# Number Properties and Operations by z2q8RQ9

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```									Mathematics Sixth Grade Core Content for Assessment Crosswalk                                                     August 2006

Number Properties and Operations

Version 3.0                                    Version 4.0                    Version 4.1

Number Sense

MA-6-1.1.1                                        MA-06-1.1.1                  MA-06-1.1.1
Students will describe properties of, define,     See 4.1=>                    Students will provide examples of and
give examples of, and/or apply to both real-                                   identify fractions, decimals and percents.
world and mathematical situations: Fractions,                                                                        DOK 1
decimals
MA-6-1.2.1
Students will perform the following
mathematical operations and/or procedures
accurately and efficiently, and explain how
they work in real-world and mathematical
situations: Add, subtract, multiply, and divide
fractions; add, subtract, and multiply decimals
to solve problems

MA-6-1.1.4                                        MA-06-1.1.1a                 MA-06-1.1.2
Students will describe properties of, define,     See 4.1=>                    Students will describe and provide examples
give examples of, and/or apply to both real-      Code Change                  of representations of numbers (whole
world and mathematical situations: Place value                                 numbers, fractions in simplest form, mixed
of whole numbers and decimals                                                  numbers, decimals, percents) and operations
MA-6-1.1.5                                                                     in a variety of equivalent forms using models,
Students will describe properties of, define,                                  diagrams and symbols (e.g., number lines, 10
give examples of, and/or apply to both real-                                   by 10 grids, rectangular arrays, number
world and mathematical situations: Positive                                    sentences), based on real-world and/or
whole number exponents                                                         mathematical situations.
MA-6-1.1.6
Students will describe properties of, define,
give examples of, and/or apply to both real-
world and mathematical situations:
Representation of fractions and decimals and
their operations

1
Mathematics Sixth Grade Core Content for Assessment Crosswalk                                                                   August 2006

MA-6-1.3.1                                        MA-06-1.1.2                                   MA-06-1.1.3
Students will show connections and how            Students will convert between any two of      Students will convert between any two of
connections are made between concepts and         the following numbers: fractions, decimals,   the following numbers: fractions, decimals
skills, explain why procedures work, and make     and percents (less than or equal to 100%;     and percents (less than or equal to100%);
generalizations about mathematics in              and will compare these numbers.               and will compare and order these numbers.
meaningful ways for the following                 DOK - 2                                                                            DOK 2
relationships: How whole numbers, fractions
and decimals, relate to each other (e.g.,
convert between forms of rational numbers,
compare, order)

Estimation

MA-6-1.2.2                                        MA-06-1.2.1                                   MA-06-1.2.1
Students will perform the following               Students will estimate to solve real-world    Students will estimate to solve real-world
mathematical operations and/or procedures         and/or mathematical problems with whole       and mathematical problems with whole
accurately and efficiently, and explain how       numbers, fractions, decimals, and             numbers, fractions, decimals, and
they work in real-world and mathematical          percents, checking for reasonable and         percents, checking for reasonable and
situations: Estimate and predict computational    appropriate computational results.            appropriate computational results.
results using whole numbers and decimals          DOK - 2                                                                             DOK 2

Number Operations

MA-6-1.2.1                                        MA-06-1.3.1                                   MA-06-1.3.1
Students will perform the following               Students will add, subtract, multiply,        Students will add, subtract, multiply and
mathematical operations and/or procedures         divide, and apply order of operations with    divide, whole numbers, fractions and
accurately and efficiently, and explain how       whole numbers, fractions, and decimals to     decimals to solve real-world problems and
they work in real-world and mathematical          solve real-world problems.                    apply order of operations to simplify
situations: Add, subtract, multiply, and divide   DOK - 2                                       numerical expressions.
fractions; add, subtract, and multiply decimals                                                                                        DOK 2
to solve problems
MA-6-1.2.2
Students will perform the following
mathematical operations and/or procedures
accurately and efficiently, and explain how
they work in real-world and mathematical
situations: Estimate and predict computational
results using whole numbers and decimals

2
Mathematics Sixth Grade Core Content for Assessment Crosswalk                                                                        August 2006

MA-6-1.3.3                                      MA-06-1.3.1a                                     MA-06-1.3.2
Students will show connections and how          See 4.1=>                                        Students will explain how operations (addition
connections are made between concepts and       Code Change                                      and subtraction; multiplication and division) are
skills, explain why procedures work, and make                                                    inversely related.
generalizations about mathematics in
meaningful ways for the following
relationships: How operations (addition and
subtraction; multiplication and division) are
inversely related

MA-06-1.3.1b
Students will check for reasonable and
appropriate computational results, using a
variety of methods (e.g., estimate, pencil and
paper, calculator, rounding, mental math).

