CCSSM Standards for Mathematical Practice and NCTM Process Standards

Problem Solving

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

Students who go through the entire problem solving process will meet this standard. Problem solving occurs when the student determines what their method of solving a given problem will be, carries out this method, making any changes as necessary throughout the process, and comes to a conclusion that makes sense in the context of the problem. 

CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.


This standard relates to problem solving in that the student needs to decide which tool would be most helpful and beneficial in solving a problem. Also, with the use of tools comes some kinds of errors which will require the students to use their problem solving skills to decipher, recognize, and fix. Tools can be used to further their understanding of the problem as well.

Reasoning and Proof

CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.

Making sense of the problem is a vital step in finding the solution and this can usually be completely in various ways. The student should recognize that every problem has many methods to reaching the solution and how to choose a method that is best for the situation. This means taking the general problem and reaching a specific conclusion using the evidence found by using methods of reasoning.

CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.

There are many patterns in math and algorithms that can be used to solve math problems that students should be able to identify and apply to appropriate problems. They will use reasoning to relate problems to one another and check to make sure that their answer makes sense. They should also know the reasoning behind the patterns and why the algorithm works to deepen their understanding.

Communication

CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.

Students should be able to create conjectures about a topic using prior knowledge and then dig deeper by looking at evidence to support or reject their claims. An important step in this process is the sharing of ideas with peers or teachers, and allowing them to critique the work. Then, the students will also look at the work of their peers and give their opinions. It is necessary for the students to communicate in a positive and professional way when completing these tasks so that everyone will be most successful.

CCSS.MATH.PRACTICE.MP6 Attend to precision.

Mathematical language is very precise and specific. It is important for students to communicate their answers and ideas using the correct math terminology so that others can understand what they are trying to express. This skill takes practice, so it is vital that students not only get practice in writing mathematical statements but verbally communicating their thoughts as well.

Connections

CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.

As a whole, mathematics have countless connections in content and is continually building off of prior knowledge and skills. Also, many skills have shortcuts that students can discover after much practice. Investigating these shortcuts are great way for students to understand the skills on a deeper level and prepare themselves to move on to the next step in the curriculum.

Representation

CCSS.MATH.PRACTICE.MP4 Model with mathematics.

Utilizing graphs and charts are a real life skill that students should be able to complete. This is important because demonstrating the data that has been found and reaching a conclusion can be difficult to execute without a visual. Models are a way to do so in an organized and systematic manner. Students should also be able to interpret models that have already been created and analyze the results of the representation.