Code of Maine Rules › 05 - DEPARTMENT OF EDUCATION › 071 - EDUCATION - GENERAL › Chapter 131 - THE MAINE FEDERAL, STATE, AND LOCAL ACCOUNTABILITY STANDARDS › Section 071-131-2 - MATHEMATICS

Current through 2024-29, July 17, 2024
2.1
Number and Operations
Grade 2
2.1.1 Students demonstrate conceptual understanding of
				  rational numbers with respect to: whole numbers from 0 to 199 using place
				  value, by applying the concepts of equivalency in composing or decomposing
				  numbers (e.g., 34 = 17 + 17; 34 = 29 + 5); and in expanded notation (e.g., 141
				  = 1 hundred + 4 tens + 1 one or 141 = 100 + 40 + 1) using models, explanations,
				  or other representations; and positive fractional numbers (benchmark fractions:
a
/2,
a
/3, or
a
/4, where
a
is a whole number greater than 0 and less than or equal to
				  the denominator) as a part to whole relationship in area and set models where
				  the denominator is equal to the number of parts in the whole using models,
				  explanations, or other representations. (M(N&O)-2-1)
2.1.2 Students demonstrate understanding of the relative
				  magnitude of numbers from 0 to 199 by ordering whole numbers; by comparing
				  whole numbers to each other or to benchmark whole numbers (10, 25, 50, 75, 100,
				  125, 150, or 175); by demonstrating an understanding of the relation of
				  inequality when comparing whole numbers by using "1 more", "1 less", "10 more",
				  "10 less", "100 more", or "100 less"; or by connecting number words and
				  numerals to the quantities they represent using models, number lines, or
				  explanations. (M(N&O)-2-2)
2.1.3 Students demonstrate conceptual understanding of
				  mathematical operations involving addition and subtraction of whole numbers by
				  solving problems involving joining actions, separating actions, part-part whole
				  relationships, and comparison situations; and addition of multiple one-digit
				  whole numbers. (M(N&O)-2-3)
2.1.4 Students demonstrate understanding of monetary value by
				  adding coins together to a value no greater than $1.99 and representing the
				  result in dollar notation; making change from $1.00 or less, or recognizing
				  equivalent coin representations of the same value (values up to $1.99).
				  (M(N&O)-2-5))
Grade 3
2.1.5 Students demonstrate conceptual understanding of
				  rational numbers with respect to: whole numbers from 0 to 999 through
				  equivalency, composition, decomposition, or place value using models,
				  explanations, or other representations; and positive fractional numbers
				  (benchmark fractions:
a/
2,
a
/3,
a
/4,
a
/6, or
a
/8, where
a
is a whole number greater than 0 and less than or equal to
				  the denominator) as a part to whole relationship in area and set models where
				  the number of parts in the whole is equal to the denominator; and decimals
				  (within a context of money) as a part of 100 using models, explanations, or
				  other representations. (M(N&O)-3-1)
2.1.6 Students demonstrate understanding of the relative
				  magnitude of numbers from 0 to 999 by ordering whole numbers; by comparing
				  whole numbers to benchmark whole numbers (100, 250, 500, or 750); or by
				  comparing whole numbers to each other; and comparing or identifying equivalent
				  positive fractional numbers (
a/
2,
a
/3,
a
/4 where
a
is a whole number greater than 0
				  and less than or equal to the denominator) using models, number lines, or
				  explanations. (M(N&O)-3-2)
2.1.7 Students demonstrate conceptual understanding of
				  mathematical operations by describing or illustrating the inverse relationship
				  between addition and subtraction of whole numbers; and the relationship between
				  repeated addition and multiplication using models, number lines, or
				  explanations. (M(N&O)-3-3)
2.1.8 Students accurately solve problems involving addition
				  and subtraction with and without regrouping; the concept of multiplication; and
				  addition or subtraction of decimals (in the context of money).
				  (M(N&O)-3-4)
Grade 4
2.1.9 Students demonstrate conceptual understanding of
				  rational numbers with respect to: whole numbers from 0 to 999,999 through
				  equivalency, composition, decomposition, or place value using models,
				  explanations, or other representations; and positive fractional numbers
				  (benchmark fractions:
a/
2,
a
/3,
a
/4,
a
/5,
a
/6,
a
/8, or
a/
10, where
a
is a
				  whole number greater than 0 and less than or equal to the denominator) as a
				  part to whole relationship in area, set, or linear models where the number of
				  parts in the whole are equal to, and a multiple or factor of the denominator;
				  and decimals as hundredths within the context of money, or tenths within the
				  context of metric measurements (e.g., 2.3 cm) using models, explanations, or
				  other representations. (M(N&O)-4-1)
2.1.10 Students demonstrate understanding of the relative
				  magnitude of numbers from 0 to 999,999 by ordering or comparing whole numbers;
				  and ordering, comparing, or identifying equivalent proper positive fractional
				  numbers; or decimals using models, number lines, or explanations.
