Vertical Articulation of Individual
Grade Expectations for Mathematics
Vermont‘s Framework of Standards and Learning Opportunities 

Standard  M:4 Procedural knowledge and understanding of the four algorithmic processes.

Introduction:

Refers to the procedural knowledge of the basic four algorithmic operations (add, subtract, multiply, and divide)  while Standard M:3
refers to the conceptual  knowledge of the four operations. 

Kindergarten

MK: 4   Accurately solves problems in context involving addition and subtraction using whole numbers

First grade

M1: 4   Accurately solves problems in and out of context involving addition and subtraction using whole numbers.

Second grade

M2: 4   No M2: 4 at this grade level

Third grade

M3: 4 Accurately solves 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

Fourth grade

M4: 4 Accurately solves 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.).

Fifth grade

M5: 4 Accurately solves 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 where the left to right computations are modified
 only by the use of parentheses.) M(N&O)–4–4

Sixth Grade

M6: 4 Accurately solves 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

Seventh Grade

M7: 4 Accurately solves 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 And accurately solves problems involving
         integers, raising numbers to whole-number powers, and determining square roots of perfect square numbers and nonperfect square numbers.

Eighth Grade

M8: 4 Accurately solves problems involving proportional reasoning (percent increase or decrease, interest rates, markups, or rates); and squares,
        cubes and taking square or cube roots.(IMPORTANT: Applies the conventions of order of operations.)

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