Lesson 12 Equivalent Fractions on a Number Line

- Let’s find fractions at the same location.

Warm-up Notice and Wonder: Running on a Trail

Boy running.

What do you notice? What do you wonder?

Tyler ran part of the length of a trail.
Han ran part of the length of the same trail.

Activity 1 Running Part of a Trail

Some students are running on a trail at a park. Decide if each pair of students ran the same distance.

You can use number lines if they are helpful to you.

Elena ran $\frac{3}{6}$ of the trail.
Han ran $\frac{1}{2}$ of the trail.
Jada ran $\frac{1}{4}$ of the trail.
Kiran ran $\frac{2}{8}$ of the trail.
Lin ran $\frac{2}{3}$ of the trail.
Mai ran $\frac{5}{6}$ of the trail.

Activity 2 Locate and Pair

Locate and label the following numbers on a number line. You can use more than one number line if you wish.

$\frac{1}{2}$ , $\frac{1}{3}$ , $\frac{1}{4}$ , $\frac{2}{3}$ , $\frac{2}{6}$ , $\frac{3}{8}$ , $\frac{3}{4}$ , $\frac{4}{6}$ , $\frac{4}{8}$ , $\frac{6}{8}$ , $\frac{7}{8}$
Find 4 pairs of fractions that are equivalent. Write equations to represent them.
$=$
$=$
$=$
$=$
If you have time… Use the number lines to generate as many equivalent fractions as you can.

Activity 3 Rolling for Equivalent Fractions

Roll 6 number cubes. If you roll any fives, they count as a wild card and can be any number you’d like.
Can you put the numbers you rolled in the boxes to make a statement that shows equivalent fractions? Work with your partner to find out.
If you cannot, re-roll as many number cubes as you’d like. You can re-roll your number cubes twice.
If you can make equivalent fractions, record your statement and show or explain how you know the fractions are equivalent. You get 1 point for each pair of equivalent fractions you write.

Round 1:

$\frac{}{} = \frac{}{}$

Show or explain how your fractions are equivalent.

Round 2:

$\frac{}{} = \frac{}{}$

Show or explain how your fractions are equivalent.

Round 3:

$\frac{}{} = \frac{}{}$

Show or explain how your fractions are equivalent.

Round 4:

$\frac{}{} = \frac{}{}$

Show or explain how your fractions are equivalent.

Round 5:

$\frac{}{} = \frac{}{}$

Show or explain how your fractions are equivalent.

Round 6:

$\frac{}{} = \frac{}{}$

Show or explain how your fractions are equivalent.

Round 7:

$\frac{}{} = \frac{}{}$

Show or explain how your fractions are equivalent.

Round 8:

$\frac{}{} = \frac{}{}$

Show or explain how your fractions are equivalent.

Practice Problem

Problem 1

Tyler draws this picture and says that $\frac{3}{4}$ is equivalent to $\frac{2}{3}$ . Explain why Tyler is not correct.
Find a fraction equivalent to $\frac{2}{3}$ .
Find a fraction equivalent to $\frac{3}{4}$ .