(M(N&O)-4-2)
2.1.11 Students demonstrate conceptual understanding of
				  mathematical operations by describing or illustrating the relationship between
				  repeated subtraction and division (no remainders); the inverse relationship
				  between multiplication and division of whole numbers; or the addition or
				  subtraction of positive fractional numbers with like denominators using models,
				  number lines, or explanations. (M(N&O)-4-3)
2.1.12 Students accurately solve problems involving multiple
				  operations on whole numbers or the use of the properties of factors and
				  multiples; and addition or subtraction of decimals and positive proper
				  fractions with like denominators. (Multiplication limited to 2 digits by 2
				  digits, and division limited to 1 digit divisors.) (IMPORTANT
: Applies
				  the conventions of order of operations where the left to right computations are
				  modified only by the use of parentheses.
) (M(N&O)-4-4)
Grade 5
2.1.13 Students demonstrate conceptual understanding of
				  rational numbers with respect to: whole numbers from 0 to 9,999,999 through
				  equivalency, composition, decomposition, or place value using models,
				  explanations, or other representations; and positive fractional numbers
				  (proper, mixed number, and improper) (halves, fourths, eighths, thirds, sixths,
				  twelfths, fifths, or powers of ten (10, 100, 1000)), decimals (to thousandths),
				  or benchmark percents (10%, 25%, 50%, 75% or 100%) as a part to whole
				  relationship in area, set, or linear models using models, explanations, or
				  other representations*. (M(N&O)-5-1)
2.1.14 Students demonstrate understanding of the relative
				  magnitude of numbers by ordering, comparing, or identifying equivalent positive
				  fractional numbers, decimals, or benchmark percents within number formats
				  (fractions to fractions, decimals to decimals, or percents to percents); or
				  integers in context using models or number lines. M(N&O)-5-2
2.1.15 Students demonstrate conceptual understanding of
				  mathematical operations by describing or illustrating the meaning of a
				  remainder with respect to division of whole numbers using models, explanations,
				  or solving problems. M(N&O)-5-3
2.1.16 Students accurately solve problems involving multiple
				  operations on whole numbers or the use of the properties of factors, multiples,
				  prime, or composite numbers; and addition or subtraction of fractions (proper)
				  and decimals to the hundredths place. (Division of whole numbers by up to a
				  two-digit divisor.) (IMPORTANT
: Applies the conventions of order of
				  operations with and without parentheses.
) (M(N&O)-5-4)
Grade 6
2.1.17 Students demonstrate conceptual understanding of
				  rational numbers with respect to ratios (comparison of two whole numbers by
				  division
a
/
b
,
a
:
b
, and
a
/
b
, where
b
1 0); and rates (e.g.,
a
out of
b
, 25%) using models, explanations,
				  or other representations*. (M(N&O)-6-1)
2.1.18 Students demonstrate understanding of the relative
				  magnitude of numbers by ordering or comparing numbers with whole number bases
				  and whole number exponents (e.g.,33,
				  43), integers, or rational numbers within and across
				  number formats (fractions, decimals, or whole number percents from 1- 100)
				  using number lines or equality and inequality symbols.
(M(N&O)-6-2)
2.1.19 Students demonstrate conceptual understanding of
				  mathematical operations by describing or illustrating the meaning of a power by
				  representing the relationship between the base (whole number) and the exponent
				  (whole number) (e.g.,33,
				  43); and the effect on the magnitude of a whole
				  number when multiplying or dividing it by a whole number, decimal, or fraction.
				  (M(N&O)-6-3)
2.1.20 Students accurately solve problems involving single or
				  multiple operations on fractions (proper, improper, and mixed), or decimals;
				  and addition or subtraction of integers; percent of a whole; or problems
				  involving greatest common factor or least common multiple. (IMPORTANT
:
				  Applies the conventions of order of operations with and without
				  parentheses.
