Mathematics Standards
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Linear, Quadratic, and Exponential Models
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Measurement and Data
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Number and Operations—Fractions
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Operations and Algebraic Thinking
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Similarity, Right Triangles, and Trigonometry
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Showing 71 - 80 of 159 Standards
Standard Identifier: 4.NF.1
Grade:
4
Domain:
Number and Operations—Fractions
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.
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.
Standard Identifier: 4.NF.2
Grade:
4
Domain:
Number and Operations—Fractions
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.
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.
Standard Identifier: 4.NF.3.a
Grade:
4
Domain:
Number and Operations—Fractions
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.
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.
Standard Identifier: 4.NF.3.b
Grade:
4
Domain:
Number and Operations—Fractions
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.
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.
Standard Identifier: 4.NF.3.c
Grade:
4
Domain:
Number and Operations—Fractions
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.
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.
Standard Identifier: 4.NF.3.d
Grade:
4
Domain:
Number and Operations—Fractions
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. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
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. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
Standard Identifier: 4.NF.4.a
Grade:
4
Domain:
Number and Operations—Fractions
Cluster:
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Standard:
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Standard:
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
Standard Identifier: 4.NF.4.b
Grade:
4
Domain:
Number and Operations—Fractions
Cluster:
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Standard:
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Standard:
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
Standard Identifier: 4.NF.4.c
Grade:
4
Domain:
Number and Operations—Fractions
Cluster:
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Standard:
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Standard:
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
Standard Identifier: 4.NF.5
Grade:
4
Domain:
Number and Operations—Fractions
Cluster:
Understand decimal notation for fractions, and compare decimal fractions.
Standard:
Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
Footnote:
Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.
Understand decimal notation for fractions, and compare decimal fractions.
Standard:
Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
Footnote:
Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.
Showing 71 - 80 of 159 Standards
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