Lesson 12

The purpose of this lesson is for students to consider strategies for adding and subtracting fractions with the same denominator, including mixed numbers, and to recognize when it is helpful to decompose numbers or write equivalent fractions when finding sums and differences of fractions.

Previously, students learned to decompose mixed numbers and write equivalent fractions for whole numbers to add and subtract fractions. In this lesson, they practice finding the value of sums and differences of fractions while also taking a closer look at their reasoning strategies. In the first activity, students complete addition and subtraction equations, each with a missing number. They then reflect on the steps they took and consider why they found certain ways of reasoning more productive than others. In the second activity, students examine and explain when it might be useful to decompose numbers when finding sums and differences of fractions. In explaining their answers and strategies, students need to be precise in their word choice and use of language (MP6).

Which way(s) of reasoning about sums and differences of fractions did most students use today? What suggestions could you offer to improve students flexibility in adding and subtracting fractions?