Mathematics Curriculum Framework
November 2000

## Learning Standards by Strand

### Number Sense and Operations 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

#### Learning Standards

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

• 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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