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

Standard  M:20 Change and Growth

Introduction: 

Standard M:20 focuses on the conceptual development of the concept of change and linear relationships as an example of a constant rate of change.

Kindergarten

MK: 20   Demonstrates a conceptual understanding of change qualitatively (growth—student growing taller).

First Grade

M1: 20  Demonstrates a conceptual understanding of linear relationships (y = kx) as a constant rate of change qualitatively (growth—student  growing taller)
 and quantitatively (measurable growth—2 inches each year).

Second Grade

M2: 20 Demonstrates a conceptual understanding of linear relationships (y = kx) as a constant rate of change  qualitatively (growth—student growing taller)
and quantitatively (measurable growth—2 inches each year) change.

Third grade

M3: 20 Demonstrates a conceptual understanding of linear relationships (y = kx) as a constant rate of change by identifying, describing, or comparing
           situations that represent constant rates of change.

Fourth Grade

M4: 20 Demonstrates a conceptual understanding of linear relationships (y = kx) as a constant rate of change by identifying, describing, or comparing
  situations that represent constant rates of change.

Fifth grade

M5: 20 Demonstrates a conceptual understanding of linear relationships (y = kx) as a constant rate of change by identifying, describing, or comparing
  situations that represent constant rates of change.

Sixth Grade

M6: 20 Demonstrates 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 describes 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

Seventh Grade

M7: 20 Demonstrates 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 distinguishes between constant and varying rates of change in concrete situations represented in
           tables or graphs; or describes 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

 Eighth Grade

M8: 20 Demonstrates 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; informally and  formally determining slopes and intercepts represented
             in graphs, tables, or problem situations; or describing the meaning of slope and intercept in context; and distinguishes between linear
             relationships (constant rates of change) and nonlinear relationships (varying rates of change) represented in tables, graphs,
             equations, or problem situations; or describes how change in the value of one variable relates to change in the value of a second
             variable in problem situations with constant and varying rates of change.

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