MAFS.5.NF.2.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
a. Interpret the product as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show , and create a story context for this equation. Do the same with . (In general, )
b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find area of rectangles and represent fraction products as rectangular areas.
MAFS.5.NF.2.6: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
MAFS.5.NF.2.5: Interpret multiplication as scaling (resizing), by:
a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
In this Unit, students will build upon the understanding acquired from work with multiplying fractions of whole numbers and multiplying fractions with unit fractions. Students will use exploration with models and patterns to build towards understanding why when multiplying fractions, the numerators of the two fractions can be multiplied as well as the denominators.
Although memorizing rules may allow students to find the product, their understanding of multiplication of fractions allows them to solve real and mathematical problems that require this skill. When beginning with models to build understanding, students can make sense of the process as well as their answers. The goals of the standards are to build both understanding and computational fluency.
Students should be provided opportunities to work with real-life contexts and situations to model in order to give them experiences they need to develop understanding of what is happening when they multiply a fraction by a fraction. Students may see the pattern and see that to multiply fractions, one may multiply the numerators and multiply the denominators. However, only references to real-life situations, using models, and visual representations will help students develop a conceptual understanding of what is actually happening when multiplying fractions.
GCG 1 Learning Goal: Use Area Models to Multiply Fractions
- Step 1: Represent the product of a unit fraction by any fraction using an area model
- Step 2: Represent the product of a non-unit fraction by a non-unit fraction using an area model
- Step 3: Solve problems using area models to multiply fractions
GCG 2 Learning Goal: Use Models to Multiply Fractions and Mixed Numbers
- Step 1: Show the product of a whole number and a fraction/mixed numbers using models
- Step 2: Connect understanding of whole number multiplication to fraction and mixed number multiplication using models
- Step 3: Solve word problems involving multiplication of fractions and mixed numbers using any strategy