4, 8 or 2, 3, 6
  or 2, 5, 10.

• Decimals may include tenths, 0.25, 0.50, and 0.75.




                                          6 NS03
                                              NS ME GS PS AS
                                    NS01 NS02 NS03 NS04 NS05
Vocabulary/Mathematical Terms:
                                                      Next Page
                                                         NS


• Terms that may be used: addition, difference, division,
  equation, factor, multiple, multiplication, operation,
  product, remainder, subtraction

• Terms that may be used with definitions or examples:
  quotient

• Terms that will not be used: addend, dividend, divisor,
  minuend, multiplicand, subtrahend



                                         6 NS03
                                             NS ME GS PS AS
                                                        NS01 NS02 NS03        NS04 NS05
      Item Characteristics:
•     .
    Items may ask students to explain or illustrate the meaning of addition      Next Page
    or subtraction of non-negative decimals and fractions.                          NS

•   Items may ask students to explain or illustrate the meaning of multiplying or dividing
    non-negative fractions and decimals.

•   Items may ask students to select and/or use an appropriate operation to show
    understanding of addition, subtraction, multiplication, or division of non-negative
    decimals and fractions.

•   Items may ask students to explain, with words or pictures, why multiplication of
    fractions can be done by multiplying denominators.

•   Items may ask students to explain, with words or pictures, why addition of fractions
    requires finding a common denominator.

•   Items may ask students to translate a given picture or illustration into an equivalent
    symbolic representation of addition, subtraction, multiplication, or division of non-
    negative decimals or fractions
                                                               6 NS03
                                                                   NS ME GS PS AS
                                               NS01 NS02 NS03 NS04 NS05

                                                                    Next Page
                                                                       NS

Content Strand 1: Number Sense

NS04 (Computation) Add and subtract non-negative
decimals and fractions (1.1.6)

Item Format:
Multiple-Choice and Short-Answer items may be used to test this learning
target.




                                                     6 NS04
                                                         NS ME GS PS AS
                                               NS01 NS02 NS03 NS04 NS05
Stimulus, Stem, and Prompt Rules:
                                                                       Next Page
                                                                          NS


• Stimulus may include words, numbers, mathematical expressions,
  illustrations, charts, graphs, or diagrams.

• Working with fractions, mixed numbers, and decimals within the
  same item may be required.

• NS04 items will be on a “no tools” day.

• Items assessing addition and/or subtraction of non-negative
  decimals and/or fractions will use the following guidelines:

    – Numbers Session Without Tools
    – Non-negative decimals up to three numbers to the thousandths place
    – Non-negative fractions up to three fractions with denominators 2, 3, 4,
      5, 6, 8, 10, 12, 15.                            6 NS04
                                                          NS ME GS PS AS
                                           NS01 NS02 NS03 NS04 NS05

Mathematical Vocabulary and Terms:                              Next Page
                                                                   NS


• Terms that may be used: addition, difference, equation, operation,
  subtraction, sum

• Terms or phrases that may be used with definitions or examples:
  simplify

• Terms that will not be used: addend, minuend, reduce, subtrahend




                                                 6 NS04
                                                     NS ME GS PS AS
                                           NS01 NS02 NS03 NS04 NS05
Item Characteristics:
                                                                 Next Page
                                                                    NS


• Items may ask students to find common denominators in order to
  add or subtract non-negative fractions.

• Items may ask students to add or subtract non-negative decimals.

• Items may ask students to do multiple step calculations requiring
  addition and/or subtraction using non-negative decimals and/or
  fractions.




                                                 6 NS04
                                                     NS ME GS PS AS
                                            NS01 NS02 NS03 NS04 NS05

                                                                  Next Page
Content Strand 1: Number Sense                                       NS


NS05 (Estimation) Identify when an approximation is
appropriate; use estimation to determine the
reasonableness of answers in situations involving
addition and subtraction of non-negative decimals and
fractions (1.1.8)

Item Format:
Multiple-Choice and Short-Answer items may be used to test this learning
target.
Multiple-Choice items will not ask students to estimate and identify the
answer.


                                                  6 NS05
                                                      NS ME GS PS AS
                                                    NS01 NS02 NS03 NS04 NS05

Stimulus, Stem, and Prompt Rules:
                                                                          Next Page
                                                                             NS


•   Stimulus may include tables, charts, diagrams, and illustrations.

•   Items will not require the use of a particular estimation strategy.

•   Items may present situations involving addition and subtraction of non-
    negative decimals and fractions.

•   NS05 items will be on a “no tools” day.




