ALEX Classroom Resource

  

Grade 6 Mathematics Module 2, Topic A: Dividing Fractions by Fractions

  Classroom Resource Information  

Title:

 Grade 6 Mathematics Module 2, Topic A: Dividing Fractions by Fractions

URL:

 https://www.engageny.org/resource/grade-6-mathematics-module-2-topic-overview

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

In Module 2, Topic A, students extend their previous understanding of multiplication and division to divide fractions by fractions.  They construct division stories and solve word problems involving the division of fractions (6.NS.1). Through the context of word problems, students understand and use partitive division of fractions to determine how much is in each group. They explore real-life situations that require them to ask, “How much is one share?” and “What part of the unit is that share?” Students use measurement to determine the quotients of fractions. They are presented with conceptual problems where they determine that the quotient represents how many of the divisor is in the dividend. For example, students understand that 6 cm/2 cm derives a quotient of 3 because 2 cm divides into 6 centimeters three times. They apply this method to quotients of fractions, understanding 6/7 divided by 2/7 = 6 sevenths/2 sevenths = 3  because, again, two-sevenths divides into six-sevenths three times. Students look for and uncover patterns while modeling quotients of fractions to ultimately discover the relationship between multiplication and division. Using this relationship, students create equations and formulas to represent and solve problems.  Later in the module, students learn to and apply the direct correlation of division of fractions to the division of decimals.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 6
4. Interpret and compute quotients of fractions using visual models and equations to represent problems.

a. Use quotients of fractions to analyze and solve problems.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given a division problem involving a fraction divided by a fraction,
  • Create an appropriate story context.
  • Solve the problem using visual fraction models and an equation.
  • Explain the relationship between the model and the problem.
  • Interpret the solution.
  • Use the inverse relationship between multiplication and division, or concept of division as repeated subtraction, to explain and justify the solution.
Teacher Vocabulary:
  • Visual fraction models
  • Dividend
  • Divisor
  • Quotient
  • Equation
  • Numerator
  • Denominator
  • Mixed number
  • Improper fraction
Knowledge:
Students know:
  • Strategies for representing fractions and operations on fractions using visual models,
  • The inverse relationship between multiplication and division (a ÷ b = c implies that a = b x c).
  • Strategies to solve mathematical and conceptual problems involving quotients of fractions.
Skills:
Students are able to:
  • Represent fractions and operations on fractions using visual models.
  • Interpret quotients resulting from the division of a fraction by a fraction.
  • Accurately determine quotients of fractions by fractions using visual models/equations.
  • Justify solutions to division problems involving fractions using the inverse relationship between multiplication and division.
Understanding:
Students understand that:
  • The operation of division is interpreted the same with fractions as with whole numbers.
  • The inverse relationship between the operations of multiplication and division that was true for whole numbers continues to be true for fractions.
  • The relationships between operations can be used to solve problems and justify solutions and solution paths.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.6.4.1: Define fraction (including numerator and denominator), reciprocal, equation, and quotient.
M.6.4.2: Construct an equation from a given word problem.
M.6.4.3: Discuss the process of multiplying by the reciprocal.
M.6.4.4: Interpret division of fractions by multiplying by the reciprocal.
M.6.4.5: Demonstrate division of fractions using a visual fraction model.
M.6.4.6: Demonstrate multiplication of fractions using a visual fraction model.

Prior Knowledge Skills:
  • Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
  • Write number sentences for word problems.
  • Identify key terms to solve multiplication word problems.
    Examples: times, every, at this rate, each, per, equal/equally, in all, total.
  • Recall basic multiplication facts.
  • Recognize key terms to solve word problems.
    Examples: times, every, at this rate, each, per, equal/equally, in all, total.
  • Label numerator, denominator, and fraction bar.
  • Recognize a fraction as a number on the number line.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.6.4 Use models to divide fractions (limit to unit fractions).
Tags: divide, division, fractions, quotients, word problems
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Comments

There are eight lessons in this topic.

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  This resource provided by:  
Author: Hannah Bradley
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