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Identify thirds

Understanding thirds means recognizing that a whole, length, area, or set has been divided into three equal parts, with each part representing one third, written 13\frac{1}{3}; three one-thirds make one whole. The learner identifies thirds in visual and number-line representations and distinguishes equal thirds from three unequal parts, without extending to fraction operations or more advanced equivalence and generalization.

Detailed Explanation: Identify thirds

To identify thirds, check that a whole is split into 3 equal parts.

  • Each equal part is called one third, written 13\frac{1}{3}.
  • The three parts together make one whole:
13+13+13=1\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=1

Example: What fraction of this rectangle is shaded?

ShadedNot shadedNot shaded
13\frac{1}{3}13\frac{1}{3}13\frac{1}{3}
  1. Count the parts. There are 3 parts.
  2. Check their sizes. The parts are equal.
  3. Therefore, the rectangle is divided into thirds.
  4. One part is shaded, so the shaded part is 13\frac{1}{3}.

On a number line, thirds divide the distance from 00 to 11 into 3 equal spaces:

0—13—23—10 \quad\text{—}\quad \frac{1}{3} \quad\text{—}\quad \frac{2}{3} \quad\text{—}\quad 1

The points 13\frac{1}{3} and 23\frac{2}{3} make three equal sections. If the three parts were different sizes, they would not be thirds.

Learn by doing: Identify thirds

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    Fractions Thirds - Which Set Makes a Whole

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