                                                           6 NS05
                                                               NS ME GS PS AS
                                           NS01 NS02 NS03 NS04 NS05

Mathematical Vocabulary and Terms:
                                                                 Next Page
                                                                    NS


• Terms that may be used: approximate (as an adjective), estimate,
  estimation, round

• Terms that may be used with definitions or examples: evaluate

• Terms that will not be used: approximate (as a verb), clustering,
  compatible numbers, front-end estimation or names of other
  estimation strategies




                                                 6 NS05
                                                     NS ME GS PS AS
                                                    NS01 NS02 NS03 NS04 NS05
Item Characteristics:
                                                                             Next Page
                                                                                NS


•   Items may ask students to identify or explain whether estimation or exact
    calculation is appropriate in situations involving addition and subtraction of
    non-negative decimals and fractions.

•   Items may ask students to estimate in situations involving addition and/or
    subtraction of non-negative decimals and fractions.

•   Items may ask students to use estimation to determine whether a
    computation result is reasonable.

•   Items may ask students to describe or explain a strategy used for estimation
    involving addition and/or subtraction of non-negative decimals and fractions.

•   Note: Students will not receive credit in estimation items for computing and
    then rounding.

                                                           6 NS05
                                                               NS ME GS PS AS
                                                  ME01 ME02 ME03 ME04

                                                                     Next Page
                                                                        ME

Content Strand 2: Measurement

   ME01 (Attributes and Dimensions)
    –   1.2.1 Understand the concepts of volume and extend the concept
        of area to surface area of rectangular prisms.
   ME02 (Units and Systems)
    –   1.2.2 Understand the differences between square and cubic units.
   ME03 (Procedures)
    –   1.2.4 Understand and apply systematic procedures to measure
        volume and capacity for solid shapes.
   ME04 (Estimated Measurements)
    –   1.2.6 Understand and apply strategies to obtain reasonable
        estimates of volume or capacity.


                                                   6 ME
                                                       NS ME GS PS AS
                                                    ME01 ME02 ME03 ME04

                                                                    Next Page
                                                                       ME
Content Strand 2: Measurement

ME01 (Attributes and Dimensions) Demonstrate
understanding of the concepts of volume and surface
area of rectangular prisms; demonstrate understanding
of the concept of angle measurement (1.2.1)

Item Format:
Multiple-Choice and Short-Answer items may be used to test this learning
target.




                                                     6 ME01
                                                         NS ME GS PS AS
                                                                   ME01 ME02 ME03 ME04

     Stimulus, Stem, and Prompt Rules:
                                                                                   Next Page
                                                                                      ME

•   Stimulus may include pictures, tables, charts, diagrams, figures, and illustrations.

•   Stimulus will include illustrations in items that involve finding area or volume.
    Items will not require students to convert from U.S. to metric or metric to U.S.

•   The answer and distractors will be stated in terms of the same system of
    measurement.

•   Items assessing understanding of measurement attributes and dimensions may use
    the following units:

     –   Attribute
     –   US Units
     –   Metric (SI) Units
     –   Length inch (in.), foot (ft), yard (yd), mile (mi)
     –   millimeter (mm), centimeter (cm), meter (m), kilometer (km)
     –   Angle measurementdegree (º)
                                                                       6 ME01
                                                                           NS ME GS PS AS
                                                   ME01 ME02 ME03 ME04

Mathematical Vocabulary and Terms:
                                                                    Next Page
                                                                       ME


• Terms that may be used: angle, area, centimeter, cube, cubic unit,
  degree, foot/feet, inch, kilometer, meter, mile, millimeter, perimeter,
  rectangle, prism, right angle, surface area, square unit, volume,
  yard

• Terms that may be used with definitions or examples: compare (tell
  how they are alike and/or how they are different)

• Terms that will not be used:

• Students are expected to know how to determine the following:

    – Perimeter of a polygon
    – Area of a rectangle
    – Area of a triangle                            6 ME01
                                                        NS ME GS PS AS
Item Characteristics:                                        ME01 ME02 ME03 ME04
•   Items may ask students to identify or describe angles in a picture,
    diagram, or object.                                                       Next Page
                                                                                 ME
•   Items may ask students to identify or describe angles by their
    relationship to a right angle.

•   Items may ask students to compare the meaning of surface area and volume of
    a rectangular prism

•   Items may ask students to compare the volume of two containers and explain
    the difference.

•   Items may ask students to identify the volume for a given rectangular prism from
    a picture or model.

•   Items may ask students to identify examples of surface area and/or volume.

•   Items may ask students to use the surface area and volume to describe a
    rectangular prism.

•   Items may ask students to label measurements of a rectangular prism to show
    understanding of the relationships among linear dimensions, surface area, and
    volume of rectangular prisms and that area is measured in square units and
    volume in cubic units.
                                                            6 ME01
•   Note: Students are expected to determine and label units.
                                                                NS ME GS PS AS
                                                    ME01 ME02 ME03 ME04

Content Strand 2: Measurement                                       Next Page
                                                                       ME

ME02 (Units and Systems) Demonstrate
understanding of the concept of degrees in angles as a
unit of measurement – specifically 30o, 45 o, 60 o, 90
o, and 180 o angle measurements; demonstrate
understanding of the differences between square and
cubic units; demonstrate understanding of how
capacity, mass, and length units are organized in the
metric system (1.2.2, 1.2.3)

Item Format:
Multiple-Choice and Short-Answer items may be used to test this learning
target.
                                                     6 ME02
                                                         NS ME GS PS AS
                                                                 ME01 ME02 ME03 ME04
     Stimulus, Stem, and Prompt Rules:
                                                                                 Next Page
•   Stimulus may include pictures, tables, charts, diagrams, figures, and           ME
    illustrations.