) (M(N&O)-6-4)
Grade 7
2.1.21 Students demonstrate conceptual understanding of
				  rational numbers with respect to percents as a means of comparing the same or
				  different parts of the whole when the wholes vary in magnitude (e.g., 8 girls
				  in a classroom of 16 students compared to 8 girls in a classroom of 20
				  students, or 20% of 400 compared to 50% of 100); and percents as a way of
				  expressing multiples of a number (e.g., 200% of 50) using models, explanations,
				  or other representations*. (M(N&O)-7-1)
2.1.22 Students demonstrate understanding of the relative
				  magnitude of numbers by ordering, comparing, or identifying equivalent rational
				  numbers across number formats, numbers with whole number bases and whole number
				  exponents (e.g., 33, 43),
				  integers, absolute values, or numbers represented in scientific notation using
				  number lines or equality and inequality symbols. (M(N&O)-7-2)
2.1.23 Students accurately solve problems involving
				  proportional reasoning; percents involving discounts, tax, or tips; and rates.
				  (IMPORTANT:
Applies the conventions of order of operations including
				  parentheses, brackets, or exponents.
) (M(N&O)-7-4)
*Specifications for area, set, and linear models for grades 5
				  - 8: Fractions: The number of parts in the whole are equal to the denominator,
				  a multiple of the denominator, or a factor of the denominator. Percents: The
				  number of parts in the whole is equal to 100, a multiple of 100, or a factor of
				  100 (for grade 5); the number of parts in the whole is a multiple or a factor
				  of the numeric value representing the whole (for grades 6-8). Decimals
				  (including powers of ten): The number of parts in the whole is equal to the
				  denominator of the fractional equivalent of the decimal, a multiple of the
				  denominator of the fractional equivalent of the decimal, or a factor of the
				  denominator of the fractional equivalent of the decimal.
Grades 9-Diploma
2.1.24 Students demonstrate understanding of the relative
				  magnitude of real numbers by solving problems involving ordering or comparing
				  rational numbers, common irrational numbers (e.g.,
Click here to view
				  Image
,
Click
				  here to view Image
) , rational bases with integer exponents, square
				  roots, absolute values, integers, or numbers represented in scientific notation
				  using number lines or equality and inequality symbols. (M(N&O
				  ;)-10-2)
2.1.25 Students accurately solve problems involving rational
				  numbers within mathematics, across content strands, disciplines or contexts
				  (with emphasis on, but not limited to, proportions, percents, ratios, and
				  rates).
(M(N&O)-10-4)
2.2
Geometry and Measurement
Grade 2
2.2.1 Students use properties, attributes, composition, or
				  decomposition to sort or classify polygons or objects by a combination of two
				  or more non-measurable or measurable attributes. (M(G&M)-2-1)
2.2.2 Students demonstrate conceptual understanding of
				  perimeter and area by using models or manipulatives to surround and cover
				  polygons.
(M(G&M)-2-6)
2.2.3 Students measure and use units of measures
				  appropriately and consistently, and make conversions within systems when
				  solving problems across the content strands. (M(G&M)-2-7)
Grade 3
2.2.4 Students use properties or attributes of angles (number
				  of angles) or sides (number of sides or length of sides) or composition or
				  decomposition of shapes to identify, describe, or distinguish among triangles,
				  squares, rectangles, rhombi, trapezoids, hexagons, or circles.
				  (M(G&M)-3-1)
2.2.5 Students demonstrate conceptual understanding of
				  perimeter of polygons, and the area of rectangles on grids using a variety of
				  models or manipulatives. Express all measures using appropriate units.
				  (M(G&M)-3-6)
2.2.6 Students measure and use units of measures
				  appropriately and consistently, and make conversions within systems when
				  solving problems across the content strands. (M(G&M)-3-7)
Grade 4
2.2.7 Students use properties or attributes of angles (number
				  of angles) or sides (number of sides, length of sides, parallelism, or
				  perpendicularity) to identify, describe, or distinguish among triangles,
				  squares, rectangles, rhombi, trapezoids, hexagons, or octagons; or classify
				  angles relative to 90° as more than, less than, or equal to.
				  (M(G&M)-4-1)
2.2.8 Students use properties or attributes (shape of bases
				  or number of lateral faces) to identify, compare, or describe three-dimensional
				  shapes (rectangular prisms, triangular prisms, cylinders, or spheres).
				  (M(G&M)-4-3)
2.2.9 Students demonstrate conceptual understanding of
				  congruency by matching congruent figures using reflections, translations, or
				  rotations (flips, slides, or turns), or as the result of composing or
				  decomposing shapes using models or explanations. (M(G&M)-4-4)
2.2.10 Students demonstrate conceptual understanding of
				  similarity by applying scales on maps, or applying characteristics of similar
				  figures (same shape but not necessarily the same size) to identify similar
				  figures, or to solve problems involving similar figures. Describe relationships
				  using models orsc explanations.
