# Math Framework

To learn more about how to use the Math Framework, watch this short video.

**Guiding Principles of Mathematics Instruction:**

- Mathematical proficiency is defined by conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition (National Research Council, 2001).
- Mathematical proficiency drives independent thinking, reasoning, and problem-solving.
- Mathematical proficiency is the foundation for careers in science, technology, engineering and mathematics (STEM), and it is increasingly becoming the foundation for careers outside of STEM (NCTM, 2018)
- Effective mathematics teaching “engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically” (NCTM, 2014).
- Standards-based instruction accelerates student gains.
- Students construct mathematical knowledge through exploration, discussion, and reflection.
- Teachers are facilitators of student learning, as they engage students in rich tasks. Administrators are change agents and have the power to create and to support a culture of mathematical proficiency.

Standard | Grade | Area/Subject | Description |
---|---|---|---|

2.NS.5 |
2 |
Number Sense |
Determine whether a group of objects (up to 20) has an odd or even number of members (e.g., by placing that number of objects in two groups of the same size and recognizing that for even numbers no object will be left over and for odd numbers one object will be left over, or by pairing objects or counting them by 2s). |

2.NS.6 |
2 |
Number Sense |
Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones (e.g., 706 equals 7 hundreds, 0 tens, and 6 ones). Understand that 100 can be thought of as a group of ten tens - called a “hundred.” Understand that the numbers 100, 200, 200, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). |

2.NS.7 |
2 |
Number Sense |
Use place value understanding to compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. |

3.AT.1 |
3 |
Computation, Algebra, and Functions |
Solve real-world problems involving addition and subtraction of whole numbers within 1000 (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). |

3.AT.2 |
3 |
Computation, Algebra, and Functions |
Solve real-world problems involving whole number multiplication and division within 100 in situations involving equal groups, arrays, and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). |

3.AT.3 |
3 |
Computation, Algebra, and Functions |
Solve two-step real-world problems using the four operations of addition, subtraction, multiplication and division (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). |

3.AT.4 |
3 |
Computation, Algebra, and Functions |
Interpret a multiplication equation as equal groups (e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each). Represent verbal statements of equal groups as multiplication equations. |

3.AT.5 |
3 |
Computation, Algebra, and Functions |
Determine the unknown whole number in a multiplication or division equation relating three whole numbers. |

3.AT.6 |
3 |
Computation, Algebra, and Functions |
Create, extend, and give an appropriate rule for number patterns within 100 (including patterns in the addition table or multiplication table). |

3.C.1 |
3 |
Computation, Algebra, and Functions |
Fluently add and subtract whole numbers within 1000 using strategies and algorithms based on place value, properties of operations, and relationships between addition and subtraction. |

3.C.2 |
3 |
Computation, Algebra, and Functions |
Represent the concept of multiplication of whole numbers with the following models: equal-sized groups, arrays, area models, and equal "jumps" on a number line. Understand the properties of 0 and 1 in multiplication. |

3.C.3 |
3 |
Computation, Algebra, and Functions |
Represent the concept of division of whole numbers with the following models: partitioning, sharing, and an inverse of multiplication. Understand the properties of 0 and 1 in division. |

3.C.4 |
3 |
Computation, Algebra, and Functions |
Interpret whole-number quotients of whole numbers (e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each). |

3.C.5 |
3 |
Computation, Algebra, and Functions |
Multiply and divide within 100 using strategies, such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8), or properties of operations. |

3.C.6 |
3 |
Computation, Algebra, and Functions |
Demonstrate fluency with mastery of multiplication facts and corresponding division facts of 0 to 10. |