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Definitions/Error 1_ Unequal Segmentation.md

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+---
+title: 'Error 1: Unequal Segmentation'
+
+---
+
+# Error 1: Unequal Segmentation
+
+## Definition
+In representing a fraction a/b on a number line, unequal segments occur when the interval from 0 to 1 (or any whole-number span) is divided into subintervals of differing lengths; thus, not all parts represent the same fraction of the whole.
+
+As long as the length of the longest interval significantly differs from (about or more than twice as long as) the shortest or other intervals, the solution should be marked as “unequal segmentation”.
+
+## Example
+If showing 3/4, one interval is about twice as long as the shortest interval, even though there are four parts total.

Definitions/Error 2_ Wrong Number of Segments (Denominator).md

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+---
+title: 'Error 2: Wrong Number of Segments (Denominator)'
+
+---
+
+# Error 2: Wrong Number of Segments (Denominator)
+
+## Definition
+When representing a fraction a/b on a number line, a wrong number of segments occurs if the interval from 0 to 1 (or any whole-number span) is divided into a number of equal subintervals that is not equal to b.
+
+The total count of equal segments must match the denominator for the fraction to be correct.
+
+## Example
+If showing 3/4, but the segment from 0 to 1 is split into 3 or 5 equal parts instead of 4, we consider this error type to be the “wrong number of segments”, regardless of whether the parts are all equal in size.

Definitions/Error 3_ Wrong Number of Segments Chosen (Numerator).md

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+---
+title: 'Error 3: Wrong Number of Segments Chosen (Numerator)'
+
+---
+
+# Error 3: Wrong Number of Segments Chosen (Numerator)
+
+## Definition
+When representing a/b on a number line, this error occurs after the line has been correctly partitioned into b equal subintervals per unit, but the number of consecutive subintervals selected, shaded, or hopped from 0 is not a.
+
+## Example
+For 3/4, the unit is split into four equal parts (which is done correctly), but the student shades two parts, showing 2/4 instead of 3/4.

Definitions/Error 4_ Incorrect Tick Labels (Confused with Whole Numbers).md

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+---
+title: 'Error 4: Incorrect Tick Labels (Confused with Whole Numbers)'
+
+---
+
+# Error 4: Incorrect Tick Labels (Confused with Whole Numbers)
+
+## Definition
+When representing a/b on a number line, tick-mark labels are incorrect due to confusion with whole numbers if the marks are labeled as a simple list of whole numbers (e.g., 1, 2, 3, 4, …) across the unit interval, or as a “denominator sweep” (e.g., 1/2, 1/3, 1/4, 1/5, …) on the number line segment, instead of using a consistent scale tied to the chosen partition b.
+
+## What Correct Labeling Looks Like
+If the unit interval from 0 to 1 is partitioned into b equal parts, the tick at the k-th mark from 0 must be labeled k/b (for k = 0, 1, …, b).
+
+Beyond 1, mixed numbers with the same denominator should be used (e.g., 1 + k/b, 2 + k/b).
+
+## Example
+For 3/4, ticks should read: 0, 1/4, 2/4, 3/4, 1.
+
+Incorrect examples include:  
+0, 1, 2, 3, 4  
+or  
+0, 1, 1/2, 1/3, 1/4  
+or  
+0, 1/2, 1/3, 1/4.

Definitions/Error 5_ Incorrect Tick Labels (Careless).md

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+---
+title: 'Error 5: Incorrect Tick Labels (Careless)'
+
+---
+
+# Error 5: Incorrect Tick Labels (Careless)
+
+## Definition
+When representing a/b on a number line, a careless tick-mark labeling error occurs if the unit interval is correctly divided into b equal parts, but the tick at the k-th mark from 0 is not labeled as k/b (for k = 0, 1, …, b), and the mistakes are random with no consistent pattern (e.g., simple writing slips, skipped numbers, or swapped numerals).
+
+It is important that only one mistake is found in all fraction tick labels if the denominator is incorrect.
+
+## Key Features
+The partition is done correctly.  
+There is no systematic mislabeling (such as whole numbers or denominator sweeps).  
+Errors are likely due to inattention or copying mistakes rather than misunderstanding of the concept.
+
+## Example
+For 3/4, correct labels should be: 0, 1/4, 2/4, 3/4, 1.
+
+Careless mistake example:  
+0, 1/4, 2/3, 3/4, 1 (wrong denominator in just one place).

Definitions/Error 6_ Incorrect 0 or 1s.md

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+---
+title: 'Error 6: Incorrect 0 or 1s'
+
+---
+
+# Error 6: Incorrect 0 or 1s
+
+## Definition
+When representing a/b on a number line, this error occurs if:
+(a) the tick marks labeled 0/N and N/N (i.e., 0 and 1) do not coincide exactly with the number line’s physical endpoints for the interval, or  
+(b) the number line does not have any tick or label to indicate 0 or 1.
+
+The fraction labels 0/N and N/N should be placed exactly at the points representing 0 and 1.
+
+Misalignment means either the endpoint tick is missing, or the labeled tick is inside or outside the drawn unit span.
+
+## Example
+For 3/4, the number line ends at the tick for 1, but the label 4/4 is shifted left so it is not on the endpoint.
+
+Or, for 3/4, the number line ends at a blank space without a specific ending tick or mark of 0 or 1, and the 3/4 label is a long distance (significantly more than 1/4 of the number line segment) away from the end.

Definitions/Error 7_ Unit of 1 and Subunits.md

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+---
+title: 'Error 7: Unit of 1 and Subunits'
+
+---
+
+# Error 7: Unit of 1 and Subunits
+
+## Definition
+When representing a fraction a/b on a 0–N number line (N > 1), a correct solution is to divide the 0–N number line into N equal intervals to identify units of 1, and then divide the unit of 1 into b equal sub-units to represent the fraction unit of 1/b, and finally to identify the a-th sub-unit of 1/b to locate a/b.
+
+## Correct Example
+On a 0–4 number line, to identify 1/4, a student should divide the 0–4 number line into four equal units to represent 1s, then divide the 0–1 number line segment into four equal parts, and find 1/4.
+
+## Mistake Example
+On a 0–4 number line, a student divides the 0–4 number line into four intervals and labels the first interval tick as 1/4.