				  (M(G&M)-4-5)
2.2.11 Students demonstrate conceptual understanding of
				  perimeter of polygons, and the area of rectangles, polygons or irregular shapes
				  on grids using a variety of models, manipulatives, or formulas. Express all
				  measures using appropriate units. (M(G&M)-4-6)
2.2.12 Students measure and use units of measures
				  appropriately and consistently, and make conversions within systems when
				  solving problems across the content strands. (M(G&M)-4-7)
Grade 5
2.2.13 Students use properties or attributes of angles
				  (right, acute, or obtuse) or sides (number of congruent sides, parallelism, or
				  perpendicularity) to identify, describe, classify, or distinguish among
				  different types of triangles (right, acute, obtuse, equiangular, or
				  equilateral) or quadrilaterals (rectangles, squares, rhombi, trapezoids, or
				  parallelograms). (M(G&M)-5-1)
2.2.14 Students use properties or attributes (shape of bases,
				  number of lateral faces, or number of bases) to identify, compare, or describe
				  three-dimensional shapes (rectangular prisms, triangular prisms, cylinders,
				  spheres, pyramids, or cones). (M(G&M)-5-3)
2.2.15 Students demonstrate conceptual understanding of
				  perimeter of polygons, and the area of rectangles or right triangles through
				  models, manipulatives, or formulas, the area of polygons or irregular figures
				  on grids, and volume of rectangular prisms (cubes) using a variety of models,
				  manipulatives, or formulas. Express all measures using appropriate units.
				  (M(G&M)-5-6)
2.2.16 Students measure and use units of measures
				  appropriately and consistently, and make conversions within systems when
				  solving problems across the content strands. (M(G&M)-5-7)
Grade 6
2.2.17 Students use properties or attributes of angles
				  (right, acute, or obtuse) or sides (number of congruent sides, parallelism, or
				  perpendicularity) to identify, describe, classify, or distinguish among
				  different types of triangles (right, acute, obtuse, equiangular, scalene,
				  isosceles, or equilateral) or quadrilaterals (rectangles, squares, rhombi,
				  trapezoids, or parallelograms). (M(G&M)-6-1)
2.2.18 Students use properties or attributes (shape of bases,
				  number of lateral faces, number of bases, number of edges, or number of
				  vertices) to identify, compare, or describe three-dimensional shapes
				  (rectangular prisms, triangular prisms, cylinders, spheres, pyramids, or
				  cones). (M(G&M)-6-3)
2.2.19 Students demonstrate conceptual understanding of
				  similarity by describing the proportional effect on the linear dimensions of
				  polygons or circles when scaling up or down while preserving the angles of
				  polygons, or by solving related problems (including applying scales on maps).
				  Describe effects using models or explanations. (M(G&M)-6-5)
2.2.20 Students demonstrate conceptual understanding of
				  perimeter of polygons, the area of quadrilaterals or triangles, and the volume
				  of rectangular prisms by using models, formulas, or by solving problems; and
				  demonstrate understanding of the relationships of circle measures (radius to
				  diameter and diameter to circumference) by solving related problems. Express
				  all measures using appropriate units. (M(G&M)-6-6)
2.2.21 Students measure and use units of measures
				  appropriately and consistently, and make conversions within systems when
				  solving problems across the content strands. (M(G&M)-6-7)
Grade 7
2.2.22 Students use properties of angle relationships
				  resulting from two or three intersecting lines (adjacent angles, vertical
				  angles, straight angles, or angle relationships formed by two non-parallel
				  lines cut by a transversal), or two parallel lines cut by a transversal to
				  solve problems. (M(G&M)-7-1)
2.2.23 Students apply theorems or relationships (triangle
				  inequality or sum of the measures of interior angles of regular polygons) to
				  solve problems. (M(G&M)-7-2)
2.2.24 Students apply the concepts of congruency by solving
				  problems on a coordinate plane involving reflections, translations, or
				  rotations.
(M(G&M)-7-4)
2.2.25 Students apply concepts of similarity by solving
				  problems involving scaling up or down and their impact on angle measures,
				  linear dimensions and areas of polygons, and circles when the linear dimensions
				  are multiplied by a constant factor. Describe effects using models or
				  explanations.
(M(G&M)-7-5)
2.2.26 Students demonstrate conceptual understanding of the
				  area of circles or the area or perimeter of composite figures (quadrilaterals,
				  triangles, or parts of circles), and the surface area of rectangular prisms, or
				  volume of rectangular prisms, triangular prisms, or cylinders using models,
				  formulas, or by solving related problems. Express all measures using
				  appropriate units.
