Standards - Mathematics

Demonstrate that a unit fraction represents one part of an area model or length model of a whole that has been equally partitioned; explain that a numerator greater than one indicates the number of unit pieces represented by the fraction.

Interpret a fraction as a number on the number line; locate or represent fractions on a number line diagram.

Represent a unit fraction $(\frac{1}{b})$ on a number line by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts as specified by the denominator.

Represent a fraction $(\frac{a}{b})$ on a number line by marking off a lengths of size $(\frac{1}{b})$ from zero.

Explain equivalence and compare fractions by reasoning about their size using visual fraction models and number lines.

Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers.

Compare two fractions with the same numerator or with the same denominator by reasoning about their size (recognizing that fractions must refer to the same whole for the comparison to be valid). Record comparisons using < , >, or = and justify conclusions.

Using area and length fraction models, explain why one fraction is equivalent to another, taking into account that the number and size of the parts differ even though the two fractions themselves are the same size.

Apply principles of fraction equivalence to recognize and generate equivalent fractions.

Compare two fractions with different numerators and different denominators using concrete models, benchmarks (0, $\frac{1}{2}$, 1), common denominators, and/or common numerators, recording the comparisons with symbols >, =, or <, and justifying the conclusions.

Explain that comparison of two fractions is valid only when the two fractions refer to the same whole.

Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.

Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.

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

Model and explain how a non-unit fraction can be represented by a whole number times the unit fraction.

Extend previous understanding of multiplication to multiply a whole number times any fraction less than one.

Solve word problems involving multiplying a whole number times a fraction using visual fraction models and equations to represent the problem.

Express, model, and explain the equivalence between fractions with denominators of 10 and 100.

Use fraction equivalency to add two fractions with denominators of 10 and 100.

Use models and decimal notation to represent fractions with denominators of 10 and 100.

Use visual models and reasoning to compare two decimals to hundredths (referring to the same whole), recording comparisons using symbols >, =, or <, and justifying the conclusions.

Model and solve real-word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, 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.

Add and subtract fractions and mixed numbers with unlike denominators, using fraction equivalence to calculate a sum or difference of fractions or mixed numbers with like denominators.

Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

Model and interpret a fraction as division of the numerator by the denominator ($\frac{a}{b} = a \div b$).

Use visual fraction models, drawings, or equations to represent word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

Apply and extend previous understandings of multiplication to find the product of a fraction times a whole number or a fraction times a fraction.

Use a visual fraction model (area model, set model, or linear model) to show $(\frac{a}{b}) \times q$ and create a story context for this equation to interpret the product as a parts of a partition of q into b equal parts.

Use a visual fraction model (area model, set model, or linear model) to show $(\frac{a}{b}) \times (\frac{c}{d})$ and create a story context for this equation to interpret the product.

Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths to show that the area is the same as would be found by multiplying the side lengths.

Interpret multiplication as scaling (resizing).

Compare 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.