Mathematical Practice 1

The Mathematical Practice 1 of the Common Core State Standards(CCSS) is that mathematically ProFicient students are able tomake sense of problems and persevere in solving them.This practice, including the other seven mathematical practices, is taught to students from kindergarten to twelve grade.

Development

The mathematical practices are adapted from the five process standards of the National Council of Teachers of Mathematics (NCTM) and the five strands of proficiency in the U.S. National Research Council's Adding It Up report. The mathematical practice 1 is the first of the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections.

Description

CCSS.MATH.PRACTICE.MP1: Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures AbOUT the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their ProgresS and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

Example of Mathematical Practice

Sample Problem: What is the best method to solve this system of equation? y = 3/2x - 2 and y = 3x + 1

MP.1: Mathematically proficient students first identify the problem which is to determine which one of the different methods to solve systems of equations is the best for the given system. Next, they identify the different methods to solve systems of equations instead of simply attempting to solve the system. Looking at the system, students may notice that the equations are already in slope-intercept form therefore determine the graphing method works best. Although the answer is not clear initially, students are able to persevere through solving this problem.

Full List of the Mathematical Practices

The CCSS mandates that varieties of expertise of mathematical practice to be taught:

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.