Topic Nine: Adding and Subtracting Fractions

Desired Results

Transfer:

1. Makes sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Established Goals:
  • 5.NF.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
  • 5.NF.2: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem.Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

Pre-Requisite Goals:
  • 4.NF.3.a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
  • 4.NF.3.b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.
  • 4.NF.3.d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and quations to represent the problem.

Student Friendly "I Can" Statements
  • I can add and subtract fractions with unlike denominators and mixed numbers.
  • I can solve word problems that involve fractions.
Big Ideas:
  • Basic Facts and Algorithms: There is more than one algorithm for each of the operations with rational numbers. Some strategies for basic facts and most algorithms for operations with rational numbers, both mental math and paper and pencil, use equivalence to transform calculations into simpler ones.
  • Estimation: Numbers can be approximated by numbers that are close. Numerical calculations can be approximated by replacing numbers with other numbers that are close and easy to compute mentally. Some measurements can be approximated using known referents as the unit in the measurement process.
  • Equivalence: Any number, measure, numerical expression, algebraic expression, or equation can be represented in an infinite number of ways that have the same value.
  • Practices, Processes, and Proficiencies: Mathematics content and practices can be applied to solve problems.
  • Numbers and the Number Line: The set of real numbers is infinite and ordered. Whole number, integers, and fractions are real numbers. Each real number can be associated with a unique point on the number line.
  • Number Uses, Classification, and Representation: Numbers can be used for different purposes, and numbers can be classified and represented in different ways.
Essential Questions:

What does it mean to add and subtract fractions with unlike denominators?

What is a standard procedure for adding and subtracting fractions with unlike denominators?
Students will know...
  • The same fractional amount can be represented by an infinite set of different but equivalent fractions. Equivalent fractions are found by multiplying or dividing the numerator and denominator by the same nonzero number.
  • A fraction is in simplest form when 1 is the only common factor of the numerator and denominator.
  • Mathematical explanations can be given using words, pictures, numbers, or symbols. A good explanation should be correct, simple, complete, and easy to understand.
  • A number line can be used to determine the nearest half or whole a fraction is closest to.
  • All non-zero whole numbers have common multiples, including a least one. Sometimes the least common multiple of tow numbers is of the numbers.
  • Fractions with unlike denominators can be added or subtracted by replacing fractions with equivalent fractions. The product of the denominators of two fractions is a common denominator of both.
  • Information in a problem can often be shown using a diagram and used to solve the problem. Some problems can be solved by writing and completing a number sentence or equation.

Vocabulary: equivalent fractions, simplest form, benchmark fraction, common multiple, least common multiple, common denominator, least common denominator
Vocabulary Cards
Vocabulary Cards-2
Students will be skilled at...
  • Writing equivalent fractions.
  • Identifying fractions that are in simplest form and find the simplest form of a fraction.
  • Explaining how they estimated fractional amounts of objects.
  • Using a number line to estimate sums and differences of fractions.
  • Determining common multiples and least common multiples of numbers.
  • Finding common denominators for fractions with unlike denominators.
  • Using models and computational procedures to add fractions with unlike denominators.
  • Using models and computational procedures to subtract fractions with unlike denominators.
  • Solving problems involving addition and subtraction of fractions.
  • Drawing a picture and writing an equation to solve a problem.

Assessment Evidence

Performance Assessment:

Cindy's Cats
Fractions
Other Evidence:

Learning Plan

Learning Activities:
9-1: The same fractional amount can be represented by an infinite set of different but equivalent fractions. Equivalent fractions are found by multiplying or dividing the numerator and denominator by the same nonzero number.
9-2: A fraction is in simplest form when 1 is the only common factor of the numerator and denominator.
9-3: Mathematical explanations can be given using words, pictures, numbers, or symbols. A good explanation should be correct, simple, complete, and easy to understand.
9-4:A number line can be used to determine the nearest half or whole a fraction is closest to.
9-5:All non-zero whole numbers have common multiples, including a least one. Sometimes the least common multiple of tow numbers is of the numbers.
9-6:Fractions with unlike denominators can be added or subtracted by replacing fractions with equivalent fractions. The product of the denominators of two fractions is a common denominator of both.
9-7:Fractions with unlike denominators can be added or subtracted by replacing fractions with equivalent fractions. The product of the denominators of two fractions is a common denominator of both.
9-8:Fractions with unlike denominators can be added or subtracted by replacing fractions with equivalent fractions. The product of the denominators of two fractions is a common denominator of both.
9-9:Fractions with unlike denominators can be added or subtracted by replacing fractions with equivalent fractions. The product of the denominators of two fractions is a common denominator of both.
9-10:Information in a problem can often be shown using a diagram and used to solve the problem. Some problems can be solved by writing and completing a number sentence or equation.
Resources:

Problem of the Month:
Got Your Number
Part and Whole
Diminishing Return
Fractured Numbers

Centers:
Identifying Fractions
Creating Equivalent Fractions to Add Unlike Fractions
Creating Equivalent Fractions to Subtract Unlike Fractions
Fraction Word Problems with Unlike Denominators
Addition Word Problems with Fractions
Subtraction Word Problems with Fractions