Ratios and Proportional Reasoning

MA-6-1.1.3                                      MA-06-1.4.1                                      MA-06-1.4.1
Students will describe properties of, define,   See 4.1=>                                        Students will describe and apply ratios to
give examples of, and/or apply to both real-                                                     solve real-world problems.
world and mathematical situations: Ratio                                                                                               DOK 2
MA-6-1.2.3
Students will perform the following
mathematical operations and/or procedures
accurately and efficiently, and explain how
they work in real-world and mathematical
situations: Apply ratios

3
Mathematics Sixth Grade Core Content for Assessment Crosswalk                                                                        August 2006

Properties of Numbers and Operations

MA-6-1.2.4                                            MA-06-1.5.1                                   MA-06-1.5.1
Students will perform the following                   See 4.1=>                                     Students will identify and apply prime
mathematical operations and/or procedures                                                           numbers, composite numbers, prime
accurately and efficiently, and explain how                                                         factorization, factors, multiples and
they work in real-world and mathematical                                                            divisibility to solve real-world and
situations: Identify and use prime numbers,                                                         mathematical problems (e.g., prime
composite numbers, prime factorization,                                                             factorization to determine a least common
factors, multiples, divisibility to solve problems.                                                 multiple [LCM] or greatest common factor
(e.g., prime factorization to determine LCM                                                         [GCF]).
and GCF)                                                                                                                                  DOK 2

MA-6-1.3.2                                            MA-06-1.5.2                                   MA-06-1.5.2
Students will show connections and how                Students will identify how the commutative    Students will identify the use of properties
connections are made between concepts and             properties, the associative properties, and   (commutative properties of addition and
skills, explain why procedures work, and make         the identity properties for addition and      multiplication, the associative properties of
generalizations about mathematics in                  multiplication are used to simplify           addition and multiplication and the identity
meaningful ways for the following                     numerical expressions.                        properties for addition and multiplication)
relationships: How properties such as                 DOK - 1                                       to simplify numerical expressions.
commutative, associative, and identities show                                                                                              DOK 1
relationships among operations

4
Mathematics Sixth Grade Core Content for Assessment Crosswalk                                                                   August 2006

Measurement

Version 3.0                                   Version 4.0                                    Version 4.1

Measuring Physical Attributes

MA-6-2.2.5                                      MA-06-2.1.1                                   MA-06-2.1.1
Students will perform the following             Students will determine:                      Students will measure lengths (to the
mathematical operations and/or procedures           measures of rectangles and figures       nearest eighth of an inch or the nearest
accurately and efficiently, and explain how            that can be divided into rectangular   centimeter) and will determine and use in
they work in real-world and mathematical               shapes, including lengths to the       real-world and mathematical problems:
situations: Use formulas to find area and              nearest eighth of an inch or nearest        area and perimeter of triangles;
perimeter of triangles (not requiring use of           centimeter; and                             area and perimeter of quadrilaterals
Pythagorean theorem as a strategy) and              the area and perimeter of triangles             (rectangles, squares); (using the
quadrilaterals (rectangle, parallelogram,              and quadrilaterals (rectangles,               Pythagorean theorem will not be
squares)                                               squares). (Using the Pythagorean              required as a strategy) and
theorem will not be required as a           area and perimeter of compound
strategy.)                                    figures composed of triangles and
DOK - 2                                              quadrilaterals.
DOK 2

MA-6-2.2.4                                      MA-06-2.1.1a                                  MA-06-2.1.2
Students will perform the following             See 4.1=>                                     Students will estimate measurements in
mathematical operations and/or procedures       Code Change                                   standard units including fractions and
accurately and efficiently, and explain how                                                   decimals.
they work in real-world and mathematical
situations: Estimate measurements in standard
units including fractions and decimals

MA-06-2.1.1b                                  MA-06-2.1.3
See 4.1=>                                     Students will explain how measurements and
Code Change                                   measurement formulas are related or different
(perimeter and area of rectangles).

