#### MAT-04.NF.04

 MAT-04 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. MAT-04.NF.04 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. a) 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 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). b) 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 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/b). c) 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?

## Student Learning Targets:

### Reasoning Targets

• I can understand a fraction is the product of a number of groups times a unit fraction (5/4 = 5 x 1/4 or 5 groups of 1/4).
• I can understand a multiple of a fraction is also the multiple of a unit fraction with the same denominator (6/5 is a multiple of both 3/5 and 1/5 because when counting by 3/5 we say 3/5, 6/5 and for 1/5 we say 1/5, 2/5, 3/5, 4/5, 5/5, 6/5.

### Skills (Performance) Targets

• I can multiply a unit fraction by a whole number.
• I can solve word problems using multiplication of a fraction by a whole number.
• I can use visual fraction models and equations to represent my understanding.

## Rubric / Proficiency Scale

 Score Description Sample Activity 4.0 Student is able to solve real world problems involving multiplication of fractions and mixed numbers using fractions models and equations to represent the problem. Find the area of a rug that is 3 1/2 feet by 6 1/3 feet long. 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 Student is able to apply and extend understandings of multiplication concepts (multiples, repeated addition, area models) to multiply fractions by a whole number in which the product result in mixed numbers. I can solve word problems using multiplication of a fraction by a whole number. I can use visual fraction models and equations to represent my understanding. I can understand a multiple of a fraction is also the multiple of a unit fraction with the same denominator. There are 5 bags of grapes. Each way 2/3 of a pound. How many pounds total? 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to solve word problems using multiplication of a fraction by a whole number in which the product does not result in mixed numbers. I can solve word problems using multiplication of a fraction by a whole number. I can use visual fraction models and equations to represent my understanding. 4 pieces of ribbon. Each piece was 1/6 of a yard in length.  How many yards in all? 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to multiply a fraction by a whole number. I can understand a fraction is the product of a number of groups times a unit fraction (5/4 = 5 x 1/4 or 5 groups of 1/4). I can multiply a unit fraction by a whole number. 3 x 1/6 = 5/8 = ____ x ____ 0.5 Limited or no understanding of the skill is demonstrated.

## Resources

### Vocabulary

• operations
• multiplication
• multiply
• repeated addition
• multiple
• product
• fraction
• unit fraction
• mixed number
• numerator
• denominator
• fraction model
• equation
• properties - rules about how numbers work