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Operations & Algebraic Thinking

Understand addition, and understand subtraction


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 Kindergarten, children build an understanding of operating with numbers from the diverse and complex tasks they have experienced. The tasks and the students’ own meanings for “number” give students the foundation upon which they can build initial understandings for addition and subtraction. The child’s past experience will also impact the complexity of the problems they will be able to solve in subsequent grades. Students can solve “put-together” and “take-away” problems using various strategies. Students should be exposed to numerous modeling situations, as well as different counting strategies, such as “counting on” and “counting back.” These will make more sense to the students if they arise from real situations. Kindergarten students can solve for “missing-addend” problems, as well as “making equal” situations to help convey the idea of subtraction. Students can be given two sets of objects that are unequal and asked to make the sets equal to illustrate “taking away” from one set and “putting together” with another set.

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.