This page describes the required fluencies for each grade. In the Common Core State Standards for Grades K-6, there are specific content standards that set expectations for fluency in computation. These standards are culminations of learning progressions that often span several grades, involving conceptual understanding, thoughtful practice, and extra support as necessary. The word "fluent" is used in the standards to mean “reasonably fast and accurate” and the ability to use certain facts and procedures with enough facility that using them does not slow down or derail the problem solver as (s)he works on more complex problems. These fluencies are learned through the use of numbers in different situations. Procedural fluency requires skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.

Developing fluency in each grade may involve a combination “just knowing” some answers, knowing some answers from patterns, and knowing some answers using strategies. There are opportunities to practice fluency and procedural skill in all lessons, particularly those lessons called "Fluency and Procedural Skill lessons", which specifically target fluency and procedural skills. Links to the units in which fluencies are primarily addressed are provided below. Specific information about how the fluency is supported and addressed in the context of the unit can be found on individual unit pages.

Fluency Standard |
Grade |
Unit(s) |

K.OA.A.5 |
K | 16* |

1.OA.C.6 |
1 | 1, 6, 9, 14, 18 |

2.NBT.B.5 |
2 | 1, 15 |

2.OA.B.2 |
2 | 1, 15 |

3.NBT.A.2 |
3 | 3, 15 |

3.OA.C.7 |
3 | 1, 7, 15 |

4.NBT.B.4 |
4 | 4, 8, 14 |

5.NBT.B.5 |
5 | 2, 15 |

6.NS.B.2 |
6 | 3 |

6.NS.B.3 |
6 | 2, 3, 5 |

**K.OA.A.5 Fluently add and subtract within 5. **

By the end of the school year, Kindergarten students are expected to add and subtract fluently within 5. This work begins with recognizing that a collection of objects is composed of two subcollections and quickly combining their cardinalities to find the cardinality of the collection (e.g., seeing a set as two subsets of cardinality 2 and saying “four”). Experience with decompositions of numbers and with "Add To" and "Take From" situations enables students to begin to fluently add and subtract within 5. Students work with decomposing numbers throughout the year, solving addition and subtraction word problems within 10 in Units 6 and 10. Adding and subtracting within 10 will continue in Grade 1. Students finalize the work of adding and subtracting within 5 with the goal of demonstrating fluency by the end of their Kindergarten year. (Unit 16)

**1.OA.C.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12 one knows that 12 - 4 = 8); creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). **

As Grade 1 students extend the range of problem types and subtypes they can solve, they also extend the range of numbers used. Students use conceptual subitizing and decomposition to add and subtract small numbers within 20, with a goal of demonstrating fluency within 10 by the end of the grade. While this standard will be finalized in Unit 14, students have opportunities to practice and develop proficiency throughout the year. (Units 1, 6, 9, 14, 18)

**2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. **

Students have multiple opportunities during Grade 2 to apply the strategies for addition and subtraction developed in prior grades to larger numbers and develop more sophisticated computational strategies. As students add ones to ones, and tens to tens, they implicitly employ a general method based on place value and the associative and commutative properties of addition. While this standard will be finalized in Unit 15, students have opportunities to practice and develop proficiency throughout the year. (Units 1,15)

**2.OA.B.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.**

After students have had extensive experiences with addition and subtraction in Kindergarten and Grade 1, they become fluent in single-digit additions and the related subtractions using mental strategies, such as “Counting On” and “Convert to an Easier Problem.” As students work on problem solving strategies involving all of the problem types in Table 1 in the CCSSM throughout the course of Grade 2, they develop automaticity for addition and subtraction within 20. While this standard will be finalized in Unit 15, students have opportunities to practice and develop proficiency throughout the year. (Units 1,15)

**3.NBT.A.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. **

Building on fluency from Grade 2 in adding and subtracting within 100, third graders achieve fluency within 1000 with strategies and algorithms that are based on place value, properties of operations, and/or the relationship between addition and subtraction. For example, students may choose to subtract 384-102 by their place values (hundreds, tens, ones) or they may choose to decompose the 102 into 100 and 2, subtracting 384-100 to get 284, then subtracting the remaining 2 to get a difference of 282. Another appropriate strategy would be to think "addition to" for the equation 102 + ? = 384 then solve for the unknown. While this standard will be finalized in Unit 15, students have opportunities to practice and develop proficiency throughout the year. (Units 3, 15)

**3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.**

Understanding single-digit multiplications and related divisions precedes developing fluency with them, and both can be time intensive as there are no general strategies for multiplying or dividing all single-digit numbers like there are for addition and subtraction. There are, however, many patterns and strategies dependent upon specific numbers. One example is when we multiply by four, we can first use a double, then double that result (e.g., 7 × 4 = ?; 7 × 2 = 14; 14 × 2 = 28, so 7 × 4 = 28 ). Another example for multiplying by four would be to multiply by five and then subtract the factor that is not the five-factor (e.g., 6 × 4 = ?; 6 × 5 = 30; 30 - 6 = 24, so 6 × 4 = 24). For this reason, it is critical for student understanding to dedicate extra time and support to students as needed. While this standard will be finalized in Unit 15, students have opportunities to practice and develop proficiency throughout the year. (Units 1, 7, 15)

**4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm. **

The algorithms for addition and subtraction rely on adding or subtracting like base-ten units (ones with ones, tens with tens, hundreds with hundreds, etc.) and composing or decomposing base-ten units as needed, such as composing 10 ones to make one ten or decomposing one hundred to make 10 tens. In mathematics, an algorithm is defined by its steps and not by the way those steps are recorded in writing. With this in mind, minor variations in methods of recording standard algorithms are acceptable. While this standard will be finalized in Unit 14, students have opportunities to practice and develop proficiency throughout the year. (Units 4, 8, 14)

**5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm. **

After students have had extensive experiences with multiplication in Grade 3 and Grade 4, they reach fluency in multiplication using the standard algorithm by the end of the year. The properties of operations and the base-ten system, concepts that students have been developing since Kindergarten, provide the foundation for for the multiplication algorithm. While this standard will be finalized in Unit 15, students have opportunities to practice and develop proficiency throughout the year. (Units 2, 15)

**6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm. **

After students have had extensive experiences with multiplication and division in Grades 3, 4, and 5, they reach fluency with division using the standard algorithm by the end of the year. Underlying the division algorithm are the properties of operations and the base-ten system. While this standard will be finalized in Unit 3, students have opportunities to further practice and develop the skill throughout the year. (Unit 3)

**6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. **

Students consolidate their work from earlier grades on operations with whole numbers and decimals by becoming fluent in the four operations on decimal numbers. Through this work, they solidify their growing understanding that whole numbers, decimals, and fractions are part of the same number system, not different number systems, and that this concept can represented by the number line. (Units 2, 3, 5)