Classroom Connection: Division and Unit Fractions

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

3, 4, 5

Overview

In this lesson video you’ll learn multiple ways to divide a number by a fraction; plus you’ll get actual examples to make this concept real.

Mathematics (2019) Grade(s): 3

MA19.3.13

Demonstrate that a unit fraction represents one part of an area model or length model of a whole that has been equally partitioned; explain that a numerator greater than one indicates the number of unit pieces represented by the fraction.

UP:MA19.3.13

Vocabulary

  • Unit fraction
  • Area model
  • Interval
  • Length (Linear) model
  • Partition
  • Numerator
  • Denominator
  • Part
  • Point
  • Whole

Knowledge

Students know:
  • Fractional parts of a whole must be of equal size but not necessarily equal shape.
  • Denominators represent the number of equal size parts that make a whole.
  • The more equal pieces in the whole, the smaller the size of the pieces.
  • The numerator represents the number of equal pieces in the whole that are being counted or considered.

Skills

Students are able to:
  • Use an area model and length model to show a unit fraction as one part of an equally partitioned whole.
  • Explain that given a fraction with a numerator greater than one, the numerator indicates the number of unit fraction pieces represented by the fraction.
    Example: 3/4 is the same as 3 units of 1/4 size, or three 1/4 pieces, 3 copies of 1/4, or 3 iterations of 1/4.
  • Identify and describe the fractional name given a visual fraction model.
  • Identify and demonstrate fractional parts of a whole that are the same size but not the same shape using concrete materials.

Understanding

Students understand that:
  • Given the same size whole, the larger the denominator, indicating the number of equal parts in the whole, the smaller the size of the pieces because there are more pieces in the whole.
  • Fractions are numbers that represent a quantity less than, equal to, or greater than 1.
  • Fractions represent equal partitions of a whole.
Mathematics (2019) Grade(s): 3

MA19.3.14

Interpret a fraction as a number on the number line; locate or represent fractions on a number line diagram.

UP:MA19.3.14

Vocabulary

  • Fraction
  • Number line
  • Number line diagram
  • Unit fraction
  • Interval
  • Partition
  • Point
  • Denominator
  • Numerator

Knowledge

Students know:
  • How to use fraction strips as a model to connect to finding fractional parts on a number line.
  • Fractions are numbers that can be represented on a number line.
  • Fractions can be placed on the number line by marking off equal parts between two whole numbers.
  • Fractions equal to 1 have the same numerator and same denominator.
  • Fractions greater than 1 have a numerator that will be greater than the denominator.

Skills

Students are able to:
  • Represent fractions on a number line.
  • Locate fractions on a number line.
  • Use a number line and partition an interval from 0 to 1 into equal parts as specified by the denominator of a fraction.
  • Represent a non unit fraction on a number line by marking off unit fraction lengths as specified by the numerator from zero.
  • Extend the number line to include fractions greater than one as a continuation of counting unit fractions.

Understanding

Students understand that:
  • A number line is a length model.
  • Fractions are numbers that represent a quantity less than, equal to, or greater than 1 and can be placed on a number line.
  • A number line can be partitioned to represent equal parts of a whole.
Mathematics (2019) Grade(s): 4

MA19.4.15

Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

UP:MA19.4.15

Vocabulary

  • Decomposition
  • Unit fraction
  • Area model
  • Length model
  • Equation
  • Mixed number
  • Visual fraction model
  • Whole
  • Sum
  • Difference
  • Recomposition

Knowledge

Students know:
  • Situation contexts for addition and subtraction problems.
  • A variety of strategies and models to represent addition and subtraction situations.
  • The fraction a/b is equivalent to the unit fraction 1/b being iterated or "copied" the number of times indicated by the numerator, a.
  • A fraction can represent a whole number or fraction greater than 1 and can be illustrated by decomposing the fraction.
    Example: 6/3 = 3/3 + 3/3 = 2 and 5/3 = 3/3 + 2/3 = 1 2/3.

Skills

Students are able to:
  • Decompose fractions as a sum of unit fractions.
  • Model decomposition of fractions as a sum of unit fractions.
  • Add and subtract fractions with like denominators using properties of operations and the relationship between addition and subtraction.
  • Solve word problems involving addition and subtraction using visual models, drawings, and equations to represent the problem.

Understanding

Students understand that:
  • A unit fraction (1/b) names the size of the unit with respect to the whole and that the denominator tells the number of parts the whole is partitioned, and the numerator indicates the number of parts referenced.
  • A variety of models and strategies can be used to represent and solve word situations involving addition and subtraction.
  • The operations of addition and subtraction are performed with quantities expressed in like units, and the sum or difference retains the same unit.
Mathematics (2019) Grade(s): 5

MA19.5.11

Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

UP:MA19.5.11

Vocabulary

  • Fraction
  • Numerator
  • Denominator
  • Division
  • Remainder
  • Dividend
  • Divisor

Knowledge

Students know:
  • Contextual situations for division.
  • Strategies to equipartition.

Skills

Students are able to:
  • Solve word problems involving division of whole numbers leading to quotients with fractions.
  • Use fraction models, drawings, equations to represent word problems.
  • Model and interpret a fraction as division.

Understanding

Students understand that:
  • a ÷ b is a division expression and can be written as a/b showing division of the numerator by the denominator (including cases where the value of a
Mathematics (2019) Grade(s): 5

MA19.5.15

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

UP:MA19.5.15

Vocabulary

  • Unit fraction
  • Whole number
  • Division
  • Dividend
  • Divisor
  • Quotient
  • Equation
  • Multiplication
  • Factor
  • Fraction models

Knowledge

Students know:
  • Contextual situations involving division with whole numbers and unit fractions.
  • Strategies for representing a division problem with a visual model.

Skills

Students are able to:
  • Use previous understandings of operations to
  • Divide unit fractions by a whole number and whole numbers by unit fractions.
  • Use visual models to illustrate quotients.
  • Create story contexts for division.
  • Use the relationship between multiplication and division to explain quotients.

Understanding

Students understand that:
  • A variety of contextual situations are represented with division of a whole number by a fraction or a fraction by a whole number.
  • Quotients resulting from division of a whole number by a fraction or a fraction by a whole number can be illustrated and justified with a visual model.
  • The relationship between multiplication and division can be used to justify quotients resulting from division of a whole number by a fraction or a fraction by a whole number.

CR Resource Type

Audio/Video

Resource Provider

PBS

License Type

CUSTOM
https://aptv.pbslearningmedia.org/resource/division-and-unit-math-4-5-video/cla…

Custom License Type (URL)

https://mpb.pbslearningmedia.org/help/terms-of-use/

Approved Date

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