In accordance with the National Council of Teachers of Mathematics Principles and Standards for School Mathematics, the Curriculum Focal Points (NCTM 2000, NCTM 2006) and the Common Core Standards for Mathematics, *Math Trailblazers* students are expected to achieve fluency with the addition and subtraction facts by the end of second grade.

### Developing Math Facts

In Grade 2, students focus on further developing their understanding of addition and subtraction with a yearlong, strategies-based program for developing and maintaining fluency with the addition and subtraction facts. The subtraction facts are studied in the same groups as the addition facts, one group per unit. Students work toward this goal by solving addition and subtraction problems in ways that make sense to them. Students also approach the math facts by systematically developing efficient strategies for the facts that will help them learn other facts. For example, the facts with sums of ten (e.g., 8 + 2 and 6 + 4) can help develop make-ten strategies for solving facts with larger sums (e.g., 8 + 7 and 6 + 8). There is a body of research that supports students working toward math facts fluency in this manner.

Throughout the curriculum, students are encouraged to invent their own strategies and to share their thinking with one another. However, particular emphasis is given to specific reasoning strategies. In second grade, students will sort the addition and subtraction facts by strategy (counting or reasoning) to help them think critically about choosing strategies that are efficient for a given problem. Specifically, students are asked to grapple with moving from less efficient (direct modeling and counting strategies) to more efficient reasoning-from-known-facts strategies. From these discussions, they develop a menu of addition strategies for the facts and a menu of subtraction strategies for the facts.

**Distributed Facts Practice.** Following research recommendations, students study and practice small groups of facts that can be found using similar strategies. See Figure 1 for distributed facts practice in Grade 2.

**Figure 1:** Distributed Facts Practice in Grade 2