21st CENTURY
6th Grade MATH
CONTENT STANDARDS AND
Janet Benincosa, TI Specialist
The West
Virginia Standards for 21st Century Learning include the following components:
21st Century Content Standards and Objectives and 21st Century Learning Skills
and Technology Tools.
All
Sixth Grade
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Grade
6 |
Mathematics |
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Standard
1 |
Number and Operations |
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M.S.6.1 |
Through
communication, representation, reasoning and proof, problem solving, and
making connections within and beyond the field of mathematics, students will ·
demonstrate
understanding of numbers, ways of representing numbers, and relationships
among numbers and number systems, ·
demonstrate meanings of operations and how they relate to one another,
and ·
compute fluently and make reasonable estimates. |
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Performance
Descriptors (M.PD.6.1) |
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Distinguished |
Above
Mastery |
Mastery |
Partial
Mastery |
Novice |
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Sixth grade students
at the distinguished level in mathematics use prime factorization to
determine GCF and LCM of more than two numbers for use in problem solving.
They create problems and expressions using the distributive, commutative,
associative, and identity properties.
They state equivalencies among fractions, decimals and percents;
between numbers written in scientific and standard notation justifying the
methods used. They create and solve
problems involving whole numbers, fractions, decimals, integer operations and
comparison, and percent of a number; they justify method used and
reasonableness of solution. They write
and explain in a clear, concise manner, the effect of multiplying and
dividing a number by a number between 0 and 1 inclusive. |
Sixth grade students
at the above mastery level in mathematics use prime factorization to
determine GCF and LCM for use in problem solving. They use the distributive, commutative,
associative, identity properties to solve problems. They state equivalencies
among fractions, decimals and percents; between numbers written in scientific
and standard notation explaining methods used. They solve problems involving whole
numbers, fractions, decimals, integer operations and comparison, and percent
of a number. They justify method used
and reasonableness of solution. They
explain the effects of multiplying and dividing numbers by numbers 0 and 1
inclusive. |
Sixth grade students
at the mastery level in mathematics determine GCF and LCM to solve problems;
finds prime factorization of a number.
They apply distributive, commutative, associative and identity
properties of addition and multiplication.
They state equivalencies among fractions, decimals, and percents;
between numbers written in scientific and standard notation. They solve problems involving whole
numbers, fractions, decimals, integer operations and comparison, and percent
of a number and justify reasonableness of solution by estimation. They
interpret the effect of multiplying and dividing whole numbers, fractions,
and decimals by numbers between zero and one, inclusive. |
Sixth grade students
at the partial mastery level in mathematics find GCF and LCM; give prime
factorization of a number. They
identify examples of distributive, commutative, associative, and identity
properties of addition and multiplication.
They identify equivalencies among fractions, decimals, and
percents. They convert a number from
scientific notation to standard notation. They solve problems involving whole
numbers, fractions, decimals; addition, multiplication, division, and
comparison of integers. They calculate benchmark percents (10%, 25%, 50%, and
75%) of a number. They interpret the effect of multiplying whole numbers,
fractions and decimals by numbers between 0 and 1, inclusive. |
Sixth
grade students at the novice level in mathematics find GCF and LCM; give
prime factorization of numbers less than 100.
