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.

A.     Patterns

By the end of Grade 2, students will:

 1.    Recognize, describe, extend, and create patterns.

·        Using concrete materials (manipulatives), pictures, rhythms, & whole numbers

·        Descriptions using words and symbols (e.g., “add two” or “+ 2”)

·        Repeating patterns

·        Whole number patterns that grow or shrink as a result of repeatedly adding or subtracting a fixed number (e.g., skip counting forward or backward)

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

 1.         Recognize, describe, extend, and create patterns.

·        Descriptions using words and number sentences/expressions

·        Whole number patterns that grow or shrink as a result of repeatedly adding, subtracting, multiplying by, or dividing by a fixed number (e.g., 5, 8, 11, . . . or 800, 400, 200, . . .)

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

 1.         Recognize, describe, extend, and create patterns.

·        Descriptions using words, number sentences/expressions, graphs, tables, variables (e.g., shape, blank, or letter)

·        Sequences that stop or that continue infinitely

·        Whole number patterns that grow or shrink as a result of repeatedly adding, subtracting, multiplying by, or dividing by a fixed number (e.g., 5, 8, 11, . . . or 800, 400, 200, . . .)

·        Sequences can often be extended in more than one way (e.g., the next term after 1, 2, 4, . . . could be 8, or 7, or … )

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

 1.         Recognize, describe, extend, and create patterns involving whole numbers.

·        Descriptions using tables, verbal rules, simple equations, and graphs

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

 1.         Recognize, describe, extend, and create patterns involving whole numbers and rational numbers.

·        Descriptions using tables, verbal rules, simple equations, and graphs

·        Formal iterative formulas (e.g., NEXT = NOW * 3)

·        Recursive patterns, including Pascal’s Triangle (where each entry is the sum of the entries above it) and the Fibonacci Sequence: 1,  1,  2,  3,  5,  8, . . .    (where NEXT = NOW + PREVIOUS)

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

 1.         Recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers.

·        Descriptions using tables, verbal and symbolic rules, graphs, simple equations or expressions

·        Finite and infinite sequences

·        Generating sequences by using calculators to repeatedly apply a formula

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

 1.         Recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers.

·        Descriptions using tables, verbal and symbolic rules, graphs, simple equations or expressions

·        Finite and infinite sequences

·        Arithmetic sequences (i.e., sequences generated by repeated addition of a fixed number, positive or negative)

·        Geometric sequences (i.e., sequences generated by repeated multiplication by a fixed positive ratio, greater than 1 or less than 1)

·        Generating sequences by using calculators to repeatedly apply a formula

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

 1.         Use models and algebraic formulas to represent and analyze sequences and series.

·        Explicit formulas for n^th terms

·        Sums of finite arithmetic series

·        Sums of finite and infinite geometric series

 2.       Develop an informal notion of limit.

 3.       Use inductive reasoning to form generalizations.