# data[].attributes.headline
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

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Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

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Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

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Use equivalent fractions as a strategy to add and subtract fractions.

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Use equivalent fractions as a strategy to add and subtract fractions.

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Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

# data[].attributes.headline
Use equivalent fractions as a strategy to add and subtract fractions.

# data[].attributes.subject
Use equivalent fractions as a strategy to add and subtract fractions.

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Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

# data[].attributes.headline
Apply and Extend previous understandings of multiplication and division

# data[].attributes.subject
Apply and Extend previous understandings of multiplication and division

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Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

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Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

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Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

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Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b.

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Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

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Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

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Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

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Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

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Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

# data[].attributes.headline
Apply and Extend previous understandings of multiplication and division.

# data[].attributes.subject
Apply and Extend previous understandings of multiplication and division.

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Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

# data[].attributes.headline
Apply and extend previous understandings of multiplication and division.

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Apply and extend previous understandings of multiplication and division.

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Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.

# data[].attributes.headline
Apply and extend previous understandings of multiplication and division.

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Apply and extend previous understandings of multiplication and division.

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Interpret division of a whole number by a unit fraction, and compute such quotients.

# data[].attributes.headline
Apply and extend previous understandings of multiplication and division.

# data[].attributes.subject
Apply and extend previous understandings of multiplication and division.

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Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.

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Extend Understanding of Fraction Equivalence and Ordering

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Extend Understanding of Fraction Equivalence and Ordering

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Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

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Extend understanding of fraction equivalence and ordering

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Extend understanding of fraction equivalence and ordering

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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.

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Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

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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.

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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.

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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

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Multiplying a Fraction by a Whole Number

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Multiplying a Fraction by a Whole Number

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Understand a fraction a/b as a multiple of 1/b.

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Multiplying a Fraction by a Whole Number

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Multiplying a Fraction by a Whole Number

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Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

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Multiplying a Fraction by a Whole Number

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Multiplying a Fraction by a Whole Number

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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.

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Understand decimal notation for fractions, and compare decimal fractions

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Understand decimal notation for fractions, and compare decimal fractions

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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 100.² For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

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Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

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Understand a fraction as a number on the number line; represent fractions on a number line diagram.

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Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

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Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

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Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

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Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.