They identify examples of commutative and associative properties of
addition and multiplication. They determine equivalent fractions, decimals and benchmark
percents. They recognize a number
written in scientific notation. They
solve problems involving whole numbers, fractions, decimals, addition and
comparison of integers. They calculate
benchmark percents 25% and 50% of numbers less than 100. They interpret the effect of multiplying
whole numbers by numbers between 0 and 1, inclusive. |
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Objectives |
Students
will |
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M.O.6.1.1 |
demonstrate
an understanding of large numbers by converting and comparing numbers in
scientific notation and standard notation (with and without technology). |
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M.O.6.1.2 |
determine
the greatest common factor and least common multiple using multiple
strategies to solve real-world problems; find prime factorization of a
number. |
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M.O.6.1.3 |
compare
and order integers using multiple strategies (e.g., symbols, manipulatives,
number line). |
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M.O.6.1.4 |
analyze
and solve real-world problems involving addition, subtraction ,
multiplication and division of ·
whole numbers, ·
fractions, mixed numbers, ·
decimals, ·
integers, and justify
the reasonableness by estimation. |
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M.O.6.1.5 |
apply the
distributive, commutative, associative and identity properties to numeric
expressions and use to prove equivalency. |
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M.O.6.1.6 |
convert
between fractions/ratios, mixed numbers, decimals and percents in appropriate
real-world problems. |
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M.O.6.1.7 |
compute
the percent of a number to solve application problems and justify the
reasonableness by estimation. |
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M.O.6.1.8 |
demonstrate
an understanding of the effect of multiplying and dividing, whole numbers,
fractions and decimals by numbers
including 0, 1 and values between 0 and 1 . |
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M.O.6.1.9 |
develop
and test hypotheses to derive the rules for addition, subtraction,
multiplication and division of integers, justify by using real-world examples
and use them to solve problems. |
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Grade
6 |
Mathematics |
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Standard
2 |
Algebra
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M.S.6.2 |
Through communication,
representation, reasoning and proof, problem solving, and making connections
within and beyond the field of mathematics, students will
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Performance
Descriptors (M.PD.6.2) |
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Distinguished |
Above
Mastery |
Mastery |
Partial
Mastery |
Novice |
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Sixth grade students
at the distinguished level in mathematics write algebraic expressions for
word phrases, simplify numeric and evaluate algebraic expressions using order
of operations; they use the expressions to solve real-world problems. They
present their method and justify solution in a clear, concise manner. They
create a rule, express it algebraically, find values by making an input
/output table, test it to determine if it is a function, and explain their thinking in a
clear, concise manner. They create a
geometric or arithmetic sequence, determine any term in the sequence, and
express the rule they used algebraically. They solve problems involving
real-world proportional situations, explaining the method they used, and by
writing a proportion; they relate their method to the proportion. They write and solve one-step equations to
solve real-world problems. They
present the justification of the use of the equation and their solution,
using clear, concise language. |
Sixth grade students
at the above mastery level in mathematics write algebraic expressions for
word phrases, simplify numeric and evaluate algebraic expressions using order
of operations; they use the expressions to solve real-world problems, and
explain their thinking. They determine the rule, output or input, given an
input/output table; write the rule as an algebraic expression, identify other
values, and explain their thinking in a clear, concise manner. They create a
geometric or arithmetic sequence and determine any term in a sequence and
explain their rule. They solve problems involving real-world proportional
situations and explain the method they used. They write and solve one-step
equations to solve real-world problems.
They justify the use of the equation and the solution. |
Sixth grade students
at the mastery level in mathematics write algebraic expressions for word
phrases, simplify numeric and evaluate algebraic expressions using order of
operations. They use the expressions to solve real-world problems. They determine the rule, output or input,
given an input/output table; write the rule as an algebraic expression; and
identify other values. They predict
the nth term of a pattern. They solve
problems involving real-world proportional situations. They write and solve one-step equations to
solve real-world problems. |
Sixth grade students
at the partial mastery level in mathematics write algebraic expressions for
word phrases and simplify numeric expressions using order of operations. They
find a rule, output or input, given an input/output table; They identify the
next three terms of a pattern. They
solve a proportion problem involving measurement. They solve one-step equations. |
Sixth grade students
at the novice level in mathematics write algebraic expressions for word
phrases involving one operation and simplify numeric expressions using order
of operations. They determine
the output, given the rule and the input. They identify the next three terms
of a pattern of one operation. They solve a proportion between equivalent
fractions. They solve one-step equations with the use of manipulatives. |
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Objectives |
Students
will |
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M.O.6.2.1 |
simplify
numerical expressions and evaluate algebraic expressions using order of
operations. |
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M.O.6.2.2 |
use
inductive reasoning to extend patterns to predict the nth term (e.g., powers
and triangular numbers). |
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M.O.6.2.3 |
create
algebraic expressions that correspond to real-world situations; use the
expressions to solve problems. |
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M.O.6.2.4 |
determine
the rule, output or input; given an input/output model using one operation,
write an algebraic expression for the rule and use to identify other