•   Items will not require students to convert from U.S. to metric or metric to U.S.

•   The answer and distractors will be stated in terms of the same system of
    measurement.

•   Items assessing understanding of measurement units and systems may use the
    following units:

     –   Attribute
     –   US Units
     –   Metric (SI) Units
     –   Length inch (in.), foot (ft), yard (yd), mile (mi)
     –   millimeter (mm), centimeter (cm), meter (m), kilometer (km)
     –   Weight/mass milligram (mg), gram (g), kilogram (kg)
     –   Capacity (liquid volume)milliliter (mL), liter (L)
     –   Angle measurementdegree (º)                                 6 ME02
                                                                       NS ME GS PS AS
                                                    ME01 ME02 ME03 ME04

Mathematical Vocabulary and Terms:
                                                                      Next Page
                                                                         ME


• Terms that may be used: angle, area, centimeter, cubic unit,
  degree, foot/feet, gram, inch, kilogram, kiloliter, kilometer, liter,
  mass, meter, mile, milligram, milliliter, millimeter, perimeter, right
  angle, square unit, volume, yard

• Terms that may be used with definitions or examples:

• Terms that will not be used: metric system, U.S. system




                                                     6 ME02
                                                         NS ME GS PS AS
                                                                    ME01 ME02 ME03 ME04
     Item Characteristics:
•   Items may ask students to identify or describe angles or angle measures of 30º       Next Page
    , 45 º, 60 º, 90 º, and/or 180 º in a picture, diagram, or object.                      ME

•   Items may ask the student to draw angles or polygons with angles of 30 º, 45 º , 60 º ,
    and/or 90 º .

•   Items may ask the student to identify cubic units as a measure of volume.

•   Items may ask the student to explain why area and volume are measured in square units
    and cubic units vs. circular or triangular units.

•   Items may ask the student to explain how the selected unit of length affects the size of
    square or cubic units.

•   Items may ask students to explain the relationship of units within the metric system using
    milli-, centi-, and/or kilo-.

•   Items may ask students to convert between units in the metric system in order to answer a
    question using capacity, weight/mass, or length.

•   Note: Students are expected to determine and label units.


                                                                     6 ME02
                                                                         NS ME GS PS AS
                                                    ME01 ME02 ME03 ME04
Content Strand 2: Measurement
                                                                    Next Page
ME03 (Procedures) Use systematic procedures to                         ME

measure, describe, and compare the area of rectangles
and right triangles and the volume of rectangular prisms
- identify area or volume as the attribute to be measured,
select and use appropriate unit for area or volume,
select and use tool that matches the unit chosen, count
to determine the number of units; use formulas to find
the perimeter and area of rectangles and right triangles
(1.2.4, 1.2.5)

Item Format(s):
Multiple-Choice and Short-Answer items may be used to test this learning
target.
                                                     6 ME03
                                                         NS ME GS PS AS
                                                          ME01 ME02 ME03 ME04

Stimulus, Stem, and Prompt Rules:
                                                                              Next Page
                                                                                 ME


•   Stimulus may include illustrations of tools that are familiar to sixth-grade
    students, e.g., meter sticks, rulers, and grids.

•   Illustrations of rectangular prisms will be used in items that involve finding
    volume.

•   The answer and distractors will be stated in terms of the same system of
    measurement.

•   Items will not require students to convert from U.S. to metric or metric to
    U.S.
    Conversion facts may be given in an item, e.g., 1 mile = 5,280 feet.




                                                           6 ME03
                                                               NS ME GS PS AS
                                                   ME01 ME02 ME03 ME04

Mathematical Vocabulary and Terms:
                                                                    Next Page
                                                                       ME


• Terms that may be used: $, cm, ft, or other common abbreviations,
  area, attribute, centimeter, foot/feet, inch, kilometer, length, meter,
  mile, millimeter, perimeter, square unit, unit, volume, yard

• Terms that may be used with definitions or examples: acre,
  compare (tell how they are alike and/or how they are different)

• Terms that will not be used: metric system, U.S. system,

• Students are expected to know how to determine the following:

    – Perimeter of a polygon
    – Area of a rectangle
    – Area of a right triangle
                                                   6 ME03
                                                       NS ME GS PS AS
                                                                     ME01 ME02 ME03 ME04
     Item Characteristics:
                                                                                          Next Page
•   Items may ask students to identify or describe the appropriate units and/or tools
    for measuring area or volume.                                                            ME

•   Items may ask students to count or compare the attribute to the units on the measurement tool
    to determine the number of units.

