In accordance with the Principles and Standards for School Mathematics (NCTM, 2000), the Curriculum Focal Points (NCTM, 2006), and the Common Core Standards for Mathematics (Council of Chief State School Officers, 2010), *Math Trailblazers* students are expected to achieve fluency with the addition and subtraction facts by the end of second grade. They work toward this goal in Grade 1 by solving addition and subtraction problems in ways that make sense to them. Students focus on developing fluency with the addition facts with sums to ten first, as fluency with these facts will help students develop strategies for the facts with larger sums. This use of meaningful strategies enables students to understand the operations, while at the same time developing fluency with the math facts.

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### Developing Math Facts

Initial work with math facts in first grade involves working with strategies in the context of counting and problem solving. The first strategy students explore is counting on. As children learn to count, they usually start at one and count all the objects. The shift from needing to count from one to counting on from a larger number is an important step in children’s development. For example, to add five and two, students need to hold five in their head as a set and then count on two more until they reach seven. This ability comes more easily to some children. Some may need to spend more time on the counting-all strategy before moving to the more efficient counting-on method for addition facts and problem solving.

**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 1.

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