5
Mathematics Sixth Grade Core Content for Assessment Crosswalk                                                                        August 2006

Systems of Measurement

MA-6-2.1.5                                           MA-06-2.2.1a                                  MA-06-2.2.1
Students will describe properties of, define,        Students will describe and provide examples   Students will convert units within the same
give examples of, and/or apply to both real-         of U.S. Customary and metric units of         measurement system and use these units to
world and mathematical situations: U.S.              measurement and use these units to solve      solve real-world problems.
customary and metric units of measure                real-world and/or mathematical problems.

Geometry

Version 3.0                                        Version 4.0                                   Version 4.1

Shapes and Relationships

MA-6-2.1.1                                           MA-06-3.1.1                                   MA-06-3.1.1
Students will describe properties of, define,        Students will describe and provide            Students will describe and provide
give examples of, and/or apply to both real-         examples of the basic geometric elements      examples of the basic geometric elements
world and mathematical situations: Segments,         (points, rays, lines, segments, angles        (points, rays, lines, segments, angles
rays, lines, angles, and planes                      [acute, right, obtuse], planes, radius,       [acute, right, obtuse], planes, radius,
diameter, circumference).                     diameter, circumference).
DOK - 2                                                                               DOK 1

MA-6-2.1.2                                           MA-06-3.1.2                                   MA-06-3.1.2
Students will describe properties of, define,        Students will describe, and provide           Students will describe and provide
give examples of, and/or apply to both real-         examples and properties of two-               examples of the elements (e.g., sides,
world and mathematical situations: Two-              dimensional figures (circles, triangles,      vertices, angles, congruent parts) of two-
dimensional shapes, regular polygons,                quadrilaterals, regular polygons), and will   dimensional figures (circles, triangles,
quadrilaterals (square, rectangle, rhombus,          apply these properties and figures to solve   quadrilaterals, regular polygons) and will
parallelogram, trapezoid) and triangles (acute,      real-world problems.                          apply these elements and figures to solve
obtuse, right)                                       DOK - 2                                       real-world and mathematical problems.
MA-6-2.2.1                                                                                                                                DOK 2
Students will perform the following
mathematical operations and/or procedures
accurately and efficiently, and explain how
they work in real-world and mathematical
situations: Identify characteristics (e.g., sides,
vertices, angles, congruent parts) of two-
dimensional shapes.

6
Mathematics Sixth Grade Core Content for Assessment Crosswalk                                                                                August 2006

MA-6-2.1.3                                           MA-06-3.1.3a                                       MA-06-3.1.3
Students will describe properties of, define,        Students will describe, provide examples of,       Students will describe, provide examples of
give examples of, and/or apply to both real-         and identify properties (e.g., vertices, angles,   and identify elements (e.g., vertices, angles,
world and mathematical situations: Three-            faces, edges, congruent parts) of common           faces, edges, congruent parts) of common
dimensional geometric shapes including               three-dimensional figures (spheres, cones,         three-dimensional figures (spheres, cones,
spheres, cones, cylinders, prisms, (with             cylinders, prisms, and pyramids).                  cylinders, prisms, and pyramids).
polygonal bases), and pyramids (with
polygonal bases)
MA-6-2.2.1
Students will perform the following
mathematical operations and/or procedures
accurately and efficiently, and explain how
they work in real-world and mathematical
situations: Identify characteristics (e.g., sides,
vertices, angles, congruent parts) of two-
dimensional shapes

MA-6-2.1.4                                           MA-06-3.1.4                                        MA-06-3.1.4
Students will describe properties of, define,        Students will describe and provide                 Students will identify and describe
give examples of, and/or apply to both real-         examples of congruent and similar figures,         congruent figures and will apply congruent
world and mathematical situations:                   and will apply congruent and similar               figures to solve real-world and
Congruence, symmetry, and similarity                 figures to solve real-world problems.              mathematical problems.
DOK - 2                                                                                 DOK 2

MA-06-3.1.4a                                       MA-06-3.1.5
See 4.1=>                                          Students will identify similar figures and apply
Code Change                                        similar figures to solve real-world and
mathematical problems.