•   Items may ask students to use and/or describe procedures for measuring length, perimeter, and
    area of a rectangle or right triangle and/or the volume of a rectangular prism:

•   identify the attribute to be measured;
           select and use appropriate unit of measurement;
           select and use a tool that matches the unit chosen;
           count or compare the attribute to the units on the tool to determine the number of units.

•   Items may ask students to determine whether measurement has been done correctly in a given
    situation.

•   Items may ask students to find the perimeter and/or area of a rectangle or right triangle.

•   Items may ask students to determine linear dimensions of a rectangle or right triangle based on
    a given perimeter or area.

•   Items may ask the student to use area or volume to compare rectangles, right triangles, or
    rectangular prisms.

•   Note: Students are expected to determine and label units.
                                                                     6 ME03
                                                                         NS ME GS PS AS
                                                      ME01 ME02 ME03 ME04

                                                                       Next Page
                                                                          ME
Content Strand 2: Measurement

ME04 (Estimated Measurements) Identify situations in
which estimated measurements are sufficient; estimate
volume using manipulatives and/or drawings; estimate
measures of angles and areas of rectangles and right
triangles (1.2.6)

Item Format:
Multiple Choice and Short-Answer items may be used to assess this learning
target.
Multiple-Choice items will not ask students to estimate and identify the answer.


                                                       6 ME04
                                                           NS ME GS PS AS
                                                  ME01 ME02 ME03 ME04

Stimulus, Stem, and Prompt Rules:
                                                                      Next Page
                                                                         ME


• Pictorial representations of objects and figures, tables, charts, and
  graphs may be used.

• Items should focus on the appropriate use of estimation rather than
  particular estimation strategies.

• Items will not require students to convert from U.S. to metric or
  metric to U.S.

• The answer and distractors will be stated in terms of the same
  system of measurement.

• ME04 items will be on a “no tools” day.

                                                   6 ME04
                                                       NS ME GS PS AS
                                                   ME01 ME02 ME03 ME04

Mathematical Vocabulary and Terms:
                                                                    Next Page
                                                                       ME


• Terms that may be used: accurate, accuracy, area, centimeters,
  cubic unit, degree, estimate, estimation, foot/feet, inch, kilometer,
  meter, mile, millimeter, perimeter, square unit, volume, yard

• Terms that may be used with definitions or examples:
  approximation

• Terms that will not be used: metric system, U.S. system

• Students are expected to know how to determine the following:
    – Perimeter of a polygon
    – Area of a rectangle
    – Area of a triangle

                                                    6 ME04
                                                        NS ME GS PS AS
                                                                   ME01 ME02 ME03 ME04
     Item Characteristics:
                                                                                        Next Page
•   Items may ask students to determine when or whether estimation is appropriate          ME
    in a given situation.

•   Items may ask students to determine if a given angle, area, or volume measurement is
    reasonable in a situation.

•   Items may ask students to identify or describe a procedure that would be an appropriate way to
    estimate angle measures, area, or volume.

•   Items may ask students to explain why they would use estimation rather than an exact
    measurement.

•   Items may ask students to estimate volume using drawings.

•   Items may ask students to estimate measures of angles or areas of rectangles and/or triangles.

•   Note: Students will not receive credit in estimation items for computing and then rounding.

•   Note: Students are expected to determine and label units.

                                                                    6 ME04
                                                                        NS ME GS PS AS
                                                                           GS01 GS02

                                                                                  Next Page
                                                                                     GS

Content Strand 3: Geometric Sense

   GS01 (Properties and Relationships)
    –   1.3.1 Understand the characteristics of circles and rectangular prisms.
    –   1.3.2 Apply understanding of angles and polygons.

   GS02 Locations and Transformations)
    –   1.3.3 Understand the relative location of integers on a number line.

    –   1.3.4 Apply understanding of rotations (turns) to two-dimensional figures.




                                                           6 GS
                                                               NS ME GS PS AS
                                                                 GS01 GS02


Content Strand 3: Geometric Sense                                   Next Page
                                                                       GS


GS01 (Properties and Relationships) Demonstrate
understanding of the characteristics of angles, polygons,
circles, and rectangular prisms; use properties of parallel
and perpendicular lines and line of symmetry and the
characteristics of angles and polygons to describe, draw,
and compare objects, shapes, and figures (1.3.1, 1.3.2)

Item Format:
Multiple-Choice and Short-Answer items may be used to test this learning
target.



                                                     6 GS01
                                                         NS ME GS PS AS
                                                               GS01 GS02

Stimulus, Stem, and Prompt Rules:
                                                                 Next Page
                                                                    GS


• Stimulus will include a box drawn in figures for right angles, hash
  marks on line segments to indicate equal lengths, and the symbol 
  to indicate perpendicular lines.

• Stimulus may include illustrations of 2-dimensional and 3-
  dimensional figures or objects.




