# Common Core State Standards Math: Ways to Implement Reasoning Abstractly and Quantitatively

The Common Core State Standards Math have been designed to strengthen mathematics instruction in the United States through rigor and deep understanding. They include a series of practice standards that are present in every grade and work in conjunction with content standards. Unlike the content standards that emphasize what students will learn, the practice standards determine how they will demonstrate their mathematical knowledge.

As part of the mathematical practice standards, students are expected to reason abstractly and quantitatively. This skill requires students be able to decontextualize a situation and then construct another way to represent it. Students must also be able create a representation of the problem using symbols, numbers, or diagrams while attending to units, meaning of quantities, and operations. These mathematical practice standards may seem abstract without concrete examples from classrooms. It is important to find meaningful ways to implement these practice standards into classroom instruction because they’re found in the Common Core State Standards math at each grade level.

• Second Grade Becoming fluent with math facts and using these basic skills to solve multi-step addition problems is an important second grade skill in the Common Core State Standards Math. Deconstructing addition scenarios and applying them to compose a number sentence shows the ability to reason quantitatively. A teacher may ask students to write an addition scenario for a classmate to complete with determined values. For example, “Write an addition scenario using three addends that equal 100.” Students then trade scenarios to solve.
• Fourth Grade Students are asked to reason quantitatively when finding all factor pairs for a whole number less than 100. For example, a teacher may assign groups of students numbers and they must represent all the factor pairs. The groups may decide the way in which they find and represent the pairs including using arrays, manipulatives, or number sentences. The method of displaying the knowledge isn’t as important as their ability to deconstruct the number and represent it with factors

Since DreamBox Learning is aligned with the Common Core State Standards Math teachers can find aligned activities to use as additional practice for struggling students. There are two different activities, “Identifying Common Multiples” and “Identifying Factors”, that are relevant to this fourth grade lesson. The DreamBox activities provide students with another opportunity for practice and an additional mode of learning.

• Fifth Grade Fifth grade students are expected to understand the place value system and apply this knowledge to the rounding of decimals. It is important for students to be able to do more than simply apply an algorithm for rounding. If a teacher asks students to round 13.256 to the nearest tenth, the student must be able to first identify which digit is in the tenth place and the two numbers that could possibly be the answer (13.2 or 13.3). Then the student must apply quantitative reasoning to complete the rounding. This requires students to deeply understand the meaning of the original number and its characteristics.

How else can students practice reasoning abstractly and quantitatively?