(M(G&M)-7-6)
Grades 9-Diploma
2.2.27 Students make and defend conjectures, construct
				  geometric arguments, use geometric properties, or use theorems to solve
				  problems involving angles, lines, polygons, circles, or right triangle ratios
				  (sine, cosine, tangent) within mathematics or across disciplines or contexts
				  (e.g., Pythagorean Theorem, Triangle Inequality Theorem).
				  (M(G&M)-10-2)
2.2.28 Students apply the concepts of congruency by solving
				  problems on or off a coordinate plane involving reflections, translations, or
				  rotations; or solve problems using congruency involving problems within
				  mathematics or across disciplines or contexts. (M(G&M)-10-4)
2.2.29 Students apply concepts of similarity by solving
				  problems within mathematics or across disciplines or contexts.
				  (M(G&M)-10-5)
2.2.30 Students solve problems involving perimeter,
				  circumference, or area of two-dimensional figures (including composite figures)
				  or surface area or volume of three-dimensional figures (including composite
				  figures) within mathematics or across disciplines or contexts. (M(G&M)-10-6
				  M)
2.2.31 Students use units of measure appropriately and
				  consistently when solving problems across content strands; make conversions
				  within or across systems and make decisions concerning an appropriate degree of
				  accuracy in problem situations involving measurement in other GLEs.
				  (M(G&M)-10-7)
2.2.32 Students solve problems on and off the coordinate
				  plane involving distance, midpoint, perpendicular and parallel lines, or slope.
				  (M(G&M)-10-9)
2.3
FUNCTIONS AND ALGEBRA
Grade 2
2.3.1 Students identify and extend to specific cases a
				  variety of patterns (linear and non-numeric) represented in models, tables, or
				  sequences by extending the pattern to the next element, or finding a missing
				  element (e.g., 2, 4, 6, ___, 10). (M(F& A)-2-1)
2. 3.2 Students demonstrate conceptual understanding of
				  equality by finding the value that will make an open sentence true
				  (e.g.,
Click
				  here to view Image
(limited to one operation and limited to use addition or
				  subtraction) (M(F& A)-2-4)
Grade 3
2. 3.3 Students identify and extend to specific cases a
				  variety of patterns (linear and non-numeric) represented in models, tables, or
				  sequences by extending the pattern to the next one, two, or three elements, or
				  finding missing elements. (M(F& A)-3-1)
2.3.4 Students demonstrate conceptual understanding of
				  equality by showing equivalence between two expressions using models or
				  different representations of the expressions; or by finding the value that will
				  make an open sentence true (e.g.,
Click
				  here to view Image
(limited to one operation and limited to use addition,
				  subtraction, or multiplication) (M(F& A)-3-4)
Grade 4
2.3.5 Students identify and extend to specific cases a
				  variety of patterns (linear and nonlinear) represented in models, tables or
				  sequences; and write a rule in words orsc symbols to
				  find the next case. (M(F& A)-4-1)
2.3.6 Students demonstrate conceptual understanding of
				  algebraic expressions by using letters or symbols to represent unknown
				  quantities to write simple linear algebraic expressions involving any one of
				  the four operations; or by evaluating simple linear algebraic expressions using
				  whole numbers. (M(F& A)-4-3)
2.3.6 Students demonstrate conceptual understanding of
				  equality by showing equivalence between two expressions using models or
				  different representations of the expressions, by simplifying numerical
				  expressions where left to right computations may be modified only by the use of
				  parentheses [e.g., 14 - (2 X 5)] (expressions consistent with the parameters of
				  M(F& A)-4-3), and by solving one-step linear equations of the form
ax
=
c
,
x
+-
b
=
c
, where
a
,
b
, and
c
are whole numbers with
a
[NOT EQUAL TO] 0. (M(F& A)-4-4)
Grade 5
2.3.7 Students identify and extend to specific cases a
				  variety of patterns (linear and nonlinear) represented in models, tables,
				  sequences, or in problem situations; and write a rule in words
				  orsc symbols for finding specific cases of a linear
				  relationship. (M(F& A)-5-1)
2.3.8 Students demonstrate conceptual understanding of
				  algebraic expressions by using letters to represent unknown quantities to write
				  linear algebraic expressions involving any two of the four operations; or by
				  evaluating linear algebraic expressions using whole numbers. (M(F&
				  A)-5-3)
2.3.9 Students demonstrate conceptual understanding of
				  equality by showing equivalence between two expressions using models or
				  different representations of the expressions (expressions consistent with the
				  parameters of M(F&
