Computation and Estimation
Focus: Applications of Operations with Rational Numbers
The student will
b) estimate solutions and then solve singlestep and multistep practical problems involving addition, subtraction, multiplication, and division of fractions. 


Essential Knowledge and Skills 
 Solve singlestep and multistep practical problems that involve addition and subtraction with fractions and mixed numbers, with and without regrouping, that include like and unlike denominators of 12 or less. Answers are expressed in simplest form.
 Solve singlestep and multistep practical problems that involve multiplication and division with fractions and mixed numbers that include denominators of 12 or less. Answers are expressed in simplest form.

Essential Understandings 
 What is the role of estimation in solving problems? Estimation helps determine the reasonableness of answers.


Vertical Articulation 
 SOL 4.5d  solve single/multistep
practical problems involving add/sub
fractions and decimals
 SOL 5.5b  create/solve single/multistep
practical problems involving
decimals

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: Adding and Subtracting Fractions (ppt)  warm up and notes and practice with adding and subtracting fractions
 Activity Adding and Subtracting Fractions: ActivEngage (flipchart)  Self Paced 20 questions
 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: Adding and Subtracting Word Problems (doc)  11 word problems with challenge questions
 Worksheet: Operations with Fractions Word Problems (doc)  14 word problems
 Worksheet: Subtracting Fractions with Unlike Denominators With Regrouping (doc)  20 practice problems
 Worksheet: Subtraction Review with Modeling (doc)  5 practice problems with modeling
 Worksheet: Adding and Subtracting Fractions Review (doc)
 Worksheet: Converting Improper Fractions to Mixed Numbers (doc)  10 practice problems using pictures
 Practice: Fraction Word Problems (flipchart)  14 slides to practice fraction word problems

SOL Mini Quiz 
 SOL 6.6b Mini Quiz: Fraction Operations (pdf)

Skills 

Videos 
 YouTube: Subtracting Mixed Numbers
 YouTube: Maths the Wacky Way  Fractions
 PH: Estimating sums or differences with fractions
 PH: Adding mixed numbers to solve problems
 PH: Subtracting mixed numbers using renaming

Explore
Learning 
 Adding Fractions (Fraction Tiles): Add fractions with the help of the Fractionator, a fractiontilemaking machine in the Gizmo. Model sums by placing the tiles on sidebyside number lines. Explore the usefulness of common denominators in adding. Express sums as improper fractions or mixed numbers.
 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.
 Fractions with Unlike Denominators: Find the sum or difference of two fractions with unlike denominators using graphic models. Find the least common denominator graphically.
 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 
 Visual Fractions: Modeling Fractions with Number Lines and Circles
 Jamit Fractions: Lesson and Fun Games for Mastering Fractions
 MathPlay: Football Math Adding Fractions
 MathPlay: Adding and Subtracting Fractions Game
 http://www.visualfractions.com
 BrainGenie: Adding and Subtracting Fractions
 BrainGenie: Mixed Numbers and Improper Fractions
 MathSlice: Fraction Operations

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 
4.NF.4c 
5.NF.6 
7.NS.1d 
7.NS.2b 
7.NS.2c 
7.NS.3 
7.EE.3 
