What fraction is at the third mark after zero when 0 to 1 is divided into five equal intervals?
Incorrect answer: 3/6
Four equal intervals require five boundary marks including 0 and 1. Counting marks instead of spaces creates the wrong fraction.
Counting number-line marks instead of intervals
The denominator counts equal spaces in one whole. The zero mark is a starting point, not an extra part.
The correction
3/5
Each step is one fifth; three steps make three fifths.
- Locate zero and one to establish the size of a whole.
- Divide that interval into the denominator’s number of equal spaces.
- Count spaces from zero, not tick marks. Continue beyond one when the numerator is larger than the denominator.
Try the reasoning in another example
Where is 5/4?
- Four quarter-spaces reach 1.
- Move one more quarter-space.
Answer: 1 1/4
Explain why each step preserves the quantity or relationship. If you can compute the answer but cannot explain the step, revisit the model before adding more questions.
The short check below reuses the first example as a retrieval question and adds a second question. It checks this method; it does not establish a grade level.
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