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MATHEMATICS – Reason Abstractly & Quantitatively


by Mrs. Jessican Mangini

The Common Core State Standards in 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. Each month, I will be explaining a standard in detail.

To refresh, here are the 8 Standards for Mathematical Practice:

  1. Make sense of problems and persevere in solving them
  2. Reason abstractly and quantitatively
  3. Construct viable arguments and critique the reasoning of others
  4. Model with mathematics
  5. Use appropriate tools strategically
  6. Attend to precision
  7. Look for and make use of structure
  8. Look for and express regularity in repeated reasoning

Standard 2- Reason abstractly and quantitatively

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. For example, becoming fluent with math facts and using these basic skills to solve multi- step problems is an important lower grades skill in the Connecticut Core State Standards Math. Deconstructing addition scenarios and applying them to compose a number sentence shows the ability to reason quantitatively. Teachers 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.

In the upper grades, teachers ask his/her students to reflect on what each number in a fraction represents as parts of a whole. They will also ask his/her students to discuss different sample operational strategies for a patterning problem, evaluating which is the most efficient and accurate means of finding a solution. In this standard, students think: I can use numbers and words to help me make sense of problems.”

Further, students are asked to reason quantitatively when finding all factor pairs for a whole number less than 100. For example, teachers assign students numbers and they must represent all the factor pairs. The students then decide ways 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.

Teachers who are developing students’ capacity to “reason abstractly and quantitatively” help their learners understand the relationships between problem scenarios and mathematical representation, as well as how the symbols represent strategies for solution.

When helping your child complete homework here are some great questions you ask them to tap into this mathematical practice:

  • What does the number ___ represent in the problem?
  • How can you represent the problem with symbols and numbers?
  • Create a representation of the problem


November 2015 Tiger Times