Transformations of Shapes

MA-6-2.1.4                                           MA-06-3.2.1a                                       MA-06-3.2.1
Students will describe properties of, define,        Students will describe, provide examples of,       Students will describe, provide examples of
give examples of, and/or apply to both real-         and apply line symmetry to real-world and/or       and apply line symmetry to real-world and
world and mathematical situations:                   mathematical situations.                           mathematical problems.
Congruence, symmetry, and similarity

7
Mathematics Sixth Grade Core Content for Assessment Crosswalk                                                                             August 2006

MA-6-2.2.3                                       MA-06-3.2.2                                        MA-06-3.2.2
Students will perform the following              Students will transform (translate and reflect     Students will:
mathematical operations and/or procedures        across a horizontal or vertical line) figures in       reflect figures across a horizontal
accurately and efficiently, and explain how      the first quadrant of the coordinate plane and            or vertical line in the first quadrant;
they work in real-world and mathematical         determine new coordinates of the shape after           translate figures in a plane in the
situations: Move shapes in Quadrant I            transformation.                                           first quadrant and
coordinate plane: translate, rotate, reflect     DOK - 2                                                determine the coordinates of the
image after transformation in the
first quadrant.
DOK 2

MA-6-2.2.3                                       MA-06-3.2.2a                                       MA-06-3.2.3
Students will perform the following              Students will move shapes in Quadrant I of the     Students will identify rotations of figures in the
mathematical operations and/or procedures        coordinate plane: rotate (turn).                   plane (90˚ and 180˚).
accurately and efficiently, and explain how
they work in real-world and mathematical
situations: Move shapes in Quadrant I
coordinate plane: translate, rotate, reflect

Coordinate Geometry

MA-6-4.1.3                                       MA-06-3.3.1                                        MA-06-3.3.1
Students will describe properties of, define,    Students will identify and graph ordered           Students will identify and graph ordered
give examples of, and/or apply to both real-     pairs on a positive coordinate system,             pairs on a positive coordinate system
world and mathematical situations: Quadrant I,   correctly identifying the origin, axes, and        (Quadrant I), correctly identifying the
ordered pairs, x and y axis, origin              ordered pairs; and will apply graphing in          origin, axes and ordered pairs; and will
the coordinate system to solve real-world          apply graphing in the coordinate system to
problems.                                          solve real-world and mathematical
DOK - 2                                            problems.
DOK 2

8
Mathematics Sixth Grade Core Content for Assessment Crosswalk                                                        August 2006

Data Analysis and Probability

Version 3.0                                     Version 4.0                     Version 4.1

Data Representations

MA-6-3.2.1                                          MA-06-4.1.1                  MA-06-4.1.1
Students will perform the following                 See 4.1=>                    Students will analyze and make inferences
mathematical operations and/or procedures                                        from data displays (drawings,
accurately and efficiently, and explain how                                      tables/charts, pictographs, bar graphs,
they work in real-world and mathematical                                         circle graphs, line plots, Venn diagrams,
situations: Organize, represent, analyze, and                                    line graphs, stem-and-leaf plots).
interpret sets of data using tables, graphs                                                                            DOK 3
(e.g., bar, line), and plots (e.g., single stem-
and-leaf)
MA-6-3.2.2
Students will perform the following
mathematical operations and/or procedures
accurately and efficiently, and explain how
they work in real-world and mathematical
situations: Construct and interpret displays of
data (e.g., tables, line graph, line plot, steam-
and-leaf plot)

MA-6-3.3.1                                          MA-06-4.1.1a                 MA-06-4.1.2
Students will show connections and how              See 4.1=>                    Students will explain how different
connections are made between concepts and           Code Change                  representations of data (e.g., tables, graphs,
skills, explain why procedures work, and make                                    diagrams, plots) are related.
generalizations about mathematics in
meaningful ways for the following
relationships: How different representations of
data (e.g tables, stem-and-leaf, bar graph, line
plot) are related

9
Mathematics Sixth Grade Core Content for Assessment Crosswalk                                                                     August 2006