A)-5-3), by solving one-step linear equations of the form
ax
=
c
,
x
+-
b
=
c
, or
x
/
a
=
c
, where
a
,
b
, and
c
are whole
				  numbers with
a
[NOT EQUAL TO] 0; or by determining which
				  values of a replacement set make the equation (multi-step of the form
ax
+-
b
=
c
where
a
,
b
, and
c
are whole
				  numbers with
a
[NOT EQUAL TO] 0) a true statement (e.g.,
				  2
x
+ 3 = 11, {
x
:
x
= 2, 3,
				  4, 5}). (M(F& A)-5-4)
Grade 6
2.3.10 Students identify and extend to specific cases a
				  variety of patterns (linear and nonlinear) represented in models, tables,
				  sequences, graphs, or in problem situations; or write a rule in words or
				  symbols for finding specific cases of a linear relationship; or write a rule in
				  words orsc symbols for finding specific cases of a
				  nonlinear relationship; and write an expression orsc
				  equation using words orsc symbols to express the
				  generalization of a linear relationship (e.g., twice the term number plus 1
				  orsc 2
n
+ 1). (M(F&
				  A)-6-1)
2.3.11 Students demonstrate conceptual understanding of
				  linear relationships (
y
=
kx
;
y
=
mx
+
b
) as a constant
				  rate of change by constructing or interpreting graphs of real occurrences and
				  describing the slope of linear relationships (faster, slower, greater, or
				  smaller) in a variety of problem situations; and describe how change in the
				  value of one variable relates to change in the value of a second variable in
				  problem situations with constant rates of change. (M(F& A)-6-2)
2.3.12 Students demonstrate conceptual understanding of
				  algebraic expressions by using letters to represent unknown quantities to write
				  linear algebraic expressions involving two or more of the four operations; or
				  by evaluating linear algebraic expressions (including those with more than one
				  variable); or by evaluating an expression within an equation (e.g., determine
				  the value of
y
when
x
= 4 given
y
= 3
x
- 2). (M(F& A)-6-3)
2.3.13 Students demonstrate conceptual understanding of
				  equality by showing equivalence between two expressions using models or
				  different representations of the expressions (expressions consistent with the
				  parameters of M(F& A)-6-3), solving multi-step linear equations of the form
ax
+-
b
=
c
, where
a
,
b
, and
c
are whole
				  numbers with
a
[NOT EQUAL TO] 0. (M(F& A)-6-4)
Grade 7
2.3.14 Students identify and extend to specific cases a
				  variety of patterns (linear and nonlinear) represented in models, tables,
				  sequences, graphs, or in problem situations; and generalize a linear
				  relationship using words and symbols; generalizes a linear relationship to find
				  a specific case; or write an expression orsc
				  equation using words orsc symbols to express the
				  generalization of a nonlinear relationship. (M(F& A)-7-1)
2.3.15 Students demonstrate conceptual understanding of
				  linear relationships (
y
=
kx
;
y
=
mx
+
b
) as a constant
				  rate of change by solving problems involving the relationship between slope and
				  rate of change, by describing the meaning of slope in concrete situations, or
				  informally determining the slope of a line from a table or graph; and
				  distinguish between constant and varying rates of change in concrete situations
				  represented in tables or graphs; or describe how change in the value of one
				  variable relates to change in the value of a second variable in problem
				  situations with constant rates of change. (M(F& A)-7-2)
2.3.16 Students demonstrate conceptual understanding of
				  algebraic expressions by using letters to represent unknown quantities to write
				  algebraic expressions (including those with whole number exponents or more than
				  one variable); or by evaluating algebraic expressions (including those with
				  whole number exponents or more than one variable); or by evaluating an
				  expression within an equation (e.g., determine the value of
y
when
x
= 4 given
y
=
				  5
x3
- 2). (M(F& A)-7-3)
2.3.17 Students demonstrate conceptual understanding of
				  equality by showing equivalence between two expressions (expressions consistent
				  with the parameters of the left- and right-hand sides of the equations being
				  solved at this grade level) using models or different representations of the
				  expressions, solving multi-step linear equations of the form
ax
+-
b
=
c
with
a
[NOT EQUAL TO] 0,
ax
+-
b
=
cx
+-
d
with
a
,
c
[NOT EQUAL TO] 0, and
				  (
x
/
a
) +-
b
=
c
with
a
[NOT EQUAL TO] 0, where
a
,
b
,
c
and
d
are whole numbers; or by translating a problem-solving
				  situation into an equation consistent with the parameters of the type of
				  equations being solved for this grade level. (M(F& A)-7-4)
Grades 9-Diploma
2.3.18 Students identify, extend, and generalize a variety of
