NCTM Mathematics Curriculum Standards for Grades K-4
Standard 1 
Mathematics as Problem Solving
Standard 2 
Mathematics as Communication 
Standard 3 
Mathematics as Reasoning 
Standard 13 
Patterns and Relationships 

Standard 1: Mathematics as Problem Solving 

In grades K-4, the study of mathematics should emphasize problem solving so that students can: 

1) use problem-solving approaches to investigate and understand mathematical content; 
2) formulate problems from everyday and mathematical situations; 
3) develop and apply strategies to solve a wide variety of problems; 
4) verify and interpret results with respect to the original problem; 
5) acquire confidence in using mathematics meaningfully. 

Standard 2: Mathematics as Communication 

In grades K-4, the study of mathematics should include numerous opportunities for communication so that students can: 

1)  relate physical materials, pictures, and diagrams to mathematical ideas; 
2) reflect on and clarify their thinking about mathematical ideas and situations; 
3) relate their everyday language to mathematical language and symbols; 
4) realize that representing, discussing, reading, writing, and listening to mathematics are a vital part of learning and using mathematics. 

Standard 3: Mathematics as Reasoning 

In grades K-4, the study of mathematics should emphasize reasoning so that students can: 

1) draw logical conclusions about mathematics; 
2) use models, known facts, properties, and relationships to explain their thinking; 
3) justify their answers and solution processes; 
4) use patterns and relationships to analyze mathematical situations; 
5) believe that mathematics makes sense. 

Standard 13: Patterns and Relationships 

In grades K-4, the mathematics curriculum should include the study of patterns and relationships so that students can: 

1) recognize, describe, extend, and create a wide variety of patterns; 
2) represent and describe mathematical relationships; 
3) explore the use of variables and open sentences to express relationships.