Join our community!

Update all PDFs

Locating Fractions Less than One on the Number Line


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

Task

  1. Mark and label the points $\frac14$, $\frac24$, $\frac34$, and $\frac44$ on the number line. Be as exact as possible.
  2. Task_statement_62f0d732f86601fec83c824677d56022
  3. Mark and label the point $\frac23$ on the number line. Be as exact as possible.
  4. Task_statement_62f0d732f86601fec83c824677d56022
  5. Mark and label the points $\frac12$, $\frac13$, $\frac14$, and $\frac15$ on the number line. Be as exact as possible.

Task_statement_62f0d732f86601fec83c824677d56022

IM Commentary

In every part of this task, students must treat the interval from 0 to 1 as a whole, partition the whole into the appropriate number of equal sized parts, and then locate the fraction(s). The first part asks them to specifically identify the coordinate of all the partitions they create in the process of finding the unit fraction, where as the other parts just ask them to attend to finding one fraction for a given partition. Some students may find it helpful to use separate number lines to complete the last part of this task.

Students learn to use the number line to represent whole numbers in second grade, but this is the first time they will use the number line to represent fractions.

Some may have difficultly creating equal sized intervals, especially for thirds and fifths. Providing strategies, such as folding a separate piece of paper, might be helpful.

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

  1. 1_21f130863b5014cd72fa12f5fe0f3a03
  2. 2_2098131ce44dd0dec60023d2db1a0fc9
  3. 3_e83e8499646bb961e809f0e1e1f92bfb

Yvonne says:

over 4 years

The CCSS clearly states that 3rd graders should work with denominators of 2, 3, 4, 6, and 8 only, why does this task require students to work with 5ths

Cam says:

over 4 years

Thanks for the comment, ydavidson.

The short answer is that the language of the CCSS was never intended to limit the discussions and activities that can take place in the classroom. There is nothing inherently abhorrent about introducing fifths into a 3rd grade classroom, only that educators and assessment-writers looking as to appropriate measures of evaluating student understanding of fractions in the third grade should restrict themselves to denominators of 2, 3, 4, 6, and 8.