Develop a Deep and Flexible Conceptual Understanding 

Students will explore and begin to apply number relationships as they develop number sense.  As first graders are involved in meaningful practice with numbers and manipulatives, they see numbers in a more flexible way, which leads them to become fluent in addition and subtraction. A rich understanding of numbers involves using a variety of tools as they make connections with patterns, shapes, data, and measurement.

Students will demonstrate procedural fluency when they apply strategies and procedures to solve problems, first conceptually and then by more efficient means. First graders connect various meanings and relationships of numbers related to addition, subtraction, and measurement.

Students will develop strategies for problem-solving when they engage in problem-based learning involving real-world mathematical situations.  Students are able to develop a strategy based on using a variety of learning tools. They apply their selected strategy to engage in the problem-solving process.

Students will engage with mathematical reasoning by explaining the reasonableness of their solutions and analyzing the solutions of their peers. Students are able to discuss their thinking and strategies about the mathematical processes involved in finding their solutions. 

Students will begin to see numbers as an essential skill that helps them understand and persevere to solve problems in the world around them. Students begin to see relationships in numbers and develop a natural curiosity for numbers and patterns. Students are encouraged to participate in the iterative process of mathematics, in that they try, modify, or generalize strategies until their answers make sense.

Develop the Ability to Make Conjectures, Model, and Generalize 

Students will develop strategies to understand number patterns and relationships by making predictions and drawing conclusions to solve everyday problems. Students use various learning tools (pictures, manipulatives, symbols, graphs, etc.) to make sense of problems through the exploration and application of those strategies. Students are encouraged to create models explaining why their methods work and make sense. They generalize their knowledge by using known strategies to apply to unknown mathematics. 

Students will begin to expand their vocabulary with math-specific language to describe the world around them.  Communication becomes the basis of the student’s exploration, solidifying their ideas through cooperative and meaningful conversations that occur when students have the opportunity to listen, question, and respond appropriately through peer interactions.