Vertical
Articulation of Individual
Grade Expectations for Mathematics
Vermont‘s Framework of Standards and Learning
Opportunities
Standard M:22 Equality and Equivalence
Introduction:
Standard 22 refers to the development of the student's conceptual understanding of equality and equivalence.
Kindergarten
MK: 22 Demonstrates
conceptual understanding of equality by showing equivalence between two
expressions (4+1=5; 2+3=5) by solving one-step
equations involving whole
number addition or subtraction using models or verbal explanations.
First Grade
M1: 22 Demonstrates conceptual understanding of
equality by showing equivalence between two expressions (4+1=5; 2+3=5) by
solving one-step
equations involving whole number addition or subtraction
using models, verbal explanations, or written equations.
Second Grade
M2: 22 Demonstrates conceptual
understanding of equality by finding the value
that will make an open sentence true (e.g., 2 +
= 7 ). (limited
to one
operation and limited to use addition or subtraction).
M(F&A)–2–4
Third grade
M3: 22 Demonstrates 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., 2 + □ = 7) (limited to one
operation and limited to use addition,
subtraction, or multiplication).
M(F&A)–3–4
Fourth Grade
M4: 22 Demonstrates 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 × 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
0
M(F&A)–4–4operations;
or by evaluating simple linear algebraic expressions using whole numbers.
M(F&A)–4–3
Fifth grade
M5: 22 Demonstrates 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 ≠ 0; or by determining which
values of a replacement set make the equation (multistep of the form ax
± b = c
where a, b, and c are whole numbers with
a ≠ 0) a true statement (e.g., 2 x + 3 = 11, { x: x = 2, 3, 4, 5}).
M(F&A)–5–4
Sixth Grade
M6: 22 Demonstrates 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 multistep linear equations of the
form
ax ± b = c, where a, b, and c are whole
numbers with a ≠ 0. M(F&A)–6–4
Seventh Grade
M7: 22 Demonstrates 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 multistep linear equations of the form ax ± b = c with a ≠‚
0, ax ± b = cx ± d with a, c ≠‚ 0, and (x/a)
± b = c with a ≠ 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
Eighth Grade
M8: 22 Demonstrates 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 formulas for a variable requiring one transformation (e.g., d =
rt; d/r = t); by solving multistep linear equations with integer
coefficients; by showing that two expressions are or are not
equivalent by applying commutative, associative, or distributive properties,
order
of operations, or
substitution; and by informally solving problems involving systems of
linear equations in a context.
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