Compare Shares of the Same Whole
Use two identical rectangles.
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: Two identical paper cards are split: one into two equal shares and one into four.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
Dividing the same whole into more equal shares makes each share smaller. One half of a particular rectangle is larger than one fourth of that same rectangle. This comparison depends on using equal wholes; different whole sizes could give a different physical result.
Use two identical rectangles. Partition one into halves and the other into fourths, then compare one piece of each. State the comparison only for the identical wholes in the supplied model.
Keep both wholes the same size in the model. A larger denominator means smaller equal pieces of the same whole. Shade one half and one fourth on two identical rectangles.
- Shade one half and one fourth on two identical rectangles.
- Follow the worked example. Point to each number or shape feature and say what it tells you.
- Use two identical rectangles.
- Try the question and then the three practice questions. Check your answers and explain any change you make.
See the method in action
Two identical paper cards are split: one into two equal shares and one into four. One half covers the area of two fourths. Thus a half is larger than a fourth of the same card. Comparing a tiny card with a large poster would not use the same whole. Keep both wholes the same size in the model. A larger denominator means smaller equal pieces of the same whole. Shade one half and one fourth on two identical rectangles.
Check your reasoning
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Helpful tips
- Keep both wholes the same size in the model.
- A larger denominator means smaller equal pieces of the same whole.
See the answer and explanation
One half
For the same whole, a half contains two fourths, so it is larger.
Take it further
Compare one fourth and one half of an identical circle. Expected: half is larger.
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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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