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Closest to 1/2


Alignments to Content Standards: 3.NF.A.2

Task

Which number is closest to \frac12?

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  1. \frac18

  2. \frac38

  3. \frac78

  4. \frac98

IM Commentary

How students tackle the problem and the amount of work they show on the number line can provide insight into the sophistication of their thinking. As students partition the interval between 0 and 1 into eighths, they will need to recognize that \frac12 = \frac48. Students who systematically plot every point, even \frac98, which is larger even than 1 may still be coming to grips with the relative size of fractions.

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?

Solutions

Solution: Finding \frac18 Intervals

(b) is correct.

Many students will mark off eighths in order to see that \frac38 is closest to \frac12.

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(So that we can see both perspectives at the same time, note that the middle tickmark has been labelled with both of the equal representations \frac{4}{8} and \frac{1}{2}.)

Solution: \frac38 is halfway between \frac14 and \frac12

(b) is correct.

A student who recognizes that \frac12=\frac48 and that of the choices, \frac38 is closest might just mark
\frac14=\frac24 halfway between 0 and \frac12 and then mark \frac38 halfway between \frac14 and \frac12.

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