Lesson 5 To the Number Line

    • Let’s learn about fractions on the number line.

Warm-up Notice and Wonder: Two Number Lines

What do you notice? What do you wonder?

Number lines.

Activity 1 Card Sort: Number Lines

Two students sorting cards.

Your teacher will give you a set of cards that show number lines. Sort the cards into categories of your choosing. Be prepared to explain the meaning of your categories.

A
Number line. Evenly spaced tick marks labeled 0 and 8 with one tick mark in between. First tick mark, 0. Last tick mark, 8.
B
Number line. 0 to 1 with 3 evenly spaced tick marks between. First tick mark, 0. Last tick mark, 1.
C
Number line. Evenly spaced tick marks 0 to 3 with a tick mark between each. First tick mark, 0. Last tick mark 3.
D
Number line. 0 to 2 with another tick mark between each number. First tick mark, 0. Last tick mark, 2.
E
Number line. Evenly spaced tick marks. First one, 0. Last one, 4. Three unlabeled tick marks between 0 and 4.
F
Number line. Tick marks at 0 and 1 with 5 unlabeled tick marks in between.
G
Number line. 0 to 6. First tick mark 0, two unlabeled tick marks, last tick mark, 6.
H
Number line. Evenly spaced tick marks 0 to 2 with two tick marks between 0 and 1 and two tick marks between 1 and 2. First tick mark, 0. Last tick mark, 2.
I
Number line. Evenly spaced tick marks labeled 0, 2, and 4, with 3 unlabeled tick marks between 0 and 2 and between 2 and 4.

Activity 2 Fold and Label the Number Line

Problem 1

Andre and Clare are talking about how to label fractions on the number line.

Andre says can be labeled like this:

Number line. Tick marks at 0 and 1 with an unlabeled tick mark in between. Two labels of one half below number line with no corresponding tick marks.

Clare says can be labeled like this:

Number line. Evenly spaced tick marks labeled zero, one half, and one. Point plotted at one half.

How could each student’s labeling make sense?

Problem 2

Your teacher will give you a set of number lines. Cut your number lines apart so that you can fold each one.

As you fold, discuss your strategies with your partner.

  1. Fold one of the number lines into halves. Draw tick marks to show the halves. Label the number .

  2. Fold one of the number lines into thirds. Draw tick marks to show the thirds. Label the number .

  3. Fold one of the number lines into fourths. Draw tick marks to show the fourths. Label the number .

  4. Fold one of the number lines into sixths. Draw tick marks to show the sixths. Label the number .

  5. Fold one of the number lines into eighths. Draw tick marks to show the eighths. Label the number .

Practice Problem

Problem 1

  1. Locate and label  on the number line. Explain your reasoning.

    Number line. Five evenly spaced tick marks, 0 and 1 labeled. First tick mark, 0. Last tick mark, 1.

  2. Locate and label  on the number line. Explain your reasoning.

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