Number and Number Sense
Focus: Relationships among Fractions, Decimals, and Percents
The student will demonstrate multiple representations of multiplication and division of fractions. 


Essential Knowledge and Skills 
 Demonstrate multiplication and division of fractions using multiple representations.
 Model algorithms for multiplying and dividing with fractions using appropriate representations.

Essential Understandings 
 When multiplying fractions, what is the meaning of the operation? When multiplying a whole by a fraction such as 3 x 1/2, the meaning is the same as with multiplication of whole numbers: 3 groups the size of 1/2 of the whole.
When multiplying a fraction by a fraction such as 2/3 times 3/4, we are asking for part of a part.
When multiplying a fraction by a whole number such as 3/2 x 6, we are trying to find a part of the whole.
 What does it mean to divide with fractions? For measurement division, the divisor is the number of groups and the quotient will be the number of groups in the dividend. Division of fractions can be explained as how many of a given divisor are needed to equal the given dividend. In other words, for 1/4 divided by 2/3 the question is, “How many 2/3 make 1/4?” For partition division the divisor is the size of the group, so the quotient answers the question, “How much is the whole?” or “How much for one?”


Vertical Articulation 
 SOL 4.5a  determine common multiples/
factors
 SOL 5.3ab  a) Identify/describe characteristics of
prime/composite numbers; b)
Identify/describe characteristics of
even/odd numbers
 SOL 8.2  describe orally/in writing
relationships between subsets of the
real number system

Instructional Materials 
 VDOE Enhanced Scope and Sequence Lesson: Modeling Multiplication of Fractions (PDF)  Modeling multiplication of fractions (Word)
 VDOE Enhanced Scope and Sequence Lesson: Modeling Division of Fractions (PDF)  Modeling division of fractions (Word)
 Notes: Modeling Multiplication and Division of Fractions (ppt)  notes on understanding modeling of multiplying and dividing fractions
 Notes: Representing Multiplication of Fractions (flipchart)  8 questions to practice modeling multiplication of fractions
 Notes: Modeling Multiplication of Fractions (ppt)  examples of taking a multiplying fractions model and finding the problem.
 Notes: Modeling Multiplication of Fractions (doc)  fill in notes to understand modeling multiplication of fractions
 Notes: Modeling Multiplication of Fractions with Pete the Spider (flipchart) 18 slides understanding and practicing modeling multiplication of fractions
 Lesson Plan: Models for Dividing Fractions (doc)  teacher guided notes
 Notes: Modeling Division of Fractions (ppt)  voice over examples of dividing fractions
 Notes: Division of Fractions (flipchart)  10 slides helping to understand and practice dividing fractions with models
 Project: Modeling Multiplying and Dividing Fractions (flipchart)  examples are done first before the student model the questions they choose
 VDOE Algebra Readiness Curriculum Companion: Working with Fractions (pdf)

Real World Lessons 
 Mathalicious: Are We Alone?  What is the probability of finding intelligent life in the cosmos?

Practice 
 Worksheet: Dividing Fractions with Modeling (doc)  3 practice problems modeling division of fractions
 Worksheet: Area Model Multiplication (pdf)  7 questions using the illustration to write the multiplication sentence
 Worksheet: Area Model Multiplication #2 (pdf)  7 questions drawing a model to help solving multiplication of fractions
 Worksheet: Representing Fraction Multiplication (doc)  8 practice problems including word problems
 Worksheet: Pattern Blocks Area For Multiplying and Dividing Fractions (pdf)
 Worksheet: Using Fraction Tiles For Multiplying and Dividing Fractions (pdf)
 Worksheet: Using Rectangles For Multiplying and Dividing Fractions (pdf)  8 questions practicing modeling multiplying and dividing fractions

SOL Mini Quiz 
 SOL 6.4 Mini Quiz: Modeling Multiplication and Division of Fractions (pdf)

Skills 

Videos 
 YouTube: Multiplying Fractions Using Models
 Song: Dividing Fractions

Explore
Learning 
 Dividing Fractions: Divide fractions using area models. Adjust the numerators and denominators of the divisor and dividend and see how the area model and calculation change.
 Dividing Mixed Numbers: Choose the correct steps to divide mixed numbers. Use stepbystep feedback to diagnose and correct incorrect steps.
 Multiplying Fractions: Multiply two fractions using an area model. Vary the vertical area to change one fraction and vary the horizontal area to change the other. Then examine the intersection of the areas to find the product.
 Multiplying Mixed Numbers: Choose the correct steps to multiply mixed numbers. Use the stepbystep feedback to diagnose incorrect steps.

Websites 
 Sadlier: Modeling Multiplication
 Learner: Models for the Multiplication and Division of Fractions
 NLVM: Modeling Multiplication of Fractions (Use Internet Explorer)
 Learn Alberta: Select Number  Fractions

VDOE Interventions 
 VDOE Algebra Readiness Curriculum Companion: Working with Fractions  The lessons focus on fraction computation, factors, and multistep practical problems with
fractions. Students are expected to model multiple representations of the multiplication and division of
fractions. (pdf)

Common Core
Standards 
5.NF.4a 
5.NF.4b 
5.NF.5a 
5.NF.5b 
5.NF.6 
5.NF.7a 
5.NF.7b 
5.NF.7c 
6.NS.1 
