Teacher Guide: Fractions on a Number Line

🎯 Learning Objective 5-10 min lesson

Students will: Represent and identify fractions on a number line by understanding that fractions are formed when a whole (the interval from 0 to 1) is partitioned into equal parts.

Why this matters for FAST: Number line questions appear frequently on FAST. Students must identify fractions on number lines, place fractions correctly, and compare fractions using number lines.

📦 Materials Needed

Whiteboard/projector
Student Concept Worksheet
Paper strips (for folding)
Colored pencils/crayons
Ruler (optional)
Number line printout

⚠️ Common Misconceptions to Address

Misconception #1: Counting Tick Marks Instead of Spaces

Students count the lines/marks instead of the intervals between them. They may label a point as 3/4 when it should be 2/3.

How to Address:

"Count the SPACES, not the lines. How many equal parts is the whole divided into? That's your denominator. Now count how many spaces from 0 to the point. That's your numerator."

Misconception #2: Larger Denominator = Larger Fraction

Students think 1/8 is larger than 1/4 because 8 > 4. They apply whole number thinking to fractions.

How to Address:

"If you share a pizza with 8 people, do you get more or less than if you share with 4 people? Less! More parts means smaller pieces."

📝 Lesson Steps

1

Activate Prior Knowledge (1 min)

Draw a number line with 0 and 1. Ask: "What numbers could go between 0 and 1?" Accept responses. Explain that fractions are numbers that fit between whole numbers.

2

Introduce the Concept (2 min)

SAY THIS:

"When we put fractions on a number line, we divide the space between 0 and 1 into EQUAL parts. The denominator tells us how many equal parts. The numerator tells us how many parts to count from 0."

3

Model with Paper Strip (2 min)

Give students a paper strip. Have them fold it into 4 equal parts. Unfold and label 0 at left edge, 1 at right edge. Mark the folds as 1/4, 2/4, 3/4. Point out: "The folds create the spaces. We count spaces, not folds."

4

Guided Practice (2-3 min)

Draw a number line divided into 3 equal parts. Place a dot at the first mark after 0. Ask:

"How many equal parts?" (3) → "That's our denominator."
"How many spaces from 0 to the dot?" (1) → "That's our numerator."
"What fraction is this?" (1/3)

5

Independent Practice

Distribute the Student Concept Worksheet. Monitor for the misconceptions above. For students who finish early, have them create their own number line showing thirds.

✅ Check for Understanding

Quick Exit Ticket (Ask the whole class):

Draw a number line from 0 to 1 with 6 equal parts. Point to the 4th mark.

Ask: "What fraction is at this point?"

Correct answer: 4/6 (Students should recognize 6 equal parts = denominator of 6, 4 spaces from 0 = numerator of 4)

💻 IXL Skills to Assign After This Lesson

Recommended IXL Practice:

Unit fractions on number lines Identify fractions on number lines Graph fractions on number lines Graph fractions less than 1 on number lines

🏠 Differentiation & Extension

For struggling students: Use only halves and fourths. Have them physically fold paper strips before drawing number lines.

For advanced students: Introduce fractions greater than 1 on number lines (e.g., 5/4). Have them find equivalent fractions using number lines (e.g., show 2/4 = 1/2).

For home: Send Parent Activity sheet. Parents can use measuring cups (1/4, 1/2, 3/4 cup) to connect fractions to real life.