input/output values. |
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M.O.6.2.5 |
solve
real-world proportion problems involving rates, probability and measurements
using multiple strategies, justify selection of strategies. |
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M.O.6.2.6 |
write and
solve one-step equations using number sense, properties of operations and the
idea of maintaining equality to represent and solve real-world problems. |
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Grade
6 |
Mathematics |
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Standard
3 |
Geometry |
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M.S.6.3 |
Through
communication, representation, reasoning and proof, problem solving, and
making connections within and beyond the field of mathematics, students will ·
analyze
characteristics and properties of two- and three-dimensional geometric shapes
and develop mathematical arguments about geometric relationships, ·
specify
locations and describe spatial relationships using coordinate geometry and
other representational systems, ·
apply
transformations and use symmetry to analyze mathematical situations, and ·
solve
problems using visualization, spatial reasoning, and geometric modeling. |
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Performance
Descriptors (M.PD.6.3) |
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Distinguished |
Above
Mastery |
Mastery |
Partial
Mastery |
Novice |
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Sixth grade students
at the distinguished level in mathematics analyze the characteristics of
geometric figures to compare and contrast the figures. They compare it to the original figures,
given a new figure. They derive the formula to determine the sum of the
measures of the interior angles of a polygon and express it algebraically;
use the formula to find the sum of the measures of an n-gon; and extend the
formula to find the measure of each angle in a regular n-gon. They use
geometric representations to solve real-world problems; they apply the
concepts of parallel, perpendicular, intersecting, and skew lines to
real-world situations and to the edges of polyhedrons; they make conjectures
regarding lines and planes. They create designs with rotational and/or line
symmetry; they apply transformations to polygons in a coordinate plane,
including rotating a quadrilateral or triangle in a coordinate plane about a
point not on the polygon; and they describe the method they used, including
mathematical notation. They create a
non-rectangular polygon on a coordinate plane with a given area; they
determine the length of the sides; they name coordinates so the polygon can
be reproduced. |
Sixth grade students
at the above mastery level in mathematics analyze the characteristics of
geometric figures to compare and contrast the figures. They derive the
formula to determine the sum of the measures of the interior angles of a
polygon and use the formula to find the sum of the measures of an n-gon. They use geometric representations to solve
real-world problems; they apply the concepts of parallel, perpendicular,
intersecting, and skew lines to real-world situations and to the edges of polyhedrons.
They create designs with rotational symmetry and/or line symmetry; they apply
transformations to polygons in a coordinate plane and describe the method
they used. They create a polygon on a
coordinate plane with a given area; they determine the length of the sides;
they name coordinates so the polygon can be reproduced. |
Sixth grade students
at the mastery level in mathematics analyze the characteristics of geometric
figures to compare the figures. They derive the formula to determine the sum
of the measures of the interior angles of a polygon. They use geometric representations to solve
real-world problems; they apply the concepts of parallel, perpendicular,
intersecting, and skew lines to real-world situations. They create designs using line and
rotational symmetry; they predict, describe, and perform transformations on
two-dimensional shapes. They plot
polygons on a coordinate grid and determine lengths and areas from the
graphs. |
Sixth grade students
at the partial mastery level in mathematics identify the characteristics of
geometric figures. They find the sum of the measures of the interior angles
of a polygon by partitioning the polygon into triangles. They identify
geometric figures; they find examples of parallel, perpendicular,
intersecting, and skew lines in the classroom and identify them. They
identify line and rotational symmetry.
They plot polygons on a coordinate plane. |
Sixth grade students at the
novice level in mathematics identify sides and angles of
polygons. They determine the sum of the measures of the angles of a polygon,
given a formula. They identify
geometric figures; shown two lines in the classroom, they identify them as
parallel, perpendicular, or intersecting. They identify lines of symmetry. They plot points on a coordinate plane. |
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Objectives |
Students
will |
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M.O.6.3.1 |
analyze
characteristics using defining properties of ·
lines, / angles, / polygons, / triangles,
and / compare these geometric figures. |
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M.O.6.3.2 |
use
inductive reasoning with the measures of interior angles in polygons and
derive the formula to determine the sum of the measures of the interior
angles. |
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M.O.6.3.3 |
apply the
concepts of parallel, perpendicular, intersecting, and skew lines to
real-world situations (i.e. roads and routes). |
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M.O.6.3.4 |
create
designs using line and rotational symmetry. |
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M.O.6.3.5 |
predict,
describe, and perform transformations on two-dimensional shapes ·
translations / rotations / reflections |
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M.O.6.3.6 |
use
geometric representations to solve real-world problems. |
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M.O.6.3.7 |
plot
polygons on coordinate grids, determine lengths and areas from the graph. |
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Grade
6 |
Mathematics |
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Standard
4 |
Measurement
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M.S.6.4 |
Through
communication, representation, reasoning and proof, problem solving, and
making connections within and beyond the field of mathematics, students will
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Performance
Descriptors (M.PD.6.4) |
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Distinguished |
Above
Mastery |
Mastery |
Partial
Mastery |
Novice |
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Sixth grade students
at the distinguished level in mathematics collect data by examination and by
graphing, determine an approximation for pi.
