All Kinds of Numbers on the Number Line

10 min

Narrative

This Warm-up prompts students to compare four number lines. 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 number lines 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,” “halves,” “fourths,” or “whole.”

Launch

  • Groups of 2
  • Display the image.
  • “Pick 3 number lines 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
Number line. Tick marks at zero and one half, a point plotted at one half.

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

C
Number line. 0 to 1 with 3 evenly spaced tick marks between. First tick mark, 0. Last tick mark, 1.

D
Number line. Evenly spaced tick marks labeled zero, one, and two. Point plotted at the one.

Solution Steps (5)
  1. 1
    Examine number line A
    →Shows 0 and 1/2 with point at 1/2; length is about 1 unit
  2. 2
    Examine number line B
    →Shows 0 and 1 with point at 1; no partitions
  3. 3
    Examine number line C
    →Shows 0 to 1 partitioned into fourths (4 equal parts); no labeled point
  4. 4
    Examine number line D
    →Shows 0 to 2 with point at 1; partitioned
  5. 5
    Compare and categorize
    →Multiple valid groupings: A,B,C (length ~1), B,C,D (show 1), A,C,D (partitioned)

Sample Response

Sample responses:

A, B, and C go together because:
  • The length of the line is close to 1 unit.
A, B, and D go together because:
  • They have a labeled point.
A, C, and D go together because:
  • They are partitioned into multiple parts.
B, C, and D go together because:
  • They have 1 marked and labeled.
Activity Synthesis (Teacher Notes)
  • “How did you know that the number line in A has a length close to 1?” (The location of 12\frac{1}{2} shows that the number line is split in half right there, and I know that 2 halves is 1. I can fit only 1 more half next to the first half.)
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.

20 min