Modeling Operations with Fractions

Text Box 8.1 A Math Happening 8a: Stuffed with Pizza

Tito and Luis are stuffed with pizza! Tito ate one-fourth of a cheese pizza. Tito ate three-eighths of a pepperoni pizza. Tito ate one-half of a mushroom pizza. Luis ate five-eighths of a cheese pizza. Luis ate the other half of the mushroom pizza. All the pizzas were the same size. Tito says he ate more pizza than Luis. Luis says they each ate the same amount of pizza. Who is correct? Show all your mathematical thinking.

—Problem from the NYC DOE Elementary School Performance-Based Assessment


In the lesson study, teachers focused on the relationship between fractions and examined how students would represent each portion of pizza that Tito and Luis ate and compare the two to determine whether someone ate more or they ate the same amount.

This lesson focused on the fourth- and fifth-grade standards where students used visuals to add fractions and compare fractions. Some specific standards that they noted in their math agenda were focusing on the following:

CCSS.Math.Content.5.NF.A.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.)

CCSS.Math.Content.5.NF.A.2: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, for example, 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.

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