Locate Unit Fractions on the Number Line

10 min

Narrative

This Warm-up prompts students to compare four images. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology to talk about characteristics of the items in comparison to one another. During the discussion, ask students to explain the meaning of any terms they use, such as “parts,” “partitions,” “mark,” “label,” “thirds,” or “fourths.”

Launch

  • Groups of 2
  • Display the image.
  • “Pick 3 representations that go together. Be ready to share why they go together.”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 2–3 minutes: partner discussion
  • Share and record responses.

Student Task

Which 3 go together?

A
Diagram. Rectangle partitioned into 3 equal parts, 1 part shaded and labeled one third.

B
Number line. Tick marks labeled zero and one with two unlabeled tick marks in between.

C
Number line. Tick marks labeled zero and one. Point plotted at one third.

D
Number line. Evenly spaced tick marks. First tick mark, zero. Last tick mark, one. Three tick marks between zero and one, the first with a point labeled one fourth.

Solution Steps (5)
  1. 1
    Examine A - fraction strip
    →Rectangle with 3 equal parts, 1 shaded, labeled 1/3
  2. 2
    Examine B - number line
    →0-1 with 2 tick marks between (thirds), unlabeled
  3. 3
    Examine C - number line
    →Point plotted and labeled at 1/3
  4. 4
    Examine D - number line
    →4 parts (fourths), point at 1/4
  5. 5
    Group by thirds
    →A, B, C show thirds; D shows fourths

Sample Response

Sample responses:

A, B, and C go together because:
  • They show thirds or 13\frac{1}{3}.
A, B, and D go together because:
  • They are partitioned into equal-size parts.
A, C, and D go together because:
  • They have a label that is a fraction.
B, C, and D go together because:
  • They are number lines.
Activity Synthesis (Teacher Notes)
  • “To make your reasoning clear while locating and labeling fractions on a number line, what are some important things to include?” (Partitions of the equal parts, a dot and label at the fraction.)
  • “We learned in a previous lesson that we label fractions on the number line at the tick marks, just like we label whole numbers on the number line.”
  • “How is this different from the way we label our fraction strips, like in A?” (In diagrams of fraction strips, we label the part that has size or length 13\frac{1}{3}. On the number line, we label the location of the number 13\frac{1}{3}.)
Standards
Addressing
  • 3.NF.2·Understand a fraction as a number on the number line; represent fractions on a number line diagram.
  • 3.NF.A.2·Understand a fraction as a number on the number line; represent fractions on a number line diagram.

15 min

20 min