In the *Math Trailblazers* classroom, one-hour every day is devoted to mathematics. The culture in a *Math Trailblazers* classroom is one that:

- Embodies problem-based learning
- Allows time for students to reason mathematically
- Provides opportunities for students to freely discuss mathematical understandings
- Requires that students explain how they solve problems
- Lets students be responsible for their own learning.
- Sets clear expectations
- Provides frequent formative assessment and feedback
- Teaches students to work like real mathematicians
- Creates a flexible and dynamic classroom environment
- Allows opportunities for further exploration of a topic

Mathematical content is connected to mathematical practices by planning lessons that include meaningful, challenging tasks or problems. The lessons and tasks that *Math Trailblazers* students are involved in:

- Build mathematical proficiency
- Challenge and enrich student thinking
- Develop mathematical vocabulary related to the ideas and concepts
- Promote the ability to learn multiple ways of thinking about and representing mathematical ideas (pictures, diagrams, concrete models, numeric/symbolic)

– NCSM Great Tasks for Mathematics K–5 (Shrock, Norris, Pualee, Seitz, & Hollingshead) 2013

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*Math Trailblazers* lessons focus on building mathematical proficiency by challenging students to become actively engaged with the work of problem solving. Students have access to an understanding of the vocabulary necessary to ask meaningful questions, clarify their thinking, explain and justify their understanding, and critique the thinking of others. The lesson tasks promote multiple solution strategies as well as multiple entry points into a problem. Students should develop greater fluency with the mathematics they know as they deepen their understanding of concepts and skills. *Math Trailblazers* lessons provide opportunities for students to make connections as they build new understandings and talk to others about their thinking. See lead author Jennifer Leimberer’s webinar on developing flexible computation strategies for more information.

The role of the *Math Trailblazers* teacher is to plan lessons that:

- Develop fluency with procedures
- Enable students to deepen their understanding of concepts and make connections among various topics
- Encourage students to use written or oral skills to explain what they know and to justify their thinking