Partition a Whole into Equal Halves or Fourths
Read how many equal shares cover the whole.
About 15 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: A rectangle is split into four equal-width strips.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
Equal shares must cover the whole and have equal area. Two equal shares are halves; four equal shares are fourths or quarters. Simply cutting a shape into two pieces does not make halves unless the pieces have equal amounts of the whole.
Read how many equal shares cover the whole. Name each share as a half or fourth, and explain how many shares rebuild the whole. Use a rectangle with equal-width strips as a checkable model.
Check equal area, not only the number of pieces. Unequal pieces do not all receive the same fraction name. Draw equal-width strips inside the same-size rectangle.
- Draw equal-width strips inside the same-size rectangle.
- Follow the worked example. Point to each number or shape feature and say what it tells you.
- Read how many equal shares cover the whole.
- Try the question and then the three practice questions. Check your answers and explain any change you make.
See the method in action
A rectangle is split into four equal-width strips. Each strip is one fourth of the rectangle. All four strips rebuild the whole. If one strip were wider, the pieces would not be four equal shares, so calling each a fourth would be inaccurate. Check equal area, not only the number of pieces. Unequal pieces do not all receive the same fraction name. Draw equal-width strips inside the same-size rectangle.
Check your reasoning
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Helpful tips
- Check equal area, not only the number of pieces.
- Unequal pieces do not all receive the same fraction name.
See the answer and explanation
A half
Two equal shares make halves.
Take it further
Split one rectangle into two equal strips and another into four. Expected names: halves and fourths.
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More practice: try new cases
Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.
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Check the subject sources
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