                                                 6 GS01
                                                     NS ME GS PS AS
                                                                GS01 GS02

Mathematical Vocabulary and Terms:
                                                                   Next Page
                                                                      GS


• Terms that may be used: acute angle, angle, attribute, base, circle,
  circumference, cube, diagonal, diameter, dimensions, edge,
  equilateral, face, figure, height, hexagon, intersecting, isosceles,
  obtuse angle, octagon, parallel, parallelogram, pentagon,
  perpendicular, polygon, quadrilateral, prism, radius/radii, rectangle,
  rhombus, right angle, side, square, symmetry, 3-dimensional,
  trapezoid, triangle, 2-dimensional, vertex/vertices

• Terms that may be used with definitions or examples: compare (tell
  how they are alike and/or how they are different)

• Terms that will not be used: plane figure, solid figure



                                                   6 GS01
                                                       NS ME GS PS AS
                                                                                      GS01 GS02
     Item Characteristics:

•   Items may ask students to identify or describe angles, polygons, and/or circles     Next Page
    using geometric properties including parallel, perpendicular, and line of symmetry.    GS


•   Items may ask students to compare, sort, and/or label angles, polygons, and/or circles
    according to their geometric properties including parallel, perpendicular, and line of symmetry.

•   Items may ask students to identify, describe, compare, sort, and/or label rectangular prisms
    using geometric properties.

•   Items may ask students to draw a figure with given characteristics.

•   Items may ask students to draw symmetrical figures or to complete a picture or design given
    the line of symmetry.

•   Items may ask students to identify and/or draw one or more lines of symmetry in a given
    geometric figure.

•   Items may ask students to describe lines of symmetry for angles, polygons, and/or circles.



                                                                     6 GS01
                                                                         NS ME GS PS AS
                                                                 GS01 GS02
Content Strand 3: Geometric Sense
                                                                    Next Page
                                                                       GS
GS02 (Locations and Transformations) Describe the
relative location of points and objects on a positive-
negative number line; recognize or draw a translation
(slide) or reflection (flip) of a 2-dimensional shape or
figure; rotate (turn) a simple 2-dimensional figure 90° or
180° about the center or a vertex of the figure (1.3.3,
1.3.4)

Item Format:
Multiple-Choice and Short-Answer items may be used to test this learning
target.


                                                     6 GS02
                                                         NS ME GS PS AS
                                                                              GS01 GS02

     Stimulus, Stem, and Prompt Rules:                                            Next Page
                                                                                     GS
•   Number lines will have the necessary reference points labeled using
    integers, fractions, and/or decimals.

•   When rotating figures, the center of the figure must be marked and labeled.

•   When figures that are rotated are on a coordinate grid, each vertex and the
    center of the figure must be on the intersection of a horizontal and a vertical grid
    line.

•   Only the first quadrant of a Cartesian plane may be used.

•   Grids will be provided in items that require students to plot a point.

•   Location grids may use ordered number pairs or letter and number
    combinations.

•   Grids will have the origin and scales labeled.
                                                                6 GS02
                                                                    NS ME GS PS AS
                                                                                         GS01 GS02
     Mathematical Vocabulary and Terms:
                                                                                           Next Page
                                                                                              GS
•   Terms that may be used: angle, axis/axes, clockwise, coordinate(s),
    counterclockwise, degree, diagonal, figure, intersect, ordered pair, origin,
    parallel, perpendicular, point, vertex/vertices, x-axis, y-axis

•   Terms that may be used with definitions or examples: reflection (flip), rotation
    (turn), translation (slide)

•   Terms that will not be used: Cartesian plane, plane, quadrant

•   Terms related to transformations:

     – Translation (slide): the image of a figure in which every point in the figure moves the
       same distance in the same direction.

     – Reflection (flip): the mirror image of a figure on the opposite side of a line.

     – Rotation (turn): the image of a figure moved through an angle around a point.

                                                                      6 GS02
                                                                          NS ME GS PS AS
Item Characteristics:                                                                    GS01 GS02

•   Items may ask students to place integers, fractions, and/or decimals on a
    number line.                                                                        Next Page
                                                                                           GS
•   Items may ask students to identify or name the location of objects or points on a number
    line using coordinates and/or labels.

•   Items may ask students to determine and/or describe the relative position - to the right, to
    the left, number of spaces apart – of points or objects on a positive/negative number line.

•   Items may ask students to identify the point of final destination on an integer number line,
    given a starting point and a movement right/left or up/down.

•   Items may ask students to use ordered pairs to identify or describe the location of a given
    object rotated 90° or 180° about the center or vertex of the figure in the first quadrant of a
    coordinate grid.

•   Items may ask students to identify, describe, or classify whether an object has been
    transformed by a translation reflection, or rotation with or without a grid.

•   Items may ask students to identify a picture or diagram of a particular translation,
    reflection, or rotation of 90° or 180° about the center or vertex of a figure, with or without a
    grid.

