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AA.2 Identify unit fractions in models

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What is a unit fraction?

A unit fraction is a fraction where the numerator (top number) is 1, and the denominator (bottom number) is a positive whole number. It represents one equal part of a whole.

Examples:
  • 12 (one-half)
  • 13 (one-third)
  • 14 (one-fourth)
  • 18 (one-eighth)
Note

Think "one piece." In a unit fraction, you are always looking at just one of the total equal parts.

Identifying unit fractions in shapes

A shape model shows a unit fraction when it is divided into equal parts and exactly one of those parts is shaded or highlighted.

How to identify:
  • First, check if the whole shape is divided into equal parts.
  • Count the total number of equal parts. This number is the denominator.
  • Count the number of shaded parts. For a unit fraction, this must be 1.
  • The unit fraction is written as 1total parts.
Note

Equal parts are key! If the parts are not the same size, it does not correctly represent a fraction.

Unit fractions in different shapes

Unit fractions can be represented using circles, rectangles, squares, and other basic shapes. The shape of the whole does not change the value of the fraction.

Examples in models:
  • A circle split into 2 equal halves; 1 part shaded = 12.
  • A rectangle split into 4 equal columns; 1 column shaded = 14.
  • A square split into 8 equal small squares; 1 small square shaded = 18.
Note

The same unit fraction, like 14, can look different depending on the shape of the whole and how it is divided, but it always means the same amount: one out of four equal parts.

Common unit fractions from 12 to 18

These are the unit fractions most commonly used in models. Knowing their names and what they look like is essential.

Fraction list and meaning:
  • 12 (one-half): The whole is split into 2 equal parts.
  • 13 (one-third): The whole is split into 3 equal parts.
  • 14 (one-fourth): The whole is split into 4 equal parts.
  • 15 (one-fifth): The whole is split into 5 equal parts.
  • 16 (one-sixth): The whole is split into 6 equal parts.
  • 17 (one-seventh): The whole is split into 7 equal parts.
  • 18 (one-eighth): The whole is split into 8 equal parts.
Note

As the denominator gets larger, the size of each unit fraction piece gets smaller because the whole is split into more parts.

Using unit fraction language

When you describe a model showing a unit fraction, use precise language to connect the visual to the number.

Describe the model:
  • "This circle is divided into three equal parts. One part is shaded. This shows the unit fraction one-third, or 13."
  • "This rectangle is divided into eight equal rows. One row is shaded. This shows the unit fraction one-eighth, or 18."
Note

Always state that the parts are equal. Then name the total number of parts and the fact that one is selected. This will lead you to the correct unit fraction.