ALEX Classroom Resource

  

Modeling Fraction Division Using Comparison, Group Size Unknown

  Classroom Resource Information  

Title:

 Modeling Fraction Division Using Comparison, Group Size Unknown

URL:

 https://aptv.pbslearningmedia.org/resource/mket-math-ee-vidpeeper/peeper/

Content Source:

 PBS
Type: Audio/Video

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.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 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.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Choose strategies based on place value, partial quotients, properties of operations, or the relationship between multiplication and division to find whole number quotients and remainders.
  • Solve word problem situations involving division.
  • Justify solution path for quotients using equations, arrays or area models.
      • Note: Standard algorithm for division is not an expectation at grade 5.
Teacher 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.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.5.7.1: Construct a division equation with an example of the division algorithm.
M.5.7.2: Illustrate the division algorithm using a one-digit divisor and a 2-digit dividend.
M.5.7.3: Identify the place value of a division problem.
M.5.7.4: Restate the inverse process of division as multiplication.
M.5.7.5: Recall basic multiplication facts.

Prior Knowledge Skills:
  • Use concrete models, drawings, and strategies to add, subtract, multiply, and divide decimals.
  • Relate strategies for operations with decimals to a written method and explain reasoning used.
  • Solve real-world context problems involving decimals.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.5.6 Model multiplication with two digit whole numbers by one digit whole numbers with regrouping using strategies such as arrays, decomposition, and manipulatives.

Mathematics
MA2019 (2019)
Grade: 5
11. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

a. Model and interpret a fraction as division of the numerator by the denominator (a/b= a รท b)

b. Use visual fraction models, drawings, or equations to represent word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Solve problems involving division of whole numbers leading to quotients of a fraction or mixed number.

    • Example: Given that 3 cookies are shared equally with 6 people, find what fraction of the cookies each person receives. Each person receives 3/6 of a cookie or 1/2 of a cookie.
    Example: Given that 3 cookies are shared equally with 2 people, find what fraction of the cookies each person receives. Each person receives 3/2 cookies or 1 1/2 cookies.
  • Model and interpret a fraction as division.
  • Use models, drawings, or equations to represent word problems.
Teacher 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 < b).
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.5.11.1: Define a mixed number.
M.5.11.2: Generate equivalent fractions.
M.5.11.3: Recognize a fraction as a number on the number line; represent fractions on a number line diagram.

Prior Knowledge Skills:
  • Find products of a fraction times a whole number and products of a fraction times a fraction.
  • Use area models, linear models or set models to represent products.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.5.11 Using vocalization, sign language, augmentative communication or assistive technology, identify models of thirds (e.g., 1/3. 2/3, 3/3) and tenths (e.g., 1/10, 2/10, 3/10, 4/10, 5/10, 6/10, 7/10, 8/10, 9/10, 10/10).
Mathematics
MA2019 (2019)
Grade: 5
15. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

a. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions and illustrate using visual fraction models, drawings, and equations to represent the problem.

b. Create a story context for a unit fraction divided by a whole number, and use a visual fraction model to show the quotient.

c. Create a story context for a whole number divided by a unit fraction, and use a visual fraction model to show the quotient.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Solve real-world problems involving division of a unit fraction by a non-zero whole number, or division of a whole number by a unit fraction.
  • Justify solutions using visual models, drawings, and equations to represent the problem context.
  • Explain quotients using the relationship between multiplication and division.
  • Create a story context for a unit fraction divided by a whole number and use models to illustrate the quotient.
  • Create a story context for a whole number divided by a unit fraction and use models to illustrate the quotient.
Teacher 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.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.5.15.1: Define quotient.
M.5.15.2: Multiply a fraction by a whole number.
M.5.15.3: Recognize key terms to solve word problems.
Examples: times, every, at this rate, each, per, equal/equally, in all, total.
M.5.15.4: Recall basic multiplication and division facts.
M.5.15.5: Express whole numbers as fractions.
M.5.15.6: Recognize fractions that are equivalent to whole numbers.
M.5.15.7: Recall basic multiplication and division facts.
M.5.15.8: Solve word problems involving multiplication of a fraction by a whole number.
M.5.15.9: Recognize key terms to solve word problems.
M.5.15.10: Recall basic multiplication and division facts.

Prior Knowledge Skills:
  • Find products of a fraction times a whole number and products of a fraction times a fraction.
  • Use area models, linear models or set models to represent products.
  • Create a story context to represent equations (a/b) × q and (a/b) × (c/d) to interpret products.
  • Find area of rectangles with fractional side lengths and represent products as rectangular areas.
  • Find the area of a rectangle by tiling the area of a rectangle with unit squares.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.5.15 Use a model to solve dividing a whole number by a unit fraction of 1/2.
Tags: denominator, divide, division, fraction, numerator
License Type: Custom Permission Type
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AccessibilityVideo resources: includes closed captioning or subtitles
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Author: Stephanie Carver
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