MA-6-3.1.3                                          MA-06-4.1.2                                   MA-06-4.1.4
Students will describe properties of, define,       Students will construct data displays (bar    Students will determine and construct
give examples of, and/or apply to both real-        graphs, line plots, Venn diagrams, tables,    appropriate data displays (bar graphs, line
world and mathematical situations:                  line graphs), and will explain why the type   plots, Venn diagrams, tables, line graphs)
Characteristics and appropriateness of graphs       of display is appropriate for the data.       and will explain why the type of display is
(e.g., bar, line), and plots (e.g., single stem-    DOK - 2                                       appropriate for the data.
and-leaf)                                                                                                                               DOK 2
MA-6-3.2.1
Students will perform the following
mathematical operations and/or procedures
accurately and efficiently, and explain how
they work in real-world and mathematical
situations: Organize, represent, analyze, and
interpret sets of data using tables, graphs
(e.g., bar, line), and plots (e.g., single stem-
and-leaf)
MA-6-3.2.2
Students will perform the following
mathematical operations and/or procedures
accurately and efficiently, and explain how
they work in real-world and mathematical
situations: Construct and interpret displays of
data (e.g., tables, line graph, line plot, steam-
and-leaf plot)
MA-6-3.3.1
Students will show connections and how
connections are made between concepts and
skills, explain why procedures work, and make
generalizations about mathematics in
meaningful ways for the following
relationships: How different representations of
data (e.g., tables, stem-and-leaf, bar graph,
line plot) are related

10
Mathematics Sixth Grade Core Content for Assessment Crosswalk                                       August 2006

Characteristics of Data Sets

MA-6-3.1.1                                      MA-06-4.2.1          MA-06-4.2.1
Students will describe properties of, define,   See 4.1=>            Students will determine and apply the
give examples of, and/or apply to both real-                         mean, median, mode and range of a set of
world and mathematical situations: Meaning of                        data.
central tendency (mean, median, mode)                                                                     DOK 2
MA-3.2.3
Students will perform the following
mathematical operations and/or procedures
accurately and efficiently, and explain how
they work in real-world and mathematical
situations: Find mean, median, mode, and
range

Experiments and Samples (not assessed at this level)

11
Mathematics Sixth Grade Core Content for Assessment Crosswalk                                                                         August 2006

Probability

MA-6-3.2.6                                              MA-06-4.4.1                                  MA-06-4.4.1
Students will perform the following mathematical        Students will describe or determine (e.g.,   Students will describe or determine (e.g.,
operations and/or procedures accurately and             tables, tree diagrams) the sample space      tables, tree diagrams) the sample space
efficiently, and explain how they work in real-world    of an event.                                 of an event for a real-world or
and mathematical situations: Use counting               DOK - 2                                      mathematical situation.
techniques, tree diagrams, and tables to solve                                                                                          DOK 2
probability problems
MA-6-3.3.4
Students will show connections and how
connections are made between concepts and skills,
explain why procedures work, and make
generalizations about mathematics in meaningful
ways for the following relationships: How probability
and statistics are used to make predictions and/or
draw conclusions

MA-6-3.2.4                                              MA-06-4.4.2                                  MA-06-4.4.2
Students will perform the following mathematical        Students will determine simple               Students will determine single event
operations and/or procedures accurately and             probabilities based on the results of an     probabilities based on the results of an
efficiently, and explain how they work in real-world    experiment and will make inferences          experiment and will make inferences
and mathematical situations: Determine sample           based on the data.                           based on the data.
space of a simple event (e.g., flipping a coin,         DOK - 3                                                                          DOK 3
number cube, spinners)
MA-6-3.2.5
Students will perform the following mathematical
operations and/or procedures accurately and
efficiently, and explain how they work in real-world
and mathematical situations: Make predictions (e.g.
fair and unfair games) and draw conclusions from
statistical data and probability experiments (e.g.,
flipping a coin, number cube, spinners)

MA-06-4.4.3
Students will explore the theoretical
probability of simple events.

