Same Distance, Different Name: Equivalent Fractions on Number Lines

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4th GradeBTC Style / Thinking ClassroomsCCSS.MATH.CONTENT.4.NF.A.160 min

Learning Objective

Students will represent fractions on a number line and identify equivalent fractions by recognizing that equivalent fractions name the same point (same distance from 0), using multiplicative relationships between numerators and denominators.

Lesson Overview

Students progress from locating unit fractions on a number line to identifying and justifying equivalent fractions using a running distance context. Tasks change one variable at a time — from simple halves to complex comparisons like 3/4 and 9/12.

Materials

Vertical whiteboards or large paper on the wall
Dry-erase markers (different colors help)
Pencils and scratch paper for each student

Scaffolded Task Progression

1Task 1

Draw a number line from

0

1

. Split it into

4

equal parts. Label every tick mark with its fraction. Where does

\frac{3}{4}

land? Mark it with a dot and label it.

[ Interactive graph / diagram, available in the full lesson ]

2Task 2

Now draw a NEW number line from

0

1

directly below your first one. This time split it into

8

equal parts. Label every tick mark. Where does

\frac{6}{8}

land? Mark it.

Look at both number lines. What do you notice about where

\frac{3}{4}

and

\frac{6}{8}

are?

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