Lesson 16

The purpose of this lesson is for students to find quotients involving a whole number and a unit fraction and assess the reasonableness of their answers.

In previous lessons students found the value of quotients of a unit fraction and a whole number. In this lesson they think about comparing the value of these quotients without calculating. For example, students know from earlier work that \(48 \div 4\) is less than \(48 \div 2\) because there are more groups of 2 in 48 than groups of 4. By the same reasoning \(10 \div \frac{1}{3}\) is less than \(10 \div \frac{1}{5}\) because \(\frac{1}{5}\)s are smaller than \(\frac{1}{3}\)s and so it takes more \(\frac{1}{5}\)s to make an amount. This kind of reasoning also shows that \(\frac{1}{4} \div 15\) is less than \(\frac{1}{4} \div 12\) because dividing the same amount into more pieces creates smaller pieces.

Reflect on a time your thinking changed about something in class recently. How will you alter your teaching practice to incorporate your new understanding?