Standards

*Use equivalent fractions as a strategy to add and subtract fractions.***5.NF.1:**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.*For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)***5.NF.2:**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.*For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.**Apply and extend previous understandings of multiplication and division to multiply and divide fractions.***5.NF.3:**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.**5.NF.4.**Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. :**5.NF.5:**Interpret multiplication as scaling (resizing)**5.NF.6:**Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.**5.NF.7:**Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

Vocabulary
benchmark fraction: common fractions that are used to compare against; common benchmark fractions include 1/10, 1/4, 1/2, and 3/4.denominator: the number below the line in a common fraction; a divisorequivalent: equalfraction: a part of a wholemixed number: a number consisting of an integer and a proper fractionnumerator: represents the number of equal parts in a fractionunit fraction: a fraction with a numerator 1 |

Strategies to Add and Subtract Fractions
Grid Model: We can add and subtract fractions with unlike denominators by creating equivalent fractions. In the model to the right, we "overlaid" the fourths model onto the thirds models. By doing so, we now have a new but equivalent fraction, 8/12. We can also overlay the thirds model onto the fourths model. Our equivalent fraction is 3/12. Both fractions have a denominator of 12 now, making it easy for us to find the sum. View the PowerPoint slide below to see how overlaying works. overlaying.pptxDownload File WCPSS tutorial |

Strategies to Multiply Fractions
Remember that multiplication is repeated addition. To model 1/8 x 3, you need to show 3 groups of 1/8. My product is 3/8. Multiply a fraction by a whole number: I know that my product is reasonable because my product is larger than one factor and smaller than the other. My product should be larger than 1/8 because I multiplied 1/8 by a factor greater than 1. My product should be smaller than 3 because I multiplied 3 by a factor less than 1 (a fraction). Multiply a fraction by a fraction: When we multiply fractions, we are taking a fraction of another fraction. We can use fraction bars, number lines, and the standard algorithm to find the product of two fractions. Our product should be smaller than both factors because we are multiplying each factor by a factor less than 1.WCPSS tutorial |

Strategies to Divide Fractions

**Divide a Unit Fraction by a Whole Number:**WCPSS tutorial**Divide a Whole Number by a Unit Fraction:**WCPSS tutorial