FRACTION DIVISION MODELS

Cluster A. Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Standard 1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fractions models and equations to represent the problem.

inverse operations 32 ÷ 8 = a 8 x a = 32

4.NF.3b: Decompose a fraction into a sum of fractions with the same denominator… for example: 4.NF.4a: Understand a fraction a/b as a multiple of 1/b… for example:

5.NF.3b: Interpret a fraction as division of the numerator by the denominator. Students use models for “equal sharing” to explain their understanding.

Grade 5 and Grade 6

OUTCOME #2 Participants will: 2. Explore a variety of models that each show what happens mathematically when values are divided by a fraction.

Area Model Number line model Tape diagram model Common denominator model

5.NF.B.7b: Interpret division of a whole number by a unit fraction, and compute such quotients

eight 2 How many parts can be partitioned from 2 “wholes”? 8 ?? How many times does a part fit into 2 “wholes”?

eight 8 How many parts can be partitioned from 2 “wholes”? 2 ?

eight onetwothreefourfivesixseveneight 8 How many parts can be partitioned from 2 “wholes”? ?

1 remainder ?

1 ? ?

The remainder equals of one part. So the answer is 1.

remainder

1

5.NF.B.7a: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.

1

The quotient must be a fraction!

1 1 1

1

15

OUTCOME #3 Participants will: 3. Compute quotients of fractions divided by fractions, and interpret the quotients.

6.NS.A.1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fractions models and equations to represent the problem.

onetwo 2 Two parts

onetwo 2

2 onetwo

one two three four one two three

one

remainder

Inverse Operations and Reciprocal Pairs

Illustrative Math Bill McCullum, CCSS lead writer Sample Lessons that illustrate specific standards Achieve The Core Jason Zimba, CCSS lead writer Multiple Resources – e.g. Lesson Plans, Assessments, Professional Development courses, Grade-at-a-Glance PARCC Information about PARCC Assessments Sample Lessons Practice Tests