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# National Standards for Grade 4 - Mathematics (page 2)

National Assessment Governing Board
Updated on Mar 14, 2011

### NAEP Mathematics Objectives – Mathematical Content Areas

#### Number Properties and Operations

Number sense is a major expectation of the 2007 NAEP. At fourth grade, students are expected to have a solid grasp of whole numbers, as represented by the decimal system, and to have the beginnings of understanding fractions.

 Grade 4 1) Number sense a) Identify the place value and actual value of digits in whole numbers. b) Represent numbers using models such as base 10 rep­resentations, number lines, and two-dimensional models. c) Compose or decompose whole quantities by place value (e.g., write whole numbers in expanded notation using place value: 342 = 300 + 40 + 2). d) Write or rename whole numbers (e.g., 10: 5 + 5, 12 – 2, 2 x 5). e) Connect model, number word, or number using various models and representations for whole numbers, fractions, and decimals. f) Order or compare whole numbers, decimals, or fractions. 2) Estimation a) Use benchmarks (well-known numbers used as meaningful points for comparison) for whole numbers, decimals, or fractions in contexts (e.g., ½ and .5 may be used as benchmarks for fractions and decimals between 0 and 1.00). b) Make estimates appropriate to a given situation with whole numbers, fractions, or decimals by: • knowing when to estimate, • selecting the appropriate type of estimate, including over­estimate, underestimate, and range of estimate, or • selecting the appropriate method of estimation (e.g., rounding). c) Verify solutions or determine the reasonableness of results in meaningful contexts. 3) Number operations a) Add and subtract: • whole numbers, or • fractions with like denominators, or • decimals through hundredths. b) Multiply whole numbers: • no larger than two-digit by two-digit with paper and pencil computation, or • larger numbers with use of calculator. c) Divide whole numbers: • up to three-digits by one-digit with paper and pencil computation, or • up to five-digits by two-digits with use of calculator. d) Describe the effect of operations on size (whole numbers). e) Interpret whole number operations and the relationships between them. f) Solve application problems involving numbers and operations. 4) Ratios and proportional reasoning a) Use simple ratios to describe problem situations. 5) Properties of number and operations a) Identify odd and even numbers. b) Identify factors of whole numbers. c) Apply basic properties of operations. d) Explain or justify a mathematical concept or relationship (e.g., explain why 15 is an odd number or why 7–3 is not the same as 3–7).