Classroom Connection: Who Ran Farther?

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

3

Overview

Number lines show the distance between numbers, and you can also use number lines to solve math problems, like the one in this lesson from Classroom Connection. This video helps students locate a fraction on a number line and use fractional reasoning to compare distances on the number line. 

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): 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.

CR Resource Type

Audio/Video

Resource Provider

PBS

License Type

CUSTOM
https://aptv.pbslearningmedia.org/resource/who-ran-farther-math-3-video/classro…

Custom License Type (URL)

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

Approved Date

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