•   Items may ask students to draw a translation, a reflection, or a rotation of 90° or 180°
    about the center or vertex of a figure.

•   Items may ask students to describe a 90o or 1800 rotation about the center or vertex of a
    figure so that another person could draw it.                  6 GS02
                                                                             NS ME GS PS AS
                                                                          PS01 PS02 PS03

                                                                                          Next Page
                                                                                             PS

Content Strand 4: Probability and Statistics

   PS01 (Probability)
    –   1.4.1 Understand probability as a ratio between and including 0 and 1.
    –   1.4.2 Understand various ways to determine outcomes of events or situations.

   PS02 (Data Collection and Central Tendencies)
    –   1.4.3 Analyze how data collection methods affect the data collected.
    –   1.4.4 Apply measures of central tendency to interpret a set of data.

   PS03 (Data Representation and Interpretation)
    –   1.4.5 Understand how to organize, display, and interpret data in text from single line
        graphs and scatter plots.
    –   1.4.6 Evaluate a data set to determine how it can be, or has been, used to support a
        point of view.




                                                                  6 PS
                                                                      NS ME GS PS AS
                                                          PS01 PS02 PS03

                                                                    Next Page
Content Strand 4: Probability and Statistics                           PS


PS01 (Probability) Demonstrate understanding of the
likelihood of simple events; demonstrate understanding
that probability is a ratio between and including 0 and 1;
determine all possible outcomes and/or the probabilities
for simple experiments or situations (1.4.1, 1.4.2)

Item Format:
Multiple-Choice and Short-Answer items may be used to test this learning
target.




                                                     6 PS01
                                                         NS ME GS PS AS
                                                       PS01 PS02 PS03

Stimulus, Stem, and Prompt Rules:
                                                                    Next Page
                                                                       PS


• Pictures of objects such as game spinners, coins, chips, marbles,
  number cubes, diagrams, tables, charts, and graphs may be used.

• A probability may be expressed as a ratio, decimal, or percent.




                                                 6 PS01
                                                     NS ME GS PS AS
                                              PS01 PS02 PS03

Mathematical Vocabulary and Terms:
                                                       Next Page
                                                          PS


• Terms that may be used: outcome, probability, random

• Terms that may be used with definitions or examples:
  event, experiment, sample space

• Terms that will not be used: expected value,
  experimental probability, permutation, theoretical
  probability




                                          6 PS01
                                              NS ME GS PS AS
                                                                     PS01 PS02 PS03
     Item Characteristics:
                                                                                 Next Page
•   Items may ask students to explain why some outcomes are equally                 PS
    likely or more or less likely to happen than others and how much more or less.

•   Items may ask students to identify, predict, or determine the probability of an event in
    a simple experiment or situation as a ratio, decimal, or percent.

•   Items may ask students to demonstrate an understanding that probability is a ratio
    between and including 0 and 1 or a percent between and including 0% and 100%.

•   Items may ask students to determine the sample space of simple experiments or
    activities.

•   Items may ask students to translate between representations of probability.

•   Items may ask students to create a spinner, game, or situation that would produce a
    given, fair or unfair, outcome.

•   Items may ask students to explain why a game is fair or unfair.
                                                             6 PS01
                                                                  NS ME GS PS AS
                                                          PS01 PS02 PS03

                                                                    Next Page
Content Strand 4: Probability and Statistics                           PS



PS02 (Data Collection and Central Tendencies)
Identify and/or describe how different collection methods
or different questions affect the data collected;
determine and use mean, median, and mode to describe
or interpret a set of data (1.4.3, 1.4.4)

Item Format:
Multiple-Choice and Short-Answer items may be used to test this learning
target.




                                                     6 PS02
                                                         NS ME GS PS AS
                                                                PS01 PS02 PS03

Stimulus, Stem, and Prompt Rules:
                                                                            Next Page
                                                                               PS


•   Items may include descriptive scenarios that involve survey questions and
    collection methods.

•   Items may include tables, charts, diagrams, pictures, bar graphs, line plots,
    pictographs, circle graphs, histograms, and line graphs.




                                                         6 PS02
                                                             NS ME GS PS AS
                                                       PS01 PS02 PS03

Mathematical Vocabulary and Terms:
                                                                  Next Page
                                                                     PS


• Terms that may be used: data, population, questionnaire, survey

• Terms that may be used with definitions or examples: bias, mean
  (average), median (middle number), mode (most common or most
  common number), variable

• Terms that will not be used: measures of central tendency, reliability




                                                  6 PS02
                                                      NS ME GS PS AS
                                                        PS01 PS02 PS03
Item Characteristics:
                                                                    Next Page
                                                                       PS


• Items may ask students to identify or write survey questions that will
  obtain the appropriate information and will avoid bias.

• Items may ask students to identify or describe how to collect data
  about a given population, taking into account collection methods.

• Items may ask students to describe how a question or data
  collection method may affect the data.

