Lesson objective: Interpret \(({a\over b})\times q\) as "a" parts of a partition of q into b equal parts.
Students bring prior knowledge of using multiplication and division to solve word problems in situations involving equal groups from 3.OA.A.2. This prior knowledge is extended to fractions as students need to partition groups into equal parts to solve problems. A conceptual challenge students may encounter is understanding the flexibility of fractions.
The concept is developed through work with a tape diagram, which helps students see how making groups of equal shares can be easier to do after the original group has been partitioned.
This work helps students deepen their understanding of operations, as they gain a greater understanding of how partitive division helps them solve problems and perform other operations.
Students engage in Mathematical Practice 1 (make sense of problems and persevere in solving them) as they use a tape diagram to partition a whole into equal parts, so they can then go on to determine the amount of a certain number of those parts.
Key vocabulary:

factor: any numbers that are multiplied together

partition: divide into parts

parts: pieces or segments of an object

product: the result of multiplying two or more factors

whole: the entire object