				  patterns (linear and nonlinear) represented by models, tables, sequences, or
				  graphs in problem solving situations. (M(F& A)-10-1)
2.3.19 Students demonstrate conceptual understanding of
				  linear and nonlinear functions and relations (including characteristics of
				  classes of functions) through an analysis of constant, variable, or average
				  rates of change, intercepts, domain, range, maximum and minimum values,
				  increasing and decreasing intervals and rates of change (e.g., the height is
				  increasing at a decreasing rate); describe how change in the value of one
				  variable relates to change in the value of a second variable; or works between
				  and among different representations of functions and relations (e.g., graphs,
				  tables, equations, function notation). (M(F& A)-10-2)
2.3.20 Students demonstrate conceptual understanding of
				  algebraic expressions by solving problems involving algebraic expressions, by
				  simplifying expressions (e.g., simplifying polynomial or rational expressions,
				  or expressions involving integer exponents, square roots, or absolute values),
				  by evaluating expressions, or by translating problem situations into algebraic
				  expressions. (M(F& A)-10-3)
2.3.21 Students demonstrate conceptual understanding of
				  equality by solving problems involving algebraic reasoning about equality; by
				  translating problem situations into equations; by solving linear equations
				  (symbolically and graphically) and expressing the solution set symbolically or
				  graphically, or providing the meaning of the graphical interpretations of
				  solution(s) in problem-solving situations; or by solving problems involving
				  systems of linear equations in a context (using equations or graphs) or using
				  models or representations. (M(F& A)-10-4)
2.4
DATA, Statistics, and
				Probability
Grade 2
2.4.1 Students interpret a given representation (pictographs
				  with one-to-one correspondence, line plots, tally charts, or tables) to answer
				  questions related to the data, or to analyze the data to formulate conclusions.
				  (IMPORTANT:
Analyzes data consistent with concepts and skills in
				  M(DSP)-2-2.
) (M(DSP)-2-1)
2.4.2 Students analyze patterns, trends, or distributions in
				  data in a variety of contexts by determining or using more, less, or equal.
				  (M(DSP)-2-2)
2.4.3 Students use counting techniques to solve problems
				  involving combinations using a variety of strategies (e.g., student diagrams,
				  organized lists, tables, tree diagrams, orsc
				  others); (e.g., How many ways can you make 50 cents using nickels, dimes, and
				  quarters") (M(DSP)-2-4)
Grade 3
2.4.4 Students interpret a given representation (line plots,
				  tally charts, tables, or bar graphs) to answer questions related to the data,
				  to analyze the data to formulate conclusions, or to make predictions.
				  (IMPORTANT:
Analyzes data consistent with concepts and skills in
				  M(DSP)-3-2
.) (M(DSP)-3-1)
2.4.5 Students analyze patterns, trends, or distributions in
				  data in a variety of contexts by determining or using most frequent (mode),
				  least frequent, largest, or smallest. (M(DSP)-3-2)
2.4.6 Students identify or describe representations or
				  elements of representations that best display a given set of data or situation,
				  consistent with the representations required in M(DSP)-3-1. (M(DSP)-3-3)
2.4.7 For a probability event in which the sample space may
				  or may not contain equally likely outcomes, students determine the likelihood
				  of the occurrence of an event (using "more likely", "less likely", or "equally
				  likely"). (M(DSP)-3-5)
Grade 4
2.4.8 Students interpret a given representation (line plots,
				  tables, bar graphs, pictographs, or circle graphs) to answer questions related
				  to the data, to analyze the data to formulate or justify conclusions, to make
				  predictions, or to solve problems. (IMPORTANT:
Analyzes data consistent
				  with concepts and skills in M(DSP)-4-2.
) (M(DSP)-4-1)
2.4.9 Students analyze patterns, trends, or distributions in
				  data in a variety of contexts by determining or using measures of central
				  tendency (median or mode), or range. (M(DSP)-4-2)
2.4.10 Students use counting techniques to solve problems in
				  context involving combinations or simple permutations (e.g., Given a map -
				  Determine the number of paths from point A to point B.) using a variety of
				  strategies (e.g., organized lists, tables, tree diagrams, or others).
				  (M(DSP)-4-4)
2.4.11 For a probability event in which the sample space may
				  or may not contain equally likely outcomes, students determine the theoretical
				  probability of an event and express the result as part to whole (e.g., two out
				  of five).
