Primary Standard:
- Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product of 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
- Understand a multiple of a/b as a multiple of 1/b and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
- Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
Content Knowledge:
In this Unit, students will work on connecting their understanding of decomposing a fraction into unit fractions (3/4 = 1/4 + 1/4 + 1/4) to multiplying that unit fraction by a whole number (3/4 = 3 × 1/4). Students will then connect this understanding of equal groups of unit fractions and extend to equal groups of non-unit fractions e.g. 6/3 = 6 × 1/3 or 3 × 2/3. By creating visual models, they are able to find products of whole numbers and non-unit fractions.
As students work on creating models and recording multiplication of fractions, they should begin to notice patterns related to multiplication facts they know. For example, 6 × 1/3 and 3 × 2/3 both give me 6 thirds, and 6 × 1 and 3 × 2 both equal 6. Students will apply this understanding of multiplication of fractions to solve word problems.
GCG 1 – Learning Goal: As a mathematician, I can connect multiplication and modeling to represent non-unit fractions as products of unit fractions
- Step 1: Use models to represent repeated addition of unit fractions as products of non-unit fractions
- Step 2: Represent non-unit fractions as being composed of unit fractions of the same denominator
GCG 2 – Learning Goal: As a mathematician, I can find products of fractions and use to solve word problems