• Items may ask students to identify, calculate, and/or use mean,
  median, and mode as appropriate to describe a set of data.

• Items may ask students to explain the difference between mode,
  median, and/or mean for a set of data in a given situation.
                                                   6 PS02
                                                       NS ME GS PS AS
                                                          PS01 PS02 PS03


Content Strand 4: Probability and Statistics                        Next Page
                                                                       PS


PS03 (Data Representation and Interpretation) Read
and interpret data presented in text, circle graphs,
histograms, and single line graphs and determine when
using these is appropriate; demonstrate understanding
of how data can be used to support a point of view
(1.4.5, 1.4.6)

Item Format:
Multiple-Choice and Short-Answer items may be used to test this learning
target.



                                                     6 PS03
                                                         NS ME GS PS AS
                                                PS01 PS02 PS03

Stimulus, Stem, and Prompt Rules:                           Next Page
                                                               PS


•
    Stimulus may include text, tables, charts, diagrams,
    pictures, circle graphs, histograms, and line graphs.




                                            6 PS03
                                                NS ME GS PS AS
                                              PS01 PS02 PS03

Mathematical Vocabulary and Terms:
                                                       Next Page
                                                          PS


• Terms that may be used: axis/axes, circle graph, graph,
  histogram, horizontal axis, line graph, origin, scale,
  vertical axis, x-axis, y-axis

• Terms that may be used with definitions or examples:
  compare (tell how they are alike and/or how they are
  different), evaluate, trend

• Terms that will not be used: continuous, discrete,
  intercept, slope


                                         6 PS03
                                             NS ME GS PS AS
Item Characteristics:                                                       PS01 PS02 PS03

                                                                                          Next Page
•   Items may ask students to read and interpret data from text, circle graphs,              PS
    histograms, and single line graphs.

•   Items may ask students to describe the accuracy and completeness of the data in a circle
    graph, histogram, or line graph.

•   Items may ask students to identify and/or explain whether a circle graph, histogram, or line
    graph is more appropriate for a given set of data, a particular situation or purpose, or answers a
    question most effectively.

•   Items may ask students to identify or describe trends or patterns in data represented in a circle
    graph, histogram, or line graph.

•   Items may ask students to compare or evaluate multiple interpretations of the same data.

•   Items may ask students to read and interpret data from a circle graph, histogram, or single line
    graph.

•   Items may ask students to evaluate the appropriateness of an inference made from a set of
    data.

•   Items may ask students to determine whether the title, labels, and/or scale(s) on a circle graph,
    histogram, or line graph accurately and appropriately represent the data, to explain why or why
    not, and/or to correct it as needed.
                                                                     6 PS03
                                                                         NS ME GS PS AS
                                                                  AS01 AS02 AS03

                                                                                Next Page
                                                                                   AS
Content Strand 5: Algebraic Sense


   AS01 (Patterns and Functions)
    –   1.5.1 Apply rules for number patterns based on two arithmetic operations.
    –   1.5.2 Apply understanding of patterns involving two arithmetic operations to
        develop a rule.
   AS02 (Symbols and Notations)
    –    1.5.3 Apply understanding of equalities and inequalities to interpret and
        represent relationships between quantities.
    –   1.5.4 Apply understanding of tables, graphs, expressions, equations, or
        inequalities to represent situations involving two arithmetic operations.
   AS03 (Evaluating and Solving)
    –    1.5.5 Understand and apply procedures to evaluate expressions and
        formulas.
    –   1.5.6 Understand and apply a variety of strategies to solve one-step
        equations.


                                                           6 AS
                                                               NS ME GS PS AS
                                                          AS01 AS02 AS03
Content Strand 5: Algebraic Sense
                                                                    Next Page
                                                                       AS
AS01 (Patterns and Functions) Extend or create
patterns of numbers, shapes, and/or objects that use
one arithmetic operation – addition, subtraction,
multiplication, or division – to move from one term to the
next; recognize or extend patterns and sequences that
use two different alternating arithmetic operations to
move from one term to the next; describe a rule for a
pattern with combinations of two arithmetic operations in
the rule (1.5.1, 1.5.2)

Item Format:
Multiple-Choice and Short-Answer items may be used to test this learning
target.                                              6 AS01
                                                         NS ME GS PS AS
                                                               AS01 AS02 AS03

Stimulus, Stem, and Prompt Rules:
                                                                           Next Page
                                                                              AS


•   Stimulus may include numbers, tables, charts, pictorial, and/or geometric
    patterns.

•   A given pattern must have a minimum of four elements or terms.

•   Number patterns may use one operation to move from one term in a pattern
    to the next.

•   Number patterns may use two different operations that alternate between
    terms.

•   Number patterns may include addition, subtraction, multiplication, or division
    with whole numbers OR addition or subtraction of non-negative decimals or
    fractions.


