Primary Standards:

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.

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.

b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater that 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n x a)/(n x b) to the effect of multiplying a/b by 1.

Content Knowledge:

In 4th grade, students were introduced to multiplication of whole number groups of fractions.  In this Unit, 5th graders will use scaling to estimate products, and extend their work with whole number factors to include finding fractions of whole numbers and multiplying fractions of fractions.

Because of experiences with whole number multiplication, students are often surprised when products from multiplying fractions are less than the factor(s).  Discussing the factors and estimating the products provide students with opportunities to rethink their understanding of fractions and multiplication.  In addition, modeling the multiplication process spurs insight as they visualize the process.

Knowing when to multiply fractions is as important as knowing how to multiply fractions.  Instruction should be focused on problem solving so students understand what the fractions represent and become familiar with situations that call for multiplying them.  Asking students to build equations to match word problems should be a regular part of lessons.

GCG 1 – Learning Goal: As a mathematician, I can Multiply a Fraction by a Whole Number

• Step 1: Use manipulatives or visual models to represent multiplication of a unit fraction by a whole number or whole number by a unit fraction
• Step 2: Use manipulatives or visual models to represent multiplication of any fraction by a whole number or a whole number by any fraction
• Step 3: Solve real world problems involving multiplication of whole numbers and fractions using visual fraction models

GCG 2 – Learning Goal: As a mathematician, I can Multiply a Fraction by a Fraction

• Step 1: Use manipulatives or visual models to represent the product of a fraction and a unit fraction
• Step 2: Use manipulatives or visual models to represent the product of a fraction and any fraction
• Step 3: Solve real world problems involving multiplication of fractions using fraction models

GCG 3 – Learning Goal: As a mathematician, I can Use Scaling to Multiply

• Step 1: Explain what happens to the product when a fraction or mixed number is one of the factors
• Step 2: Interpret, reason and generalize multiplication scaling by comparing the size of the product to the size of one factor based on the size of the other factor