They develop a formula for the circumference of a circle from this
information. They determine
formulas for perimeter of polygons, area of parallelograms and triangles,
circumference and area of circles, volume of rectangular prisms, and
perimeter and area of composite figures; they justify the formulas; they use
these formulas in problem solving situations.
They describe surface area of rectangular prisms and cylinders; they
find the surface area of rectangular prisms; they find the volume of
cylinders, including those in real-world situations; they justify the methods
and their answers; they express formulas algebraically. They construct scale drawings, and describe
mathematically in writing the method they used. |
Sixth grade students
at the above mastery level in mathematics collect data, by examination,
determine an approximation for pi.
They develop a formula for the circumference of a circle from this
information. They determine
formulas for perimeter of polygons, area of parallelograms and triangles,
circumference and area of circles, volume of rectangular prisms, and
perimeter and area of composite figures; they use these formulas in problem
solving situations. They describe
surface area of rectangular prisms and cylinders; they find the surface area
of rectangular prisms; they find the volume of cylinders, including those in
real-world situations; they justify the methods and their answers. They construct scale drawings of regular
polygons, and explain the method they used.
They demonstrate and compare the relationship between area and
perimeter of plane figures. They apply the formulas for area of rectangles
and the volume of a rectangular prism. |
Sixth grade students
at the mastery level in mathematics determine an approximation for pi using
actual measurements. They determine formulas for perimeter of polygons, area
of parallelograms and triangles, circumference and area of circles, volume of
rectangular prisms, and perimeter and area of composite figures. They
describe surface area of rectangular prisms and cylinders; they find the
surface area of rectangular prisms; they find the volume of cylinders,
including those in real-world situations. They construct scale drawings of
regular polygons. |
Sixth grade students
at the partial mastery level in mathematics measure and state that the
distance around a circle is about three times the diameter. They calculate the area of rectangles and
identify through modeling the formula
for the area of a triangle and the volume of a rectangular prism. They
identify and find the area of the surfaces of a rectangular prism. They identify similar polygons and
construct scale drawings of rectangles. |
Sixth grade students at the novice
level in mathematics states that the distance around a circle is about three
times the diameter. They identify the formula for area of a rectangle and
model the formula for volume of a rectangular prism. They identify the
surfaces of a rectangular prism. They
identify similar polygons. |
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Objectives |
Students
will |
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M.O.6.4.1 |
determine
an approximation for pi using actual measurements. |
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M.O.6.4.2 |
develop and
test hypotheses to determine formulas for ·
perimeter
of polygons, including composite figures ·
area
of parallelograms ·
area
of triangles ·
area
of composite figures made of parallelograms and triangles ·
circumference
of a circle ·
area
of a circle ·
volume
of a rectangular prism |
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M.O.6.4.3 |
investigate,
model and describe surface area of rectangular prisms and cylinders; develop
strategies to determine the surface area of rectangular prisms |
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M.O.6.4.4 |
develop
strategies to determine volume of cylinders; solve real-world problems involving
volume of cylinders, justify the results. |
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M.O.6.4.5 |
given a
two-dimensional polygon, construct a scale drawing given the scale factor. |
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Grade
6 |
Mathematics |
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Standard
5 |
Data Analysis and Probability |
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M.S.6.5 |
Through
communication, representation, reasoning and proof, problem solving, and
making connections within and beyond the field of mathematics, students will
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Performance
Descriptors (M.PD.6.5) |
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Distinguished |
Above
Mastery |
Mastery |
Partial
Mastery |
Novice |
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Sixth grade students
at the distinguished level in mathematics design an experiment from a
problem-solving situation in order to collect, organize, display, and
interpret data in bar, line, and circle graphs, stem and leaf plots, and/or
frequency tables. They draw
conclusions from the data and justify the use of the graphical representation
they used. They create a data set for
a specific mean, median, mode and range.
They design an experiment involving either fair or unfair probability,
determine the theoretical probability, make a prediction based on it,
experiment and draw conclusions from their findings. They compare and contrast combinations and
permutation; they find and explain ways to determine the number of
combinations and permutations; they find and describe ways that this
information is useful in real-world situations. |
Sixth grade students at the above mastery level in mathematics design an experiment from a problem-solving situation in order to collect, organize, display, and interpret data in bar, line, and circle graphs, stem and leaf plots, and/or frequency tables. They justify the use | |||||||