**Problem Solving**

**Instructional programs from prekindergarten through grade 12**

should enable all students to—

- Build new mathematical knowledge through problem solving
- Solve problems that arise in mathematics and in other contexts
- Apply and adapt a variety of appropriate strategies to solve problems
- Monitor and reflect on the process of mathematical problem solving

**Reasoning and Proof**

**Instructional programs from prekindergarten through grade 12 should enable**

all students to—

- Recognize reasoning and proof as fundamental aspects of mathematics
- Make and investigate mathematical conjectures
- Develop and evaluate mathematical arguments and proofs
- Select and use various types of reasoning and methods of proof

**Communication**

**Instructional programs from prekindergarten through grade 12 should enable**

all students to—

- Organize and consolidate their mathematical thinking through communication
- Communicate their mathematical thinking coherently and clearly to peers, teachers, and others
- Analyze and evaluate the mathematical thinking and strategies of others;
- Use the language of mathematics to express mathematical ideas precisely.

**Connections**

**Instructional programs from prekindergarten through grade 12 should enable**

all students to—

- Recognize and use connections among mathematical ideas
- Understand how mathematical ideas interconnect and build on one another to produce a coherent whole
- Recognize and apply mathematics in contexts outside of mathematics

**Representation**

**Instructional programs from prekindergarten through grade 12 should enable**

all students to—

- Create and use representations to organize, record, and communicate mathematical ideas
- Select, apply, and translate among mathematical representations to solve problems

- Use representations to model and interpret physical, social, and mathematical phenomena