**Grade K**

Numbers represent quantity.

Addition and subtraction equations.

Description of 2-D and 3-D shapes.

Fluency Goal

- Add and subtract within 5

**Grade 1**

Strategies to develop addition and subtraction within 20

Links between addition and subtraction and counting, number line, construction and destruction

Understanding of length and its units

Composition of plane and solid figures

Fluency Goals

- 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 = 10 + 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 12 – 8 = 4); and
- creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

**Grade 2**

Understanding of Base ten notation and place value

Counting by 5’s, 10’s, 100’s

Use of tools to measure and the understanding of standard units of measure

Analyze shapes by their sides and angles

Use building and drawing as a foundation for understanding area, volume, congruence, similarity, and symmetry in later grades

Fluency Goals

- Fluently add and subtract within 20 using mental strategies.
- By end of Grade 2, know from memory all sums of two one-digit numbers.
- Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

**Grade 3**

Students understand the relationship between multiplication and division

Develop understanding of fractions as a part relative to a whole

Area is an attribute of 2-D regions, and the connection of rectangular area to multiplication

Students relate fraction work to geometry by expressing the area of part of a shape as a unit fraction of the whole

Fluency Goals

- 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.
- 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.

**Grade 4**

Multiplication procedures work, based on place value and properties of operations and use them to solve problems.

Different fractions can be equivalent

Fractions are a composition of unit fractions

Shapes can be classified by properties of their lines and angles

Fluency goals

- Fluently add and subtract multi-digit whole numbers using the standard algorithm.

**Grade 5**

Fractions are the division of numbers

Explain why the procedure for multiplication and division of fractions makes sense

Place value systems relation to computational methods

Multiplication as scaling

Volume of solid objects can be calculated and is additive

Fluency Goals

- Fluently multiply multi-digit whole numbers using the standard algorithm.

**Fluencies**

Students must learn to perform calculations and solve
problems both quickly and accurately. At each grade level in the Standards, one or two fluencies are
expected:

** Grade ** | ** Fluency** |

Kindergarten | add/subtract within 5 |

Grade 1 | add/subtract within 10 |

Grade 2 | add/subract within 20 add/subract within 100 (pencil and paper) |

Grade 3 | Multiply and Divide within 100 add/subtract within 1000 |

Grade 4 | add/subtract within 1,000,000 |

Grade 5 | Multi-digit multiplication |

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