(M(DSP)-4-5)
Grade 5
2.4.12 Students interpret a given representation (tables, bar
				  graphs, circle graphs, or line graphs) to answer questions related to the data,
				  to analyze the data to formulate or justify conclusions, to make predictions,
				  or to solve problems. (IMPORTANT:
Analyzes data consistent with
				  concepts and skills in M(DSP)-5-2
.) (M(DSP)-5-1)
2.4.13 Students analyze patterns, trends, or distributions in
				  data in a variety of contexts by determining or using measures of central
				  tendency (mean, median, or mode) or range to analyze situations, or to solve
				  problems. (M(DSP)-5-2)
2.4.14 Students identify or describe representations or
				  elements of representations that best display a given set of data or situation,
				  consistent with the representations required in M(DSP)-5-1. (M(DSP)-5-3)
2.4.15 For a probability event in which the sample space may
				  or may not contain equally likely outcomes, students determine the experimental
				  or theoretical probability of an event and express the result as a fraction.
				  (M(DSP)-5-5)
Grade 6
2.4.15 Students interpret a given representation (circle
				  graphs, line graphs, or stem-and-leaf plots) to answer questions related to the
				  data, to analyze the data to formulate or justify conclusions, to make
				  predictions, or to solve problems. (IMPORTANT:
Analyzes data consistent
				  with concepts and skills in M(DSP)-6-2
.) (M(DSP)-6-1)
2.4.16 Students analyze patterns, trends or distributions in
				  data in a variety of contexts by determining or using measures of central
				  tendency (mean, median, or mode) or dispersion (range) to analyze situations,
				  or to solve problems. (M(DSP)-6-2)
2.4.17 Students use counting techniques to solve problems in
				  context involving combinations or simple permutations using a variety of
				  strategies (e.g., organized lists, tables, tree diagrams, models, Fundamental
				  Counting Principle, or others). (M(DSP)-6-4)
2.4.18 For a probability event in which the sample space may
				  or may not contain equally likely outcomes, students determine the experimental
				  or theoretical probability of an event in a problem-solving situation.
(M(DSP)-6-5)
Grade 7
2.4.19 Students interpret a given representation (circle
				  graphs, scatter plots that represent discrete linear relationships, or
				  histograms) to analyze the data to formulate or justify conclusions, to make
				  predictions, or to solve problems. (IMPORTANT:
Analyzes data consistent
				  with concepts and skills in M(DSP)-7-2.
)
(M(DSP)-7-1)
2.4.20 Students analyze patterns, trends, or distributions in
				  data in a variety of contexts by solving problems using measures of central
				  tendency (mean, median, or mode), dispersion (range or variation), or outliers
				  to analyze situations to determine their effect on mean, median, or mode; and
				  evaluate the sample from which the statistics were developed (bias).
				  (M(DSP)-7-2)
2.4.21 Students interpret or describe representations or
				  elements of representations that best display a given set of data or situation,
				  consistent with the representations required in M(DSP)-7-1. (M(DSP)-7-3)
2.4.22 For a probability event in which the sample space may
				  or may not contain equally likely outcomes, students determine the experimental
				  or theoretical probability of an event in a problem-solving situation.
				  (M(DSP)-7-5)
Grades 9-Diploma
2.4.23 Students Interpret a given representation(s) (e.g.,
				  box-and-whisker plots, scatter plots, bar graphs, line graphs, circle graphs,
				  histograms, frequency charts) to make observations, to answer questions, to
				  analyze the data to formulate or justify conclusions, critique conclusions,
				  make predictions, or to solve problems within mathematics or across disciplines
				  or contexts (e.g., media, workplace, social and environmental situations).
				  (IMPORTANT:
Analyzes data consistent with concepts and skills in
				  M(DSP)-10-2
.) (M(DSP)-10-1)
2.4.24 Students analyze patterns, trends, or distributions in
				  data in a variety of contexts by determining, using, or analyzing measures of
				  central tendency (mean, median, or mode), dispersion (range or variation),
				  outliers, quartile values, estimated line of best fit, regression line, or
				  correlation (strong positive, strong negative, or no correlation) to solve
				  problems; and solve problems involving conceptual understanding of the sample
				  from which the statistics were developed. (M(DSP)-10-2)
2.4.25 Students Identify or describe representations or
				  elements of representations that best display a given set of data or situation,
				  consistent with the representations required in (M(DSP)-10-3)
2.4.26 Students use counting techniques to solve problems in
				  context involving combinations or permutations using a variety of strategies
				  (e.g., organized lists, tables, tree diagrams, models, Fundamental Counting
				  Principle, orsc others). (M(DSP)-10-4)
2.4.27 Students solve problems involving experimental or
				  theoretical probability. (M(DSP)-10-5)