Course 1 Online!
Henrico County Public Schools, Virginia
Number and Number Sense

Computation and Estimation

Measurement and Geometry

Probability, Statistics, Patterns, Functions, and Algebra

SOL Review Materials
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
  1. SOL 4.5a - determine common multiples/ factors
  2. SOL 5.3ab - a) Identify/describe characteristics of prime/composite numbers; b) Identify/describe characteristics of even/odd numbers
  3. SOL 8.2 - describe orally/in writing relationships between subsets of the real number system
Instructional Materials
  1. VDOE Enhanced Scope and Sequence Lesson: Modeling Multiplication of Fractions (PDF) - Modeling multiplication of fractions (Word)
  2. VDOE Enhanced Scope and Sequence Lesson: Modeling Division of Fractions (PDF) - Modeling division of fractions (Word)
  3. Notes: Modeling Multiplication and Division of Fractions (ppt) - notes on understanding modeling of multiplying and dividing fractions
  4. Notes: Representing Multiplication of Fractions (flipchart) - 8 questions to practice modeling multiplication of fractions
  5. Notes: Modeling Multiplication of Fractions (ppt) - examples of taking a multiplying fractions model and finding the problem.
  6. Notes: Modeling Multiplication of Fractions (doc) - fill in notes to understand modeling multiplication of fractions
  7. Notes: Modeling Multiplication of Fractions with Pete the Spider (flipchart) -18 slides understanding and practicing modeling multiplication of fractions
  8. Lesson Plan: Models for Dividing Fractions (doc) - teacher guided notes
  9. Notes: Modeling Division of Fractions (ppt) - voice over examples of dividing fractions
  10. Notes: Division of Fractions (flipchart) - 10 slides helping to understand and practice dividing fractions with models
  11. Project: Modeling Multiplying and Dividing Fractions (flipchart) - examples are done first before the student model the questions they choose
  12. VDOE Algebra Readiness Curriculum Companion: Working with Fractions (pdf)
Real World Lessons
  1. Mathalicious: Are We Alone? - What is the probability of finding intelligent life in the cosmos?
Practice
  1. Worksheet: Dividing Fractions with Modeling (doc) - 3 practice problems modeling division of fractions
  2. Worksheet: Area Model Multiplication (pdf) - 7 questions  using the illustration to write the multiplication sentence
  3. Worksheet: Area Model Multiplication #2 (pdf) - 7 questions drawing a model to help solving multiplication of fractions
  4. Worksheet: Representing Fraction Multiplication (doc) - 8 practice problems including word problems
  5. Worksheet: Pattern Blocks Area For Multiplying and Dividing Fractions (pdf)
  6. Worksheet: Using Fraction Tiles For Multiplying and Dividing Fractions (pdf)
  7. Worksheet: Using Rectangles For Multiplying and Dividing Fractions (pdf) - 8 questions practicing modeling multiplying and dividing fractions
SOL Mini Quiz
  1. SOL 6.4 Mini Quiz: Modeling Multiplication and Division of Fractions (pdf)
Skills
Videos
  1. YouTube: Multiplying Fractions Using Models
  2. Song: Dividing Fractions
Explore Learning
  1. 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.
  2. Dividing Mixed Numbers: Choose the correct steps to divide mixed numbers. Use step-by-step feedback to diagnose and correct incorrect steps.
  3. 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.
  4. Multiplying Mixed Numbers: Choose the correct steps to multiply mixed numbers. Use the step-by-step feedback to diagnose incorrect steps.
Websites
  1. Sadlier: Modeling Multiplication
  2. Learner: Models for the Multiplication and Division of Fractions
  3. NLVM: Modeling Multiplication of Fractions (Use Internet Explorer)
  4. Learn Alberta: Select Number - Fractions
VDOE Interventions
  1. 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