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Lesson objective: Practice dividing whole numbers by unit fractions using the question "How many (unit fractions) are in (this whole number)?"
This lesson helps to build procedural skill with dividing whole numbers by unit fractions by thinking about how many of the unit fraction are in 1, and then how many 1's are in the whole number. Number lines and tape diagrams are used here because they support students as they identify the whole number, one, and the size of the unit fraction as it relates to one.
This work develops students' understanding that the meaning of division as making equal size groups of pieces holds when dividing whole numbers by unit fractions. In this case, we know the whole (which is not necessarily 1) and we know the size of the pieces. The goal is to find the number of those peices. We're guaranteed to get a whole number because there is a whole number of unit fractions in 1, and a whole number of 1's in every whole number.
Students engage in Mathematical Practice 5 (use appropriate tools strategically) as they connect their work with dividing whole numbers by fractions to dividing whole numbers using a number line. Students attend to precision (MP6) as they solve problems in which the quotient is a number, not the same units as the dividend and divisor.