Unit SummaryDownload

Primary Standard:

MAFS.4.NF.2.4: 

  1. 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). 
  2. 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.)
  3. 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

  • Step 1: Model products of equal groups of non-unit fractions
  • Step 2: Look for and apply structure (patterns) in finding products of non-unit fractions, relate to basic multiplication facts
  • Step 3: Apply multiplication of fractions to solve word problems (including multi-step problems)