Creating Equal Shares

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

3, 4, 5

Overview

In this lesson, students are asked to share certain numbers of objects among different numbers of people. They begin with unit fractions and move to divide multiple objects (a) among multiple people, (b) in which a < b, to produce fractions less than one. This CYBERCHASE activity is motivated by two video clips in which the CyberSquad has to share objects fairly in order to overcome obstacles and challenges assigned to them by Zeus as they try to recover Pandora's Box, which was stolen by their nemesis, Hacker.

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

MA19.3.15

Explain equivalence and compare fractions by reasoning about their size using visual fraction models and number lines.

UP:MA19.3.15

Vocabulary

  • Equivalence
  • Visual fraction model
  • Number line
  • Numerator
  • Denominator
  • Reasoning
  • Conclusions
  • Comparison
  • Point

Knowledge

Students know:
  • Fractions with different names can be equal.
  • Two fractions are equivalent if they are the same size, cover the same area, or are at the same point on a number line.
  • Unit fraction counting continues beyond 1 and whole numbers can be written as fractions.
  • Use a variety of area models and length models to show that a whole number can be expressed as a fraction and to show that fractions can be equivalent to whole numbers.
  • Comparing two fractions is only reasonable if they refer to the same whole.
  • The meaning of comparison symbols , = .
  • Reason about the size of a fraction to help compare fractions.
  • Use a variety of area and length models to represent two fractions that are the same size but have different names.
  • Use a fraction model to explain how equivalent fractions can be found.
  • Use a variety of area models and length models to demonstrate that any fraction that has the same nonzero numerator and denominator is equivalent to 1.
  • Use models to show that the numerator of a fraction indicates the number of parts, so if the denominators of two fractions are the same, the fraction with the greater numerator is the greater fraction.
  • Use models to show that the denominator of a fraction indicates the size of equal parts a whole is partitioned into, and that the greater the denominator, the smaller the parts.-Determine when two fractions can not be compared because they do not refer to the same size whole.

Skills

Students are able to:
  • Explain equivalence of two fractions using visual models and reasoning about their size.
  • Compare two fractions with same numerators or with same denominators using visual models and reasoning about their size.
  • Express whole numbers as fractions.
  • Identify fractions equivalent to whole numbers.
  • Record comparisons of two fractions using , or = and justify conclusion.
  • Explain that the whole must be the same for the comparing of fractions to be valid.

Understanding

Students understand that:
  • A fraction is a quantity which can be illustrated with a length model or an area model.
  • Two fractions can be the same size but have different fraction names.
  • A fraction can be equivalent to a whole number.
  • Any fraction that has the same nonzero numerator and denominator is equivalent to 1.
  • The numerator of a fraction indicates the number of parts, so if the denominators of two fractions are the same, the fraction with the greater number of parts is the greater fraction.
  • The denominator of a fraction indicates the size of equal parts in a whole, so the greater the denominator, the smaller the size of the parts in 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

MA19.5.15

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

Lesson/Unit Plan

Resource Provider

PBS

License Type

CUSTOM
https://aptv.pbslearningmedia.org/resource/vtl07.math.number.ope.lpequal/creati…

Custom License Type (URL)

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

Approved Date

ALSDE LOGO

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