Joshua MarksAptos, Alabama, US,

September 21, 2007

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Grades 3-4 - Number Sense and Operations

- Mathematics > General

- Grade 3
- Grade 4
- Grade 5

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Mathematics Curriculum Framework

November 2000## Learning Standards by Strand

### Number Sense and Operations

for Grades 3-4

#### Learning Standards

Students engage in problem solving, communicating, reasoning, connecting, and representing as they:

Although this standard is appropriate as stated for this grade span, the state assessment program as the 3-4 grade span will test multiplication of only up to two digits by two digits at the present time.

#### Exploratory Concepts and Skills

November 2000

for Grades 3-4

Understand numbers, ways of representing numbers, relationships among numbers, and number systems | |

Understand meanings of operations and how they relate to one another | |

Compute fluently and make reasonable estimates |

4.N.1 | Exhibit an understanding of the base ten number system by reading, modeling, writing, and interpreting whole numbers to at least 100,000; demonstrating an understanding of the values of the digits; and comparing and ordering the numbers. |

4.N.2 | Represent, order, and compare large numbers (to at least 100,000) using various forms, including expanded notation, e.g., 853 = 8 x 100 + 5 x 10 + 3. |

4.N.3 | Demonstrate an understanding of fractions as parts of unit wholes, as parts of a collection, and as locations on the number line. |

4.N.4 | Select, use, and explain models to relate common fractions and mixed numbers (1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10, 1/12, and 1-1/2), find equivalent fractions, mixed numbers, and decimals, and order fractions. |

4.N.5 | Identify and generate equivalent forms of common decimals and fractions less than one whole (halves, quarters, fifths, and tenths). |

4.N.6 | Exhibit an understanding of the base ten number system by reading, naming, and writing decimals between 0 and 1 up to the hundredths. |

4.N.7 | Recognize classes (in particular, odds, evens; factors or multiples of a given number; and squares) to which a number may belong, and identify the numbers in those classes. Use these in the solution of problems. |

4.N.8 | Select, use, and explain various meanings and models of multiplication and division of whole numbers. Understand and use the inverse relationship between the two operations. |

4.N.9 | Select, use, and explain the commutative, associative, and identity properties of operations on whole numbers in problem situations, e.g., 37 x 46 = 46 x 37, (5 x 7) x 2 = 5 x (7 x 2). |

4.N.10 | Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those involving money. |

4.N.11 | Know multiplication facts through 12 x 12 and related division facts. Use these facts to solve related multiplication problems and compute related problems, e.g., 3 x 5 is related to 30 x 50, 300 x 5, and 30 x 500. |

4.N.12 | *Add and subtract (up to five-digit numbers) and multiply (up to three digits by two digits) accurately and efficiently. |

4.N.13 | Divide up to a three-digit whole number with a single-digit divisor (with or without remainders) accurately and efficiently. Interpret any remainders. |

4.N.14 | Demonstrate in the classroom an understanding of and the ability to use the conventional algorithms for addition and subtraction (up to five-digit numbers), and multiplication (up to three digits by two digits). |

4.N.15 | Demonstrate in the classroom an understanding of and the ability to use the conventional algorithm for division of up to a three-digit whole number with a single-digit divisor (with or without remainders). |

4.N.16 | Round whole numbers through 100,000 to the nearest 10, 100, 1000, 10,000, and 100,000. |

4.N.17 | Select and use a variety of strategies (e.g., front-end, rounding, and regrouping) to estimate quantities, measures, and the results of whole-number computations up to three-digit whole numbers and amounts of money to $1000, and to judge the reasonableness of the answer. |

4.N.18 | Use concrete objects and visual models to add and subtract common fractions. |

- Extend multiplication and division to larger-digit numbers.
- Use models to explore multiplication and division with fractions (to twelfths) and decimals.
- Investigate number theory concepts, e.g., prime and composite numbers.
- Investigate the concept of ratio, e.g., the number of students to the number of teachers.
- Use concrete objects and visual models to add and subtract common decimals.
- Explore numbers less than zero by extending the number line and by using familiar applications such as temperature.
- Use concrete objects and visual models to add and subtract common decimals.
- Investigate the distributive property of multiplication over addition for single-digit multipliers, e.g., 7 x 15 is equivalent to 7 x (10 + 5) is equivalent to 7 x 10 + 7 x 5.

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