Mathematics Cumulative Progress Indicators (CPIs) for the end of the designated grade span

Place a "+" for an expectation that represents a strength & a "-" for a weakness

+ or -

STANDARD 4.3     (PATTERNS AND ALGEBRA)     ALL STUDENTS WILL REPRESENT AND ANALYZE RELATIONSHIPS AMONG VARIABLE QUANTITIES  AND SOLVE PROBLEMS INVOLVING PATTERNS, FUNCTIONS, AND ALGEBRAIC CONCEPTS AND PROCESSES.

C.     Modeling

By the end of Grade 2, students will:

 1.    Recognize and describe changes over time (e.g., temperature, height).

 2.    Construct and solve simple open sentences involving addition or subtraction.

·        Result unknown (e.g., 6 – 2  = __  or  n = 3 + 5)

·        Part unknown (e.g., 3 + ÿ = 8)

Building upon knowledge and skills gained in preceding grades, by the end of Grade 3, students will:

 1.         Recognize and describe change in quantities.

·        Graphs representing change over time (e.g., temperature, height)

2.         Construct and solve simple open sentences involving addition or subtraction (e.g., 3 + 6 = __,  n = 15 – 3,  3 + __ = 3,  16 – c = 7).

Building upon knowledge and skills gained in preceding grades, by the end of Grade 4, students will:

 1.         Recognize and describe change in quantities.

·        Graphs representing change over time (e.g., temperature, height)

·        How change in one physical quantity can produce a corresponding change in another (e.g., pitch of a sound depends on the rate of vibration)

 2.         Construct and solve simple open sentences involving any one operation (e.g., 3 x 6 = __, n = 15 ¸ 3,  3 x __ = 0,  16 – c = 7).

Building upon knowledge and skills gained in preceding grades, by the end of Grade 5, students will:

 1.         Use number sentences to model situations.

·        Using variables to represent unknown quantities

·        Using concrete materials, tables, graphs, verbal rules, algebraic expressions/equations

 2.         Draw freehand sketches of graphs that model real phenomena and use such graphs to predict and interpret events.

·        Changes over time

·        Rates of change (e.g., when is plant growing slowly/rapidly, when is temperature dropping most rapidly/slowly)

Building upon knowledge and skills gained in preceding grades, by the end of Grade 6, students will:

 1.         Use patterns, relations, and linear functions to model situations.

·        Using variables to represent unknown quantities

·        Using concrete materials, tables, graphs, verbal rules, algebraic expressions/equations/inequalities

 2.         Draw freehand sketches of graphs that model real phenomena and use such graphs to predict and interpret events.

·        Changes over time

·        Relations between quantities

·        Rates of change (e.g., when is plant growing slowly/rapidly, when is temperature dropping most rapidly/slowly)

Building upon knowledge and skills gained in preceding grades, by the end of Grade 7, students will:

1.      Analyze functional relationships to explain how a change in one quantity can result in a change in another, using pictures, graphs, charts, and equations.

  2.         Use patterns, relations, symbolic algebra, and linear functions to model situations.

·        Using manipulatives, tables, graphs, verbal rules, algebraic expressions/equations/inequalities

·        Growth situations, such as population growth and compound interest, using recursive (e.g., NOW-NEXT) formulas (cf. science standard 5.5 and social studies standard 6.6)

Building upon knowledge and skills gained in preceding grades, by the end of Grade 8, students will:

 1.         Analyze functional relationships to explain how a change in one quantity can result in a change in another, using pictures, graphs, charts, and equations.

 2.         Use patterns, relations, symbolic algebra, and linear functions to model situations.

·        Using concrete materials (manipulatives), tables, graphs, verbal rules, algebraic expressions/equations/inequalities

·        Growth situations, such as population growth and compound interest, using recursive (e.g., NOW-NEXT) formulas (cf. science standard 5.5 and social studies standard 6.6)

Building upon knowledge and skills gained in preceding grades, by the end of Grade 12, students will:

 1.       Use functions to model real-world phenomena and solve problems that involve varying quantities.

·        Linear, quadratic, exponential, periodic (sine and cosine), and step functions (e.g., price of mailing a first-class letter over the past 200 years)

·        Direct and inverse variation

·        Absolute value

·        Expressions, equations and inequalities

·        Same function can model variety of phenomena

·        Growth/decay and change in the natural world

·        Applications in mathematics, biology, and economics (including compound interest)

 2.       Analyze and describe how a change in an independent variable leads to change in a dependent one.

 3.       Convert recursive formulas to linear or exponential functions (e.g., Tower of Hanoi and doubling).