                                                         6 AS01
                                                             NS ME GS PS AS
                                                     AS01 AS02 AS03

Mathematical Vocabulary and Terms:
                                                               Next Page
                                                                  AS


• Terms that may be used: pattern, predict, rule, sequence

• Terms that may be used with definitions or examples: function,
  interval

• Terms that will not be used:




                                                6 AS01
                                                    NS ME GS PS AS
                                                                     AS01 AS02 AS03
     Item Characteristics:
                                                                                 Next Page
                                                                                    AS
•   Items may ask students to extend a pattern by identifying or supplying missing
    elements in the beginning, middle and/or end and/or describe the pattern or write a
    rule with one operation.

•   Items may ask students to identify a pattern that is equivalent to a given pattern.

•   Items may ask students to identify or describe a number pattern given in tables,
    graphs, rules, or words.

•   Items may ask students to extend a pattern by identifying or supplying missing
    elements in the beginning, middle, and/or end and/or describe the pattern or write a
    rule with alternating operations between terms.

•   Items may ask students to create a pattern that uses the same rule as a given
    pattern.

•   Items may ask students to create a pattern and explain what makes it a pattern.
                                                            6 AS01
                                                                NS ME GS PS AS
                                                          AS01 AS02 AS03


Content Strand 5: Algebraic Sense                                   Next Page
                                                                       AS


AS02 (Symbols and Notations) Express relationships
between quantities using =, ≠, <, >, ≤, and ≥; use
variables to write expressions, equations, and
inequalities that represent situations involving two
arithmetic operations with non-negative decimals and
fractions (1.5.3, 1.5.4)

Item Format:
Multiple-Choice and Short-Answer items may be used to test this learning
target.



                                                     6 AS02
                                                         NS ME GS PS AS
                                                         AS01 AS02 AS03
Stimulus, Stem, and Prompt Rules:
                                                                     Next Page
                                                                        AS


• Stimulus may include pictorial representations, tables, charts, or
  graphs.

• Stimulus may include the use of variables to represent an unknown
  quantity in expressions or equations.

• Stimulus may use addition and subtraction of non-negative decimals
  and fractions.

• Stimulus should avoid the use of the letters a, b, c, d, or x as
  variables.




                                                    6 AS02
                                                        NS ME GS PS AS
                                                      AS01 AS02 AS03

Mathematical Vocabulary and Terms:
                                                                    Next Page
                                                                       AS


• Terms that may be used: =, ≠, <, >, ≤, ≥, equation, expression,
  relationship

• Terms that may be used with definitions or examples: function,
  inequality, interval, variable

• Terms that will not be used:




                                                 6 AS02
                                                     NS ME GS PS AS
                                                         AS01 AS02 AS03
Item Characteristics
                                                                       Next Page
                                                                          AS


• Items may ask students to identify or write a simple expression,
  using variables, to represent a given situation.

• Items may ask students to identify or write a simple equation or
  simple inequality, with variables, to represent a given situation,
  using =, ≠, <, >, ≤, or ≥.

• Items may ask students to explain the meaning of a variable in a
  formula, expression, equation, or inequality.

• Items may ask students to identify a situation that corresponds to a
  given expression, equation, or inequality.


                                                   6 AS02
                                                       NS ME GS PS AS
                                                AS01 AS02 AS03

                                                        Next Page
                                                           AS
Content Strand 5: Algebraic Sense

AS03 (Evaluating and Solving) Evaluate simple
expressions and formulas using pictures and/or
symbols; solve one-step equations using pictures and
symbols (1.5.5, 1.5.6)

Item Format:
Multiple-Choice and Short-Answer items may be used to test this
learning target.



                                           6 AS03
                                               NS ME GS PS AS
                                                         AS01 AS02 AS03

Stimulus, Stem, and Prompt Rules:
                                                                     Next Page
                                                                        AS


• Stimulus may include pictorial representations, tables, charts, or
  graphs.

• Stimulus may include the use of a variable to represent an unknown
  quantity in an expression or equation.

• Equations will require a maximum of one step to solve and will have
  whole number solutions.

• Stimulus should avoid the use of the letters a, b, c, d, or x as
  variables.




                                                    6 AS03
                                                        NS ME GS PS AS
                                                     AS01 AS02 AS03

Mathematical Vocabulary and Terms:
                                                                  Next Page
                                                                     AS


• Terms that may be used: equation, expression, formula, solve,
  symbol, unknown

• Terms that may be used with definitions or examples: evaluate,
  function, variable

• Terms that will not be used: set up




                                                6 AS03
                                                    NS ME GS PS AS
                                                      AS01 AS02 AS03

Item Characteristics:



• Items may ask students to write a simple expression for a given
  situation and evaluate the expression given the values for the
  variables.

• Items may ask students to evaluate an expression or formula given
  the values for the variables.

• Items may ask students to solve one-step single-variable equations
  for a given situation.

• Items may ask students to write and solve one-step single-variable
  equations for a given situation.


                                                 6 AS03
                                                     NS ME GS PS AS

								
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