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Algebraic Thinking

Chapter 12

Algebra

•Study of patterns and relationships

•Way of thinking

•An art—characterized by order and internalconsistency

•Language that uses carefully defined termsand symbols

•Tool

Algebra

•Traditionally students don’t begin Algebrauntil they have a solid foundation inarithmetic, unfortunately students who didn’tdo well in math were not offered theopportunity to study Algebra

•NCTM standards infused Algebra into allelementary grades in an effort to producebetter problem solvers

NCTM standards for Algebra K-5(see pg 311)

•Algebra

•Instructional programs from prekindergarten through grade 12should enable all students to—

•Understand patterns, relations, and functions

•Represent and analyze mathematical situations and structures using algebraic symbols

•Use mathematical models to represent and understand quantitative relationships

•Analyze change in various contexts

•Understand patterns, relations, and functions

•Pre-K–2 Expectations: In pre-K through grade 2 all students should–

•sort, classify, and order objects by size, number, and other properties;

•recognize, describe, and extend patterns such as sequences of sounds and shapes or simplenumeric patterns and translate from one representation to another;

•analyze how both repeating and growing patterns are generated.

•Grades 3–5 Expectations: In grades 3–5 all students should–

•describe, extend, and make generalizations about geometric and numeric patterns;

•represent and analyze patterns and functions, using words, tables, and graphs.