Previously, students learned that any unit fraction multiplied by a whole number results in multiples of that unit fraction. They also learned that any fraction can be written as a multiplication expression of a unit fraction by a whole number. In this lesson, students notice that they can multiply any fraction and a whole number by reasoning about the number of groups and the amount in each group. They generalize that they can multiply the numerator by the whole number to find the number of parts. They also see that the denominator remains the same because the size of each part is the same. In other words: .
Representation
MLR6
Describe (orally) patterns in the products of whole numbers and non-unit fraction.
Explain (orally and in writing) strategies for determining the product of a whole number and a non-unit fraction.
Understand a multiple of as a multiple of , and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express as , recognizing this product as . (In general, )