Modeling Fraction Division Using Comparison, Group Size Unknown

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

5

Overview

This video illustrates a visual model for solving a word problem involving the division of fractions. The problem asks students to determine the length of a losing frog's jump in a jumping frog contest based on a comparison with the length of the winning jump. The accompanying classroom activity requires students to use visual models to work through the challenge problem presented at the end of the video, which also involves the division of fractions and comparison.

Mathematics (2019) Grade(s): 5

MA19.5.7

Use strategies based on place value, properties of operations, and/or the relationship between multiplication and division to find whole-number quotients and remainders with up to four-digit dividends and two-digit divisors. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

UP:MA19.5.7

Vocabulary

  • Quotient
  • Dividend
  • Divisor
  • Divide
  • Multiply
  • Equation
  • Remainder
  • Multiple
  • Area model
  • Decompose
  • Partial quotient
  • Equation

Knowledge

Students know:
  • Efficient strategies to find a whole number quotient when a multi-digit number (up to 4-digit dividend) is divided by a single-digit divisor.
  • How to justify quotients using an illustration or the relationship between multiplication and division.

Skills

Students are able to:
  • Find whole number quotients and remainders using a variety of strategies based on place value and properties of operations.
  • Illustrate and explain the calculation using equations, arrays, and area models.

Understanding

Students understand that:
  • Strategies for division by a one-digit divisor are extended to two-digit divisors.
  • Visual models are used to illustrate division.
  • Remainders may be written as a fraction or decimal and interpreted based on context of the problem situation.
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
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