# Operations & Algebraic Thinking

#### Represent and solve problems involving addition and subtraction

#### Add and subtract within 20

#### Work with equal groups of objects to gain foundations for multiplication

The Operations and Algebraic Thinking Standards emphasize 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 second grade, students need to explore and model relationships using language and notation that are meaningful for them. Students need to see different relationships and make generalizations from their experiences with numbers. Students can model the same quantity in different ways. This helps to deepen their understanding of the concept of number.

Children in second grade build on their understanding of addition and their fluency of addition and subtraction within 10 to develop quick recall of those addition and subtraction facts. They extend this fluency to adding and subtracting within 20 and adding and subtracting within 100 using a paper and pencil. Students are now beginning to solve problems that involve modeling addition and subtraction, place value, and even the Commutative and Associative Properties of Addition. Students should develop strategies to add and subtract multi-digit numbers. They need to be engaged in conversations that lead them to develop and select the most efficient strategies. They should be able to explain why their strategy works. Children in second grade also need to have experiences with estimation on a regular basis so they can begin to estimate sums and differences.

In second grade, pattern development with skip counting builds the foundation upon which multiplication will be developed in third grade. Skip counting using different numbers, as well as using a hundred chart, reveals numerous patterns that students will easily recognize and be able to talk about. How students use the hundred chart will reveal students’ understanding of counting patterns.

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.