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Represent fractions with set models

A set model represents a fraction as a collection partitioned into equal-sized groups, with the denominator naming the total number of equal groups and the numerator naming how many groups are selected or described. At this level, the understanding centers on halves, thirds, and fourths, including simple fractions such as 2/42/4, and that equal partitioning—not the total number of objects alone—is essential; this foundation supports interpreting fractions as numbers and comparing them later.

Detailed Explanation: Represent fractions with set models

A set model shows a fraction by putting objects into equal-sized groups.

  • The denominator tells the total number of equal groups.
  • The numerator tells how many groups are selected or shaded.

Example: Represent 24\frac{2}{4} using 8 counters.

  1. Look at the denominator, 44. Make 4 equal groups.

  2. Share the 8 counters equally:

∙ ∙∙ ∙∙ ∙∙ ∙\boxed{\bullet\ \bullet}\quad \boxed{\bullet\ \bullet}\quad \boxed{\bullet\ \bullet}\quad \boxed{\bullet\ \bullet}

Each group has 2 counters. 3. Look at the numerator, 22. Select or shade 2 of the 4 groups:

∙ ∙∙ ∙∙ ∙∙ ∙\boxed{\color{gray}{\bullet\ \bullet}}\quad \boxed{\color{gray}{\bullet\ \bullet}}\quad \boxed{\bullet\ \bullet}\quad \boxed{\bullet\ \bullet}

  1. Two groups are selected out of four equal groups, so the fraction shown is

24.\frac{2}{4}.

The groups must be equal in size. Counting only the total number of objects does not show the fraction; the objects must first be partitioned into equal groups.

Learn by doing: Represent fractions with set models

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    Fraction Concept Intro - Picture to Fraction, Simple Fraction

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