Locating Fractions Greater than One on the Number Line
Task
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Mark and label points on the number line for \frac12, \frac22, \frac32, \frac42, \frac52, and \frac62.
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Mark and label a point on the number line for \frac{11}{3}. Be as exact as possible.
IM Commentary
This first part of this task requires students to represent a fraction \frac{a}{b} on a number line diagram by marking off a intervals of length \frac1b (in this case \frac12) starting at 0.
Students may solve the second part of the task either by marking of 11 intervals of length \frac13 or by knowing that \frac{11}{3} is \frac23 of the way between 3 and 4. Although a few students may be able to do it using the later of these approaches, most students will identify all of the points related to \frac13, \frac23, \frac33, etc., even if they do not label those points.
The following lists related tasks in order of sophistication:
- Locating Fractions Less than One on the Number Line
- Locating Fractions Greater than One on the Number Line
- Closest to \frac12
- Find 1
- Find \frac23
- Which is Closer to 1?
Solution
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Here is one way to draw and label the number line for this task:
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Here is one way to draw and label the number line for this task:
Locating Fractions Greater than One on the Number Line
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Mark and label points on the number line for \frac12, \frac22, \frac32, \frac42, \frac52, and \frac62.
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Mark and label a point on the number line for \frac{11}{3}. Be as exact as possible.