Lesson objective: Investigate multiplication of fractions through tiling.
Students bring prior knowledge of finding the area of a rectangle by tiling from 3.MD.C.7.C and solving realworld and mathematical problems involving using the area formula for a rectangle from 4.MD.A.3. This prior knowledge is extended to multiplying fractions as students practice their understanding of what is happening when two fractions are being multiplied together. A conceptual challenge students may encounter is thinking that multiplication always results in a product greater that its factors.
The concept is developed through work with an area model, which helps students conceptualize the idea of multiplying two fractions by providing students opportunity to reason about fractions, relating to a whole.
This work helps students deepen their understanding of operations, because they will be operating on fractions just as they operated on whole numbers.
Students engage in Mathematical Practice 1 (make sense of problems and persevere in solving them) as they use an area model to help them understand multiplying a fraction by a fraction. They will also engage in Mathematical Practice 4 (model with mathematics) by using area models to multiply fractions.
Key vocabulary:

area: the measure of the amount of surface inside a closed boundary of a twodimensional shape

area model: a representation for multiplication where the length and width represent each factor and the total area represents the product.

tiling: fitting individual tiles together with no gaps or overlaps to fill a twodimensional space