12
Mathematics Sixth Grade Core Content for Assessment Crosswalk                                                                  August 2006

Algebraic Thinking

Version 3.0                                     Version 4.0                                   Version 4.1

Patterns, Relations and Functions

MA-6-4.1.2                                       MA-06-5.1.1                                   MA-06-5.1.1
Students will describe properties of, define,    Students will extend and describe rules for   Students will extend, describe rules for
give examples of, and/or apply to both real-     patterns from real-world and/or               patterns and find a missing term in a
world and mathematical situations: Functions     mathematical problems                         pattern from real-world and mathematical
using tables, graphs, and verbal rules           DOK - 3                                       problems.
MA-6-4.2.4                                                                                                                           DOK 3
Students will perform the following
mathematical operations and/or procedures
accurately and efficiently, and explain how
they work in real-world and mathematical
situations: Identify, create, and continue
patterns (give an informal description for the
continuance of the pattern and/or generalize
patterns through a verbal rule)
MA-6-4.3.1
Students will show connections and how
connections are made between concepts and
skills, explain why procedures work, and make
generalizations about mathematics in
meaningful ways for the following
relationships: How tables and graphs and
recognize patterns relate to each other

13
Mathematics Sixth Grade Core Content for Assessment Crosswalk                                                                           August 2006

MA-6-4.1.2                                       MA-06-5.1.2                                       MA-06-5.1.2
Students will describe properties of, define,    See 4.1=>                                         Students will create tables for functions
give examples of, and/or apply to both real-                                                       and will apply the tables to solve real-world
world and mathematical situations: Functions                                                       problems.
using tables, graphs, and verbal rules                                                                                                    DOK 2
MA-6-4.2.5
Students will perform the following
mathematical operations and/or procedures
accurately and efficiently, and explain how
they work in real-world and mathematical
situations: Create tables for functions

MA-6-4.2.5                                       MA-06-5.1.2a                                      MA-06-5.1.3
Students will perform the following              Students will describe, define, provide           Students will describe, define, provide
mathematical operations and/or procedures        examples of, and apply to real-world and/or       examples of and apply to real-world and
accurately and efficiently, and explain how      mathematical situations functions using tables,   mathematical problems functions using tables,
they work in real-world and mathematical         graphs and verbal rules.                          graphs and verbal rules.
situations: Create tables for functions

MA-6-4.3.1                                       MA-06-5.1.2b                                      MA-06-5.1.4
Students will show connections and how           See 4.1=>                                         Students will explain how tables, graphs and
connections are made between concepts and        Code Change                                       patterns relate to each other.
skills, explain why procedures work, and make
generalizations about mathematics in
meaningful ways for the following
relationships: How tables and graphs and
recognize patterns relate to each other

MA-6-4.3.2                                       MA-06-5.1.3a                                      MA-06-5.1.5
Students will show connections and how           See 4.1=>                                         Students will explain how the change in one
connections are made between concepts and        Code Change                                       quantity affects change in another quantity
skills, explain why procedures work, and make                                                      (e.g., in tables or graphs, input/output tables).
generalizations about mathematics in
meaningful ways for the following
relationships: How the change in one quantity
affects a change in another quantity (e.g., in
tables/graphs, input/output tables)

14
Mathematics Sixth Grade Core Content for Assessment Crosswalk                                                                    August 2006

Variables, Expressions and Operations

MA-6-4.2.1                                      MA-06-5.2.1                                    MA-06-5.2.1
Students will perform the following             See 4.1=>                                      Students will substitute values for
mathematical operations and/or procedures                                                      variables (up to two different variables) and
accurately and efficiently, and explain how                                                    evaluate algebraic expressions.
they work in real-world and mathematical                                                                                              DOK 2
situations: Simplify numerical expressions

MA-6-4.1.1                                      MA-06-5.2.1a                                   MA-06-5.2.2
Students will describe properties of, define,   Students will describe, define, and provide    Students will describe, define and provide
give examples of, and/or apply to both real-    examples of variables and expressions with a   examples of variables and expressions with a
world and mathematical situations: Variables,   missing value based on real-world and/or       missing value based on real-world and
expressions, and equations with a missing       mathematical situations.                       mathematical problems.
value

Equations and Inequalities

MA-6-4.2.2                                      MA-06-5.3.1                                    MA-06-5.3.1
Students will perform the following             See 4.1=>                                      Students will model and solve real-world
mathematical operations and/or procedures                                                      and mathematical problems with simple
accurately and efficiently, and explain how                                                    equations and inequalities (e.g., 8x = 4,
they work in real-world and mathematical                                                       x+2 > 5).
situations: Solve simple equations and                                                                                                DOK 2
inequalities
MA-6-4.2.6
Students will perform the following
mathematical operations and/or procedures
accurately and efficiently, and explain how
they work in real-world and mathematical
situations: Matching verbal rules with
expressions to solve everyday situations

15

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