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Operations & Algebraic Thinking

Represent and solve problems involving addition and subtraction


Understand and apply properties of operations and the relationship between addition and subtraction


Add and subtract within 20


Work with addition and subtraction equations


The Operations and Algebraic Thinking Standards emphasizes relationships among quantities, including functions, patterns, ways of representing mathematical relationships, and the analysis of change. Algebra is best learned as a set of concepts and techniques tied to the representation of quantitative relations. It is a style of mathematical thinking for formalizing patterns, functions, and generalizations. Although many adults think that algebra is an area of mathematics more suited to middle school or high school students, even young children can be encouraged to use algebraic reasoning as they study numbers and operations and as they investigate patterns and relations among sets of numbers. In these standards, the connections of algebra to numbers and everyday situations are extended in the later grade bands to include geometric ideas.

In first grade, children continue building upon their previous experience with addition and subtraction to include problem solving. They begin to have a fuller understanding of the equal sign, as well as the plus sign and the minus sign, and what these mean in both a real-life context as well as the abstract. Through working with sets of objects, students begin to understand the ideas of the Commutative Property of Addition and the Associative Property of Addition. Students also relate subtraction as the inverse of addition – the unknown addend problem. Children further develop their fluency with basic math facts and working with fact families.

This continuum contains Counting and Cardinality standards for K, Number and Operations and Algebraic Thinking standards K-3, Number and Operations in Base Ten standards K-3, Number and Operations – Fractions standards for grade 3.