Search the California Content Standards

Cluster:
Generalize place value understanding for multi-digit whole numbers.

Standard:
Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Cluster:
Generalize place value understanding for multi-digit whole numbers.

Standard:
Use place value understanding to round multi-digit whole numbers to any place.

Cluster:
Use place value understanding and properties of operations to perform multi-digit arithmetic.

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

Cluster:
Use place value understanding and properties of operations to perform multi-digit arithmetic.

Standard:
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Cluster:
Use place value understanding and properties of operations to perform multi-digit arithmetic.

Standard:
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Cluster:
Extend understanding of fraction equivalence and ordering.

Standard:
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Footnote:
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Cluster:
Extend understanding of fraction equivalence and ordering.

Standard:
Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Cluster:
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Standard:
Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Cluster:
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Standard:
Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

Cluster:
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Standard:
Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.