Lesson Plan: Fractions on a Number Line

Lesson Objectives

• Students will be able to represent fractions on a number line.
• Students will be able to identify and plot fractions on a number line.

Common Core Standards

• 3.NF.A.2 - Understand a fraction as a number on the number line; represent fractions on a number line diagram. 

Prerequisite Skills

• Understanding of fractions (Review lesson 1 as necessary: https://www.media4math.com/library/76927/asset-preview)
• Familiarity with number lines

Key Vocabulary

• Number line: A horizontal line used to mark numerical quantities.
• Fraction: A number representing part of a whole.
• Numerator: The top number in a fraction, representing the number of parts.
  • Multimedia Resource: https://www.media4math.com/library/42906/asset-preview
  • Multimedia Resource: https://www.media4math.com/library/74783/asset-preview
• Denominator: The bottom number in a fraction, representing the total number of equal parts in the whole.
  • Multimedia Resource: https://www.media4math.com/library/42907/asset-preview
  • Multimedia Resource: https://www.media4math.com/library/74764/asset-preview

Multimedia Resources

• Math Definitions Collection: Fractions https://www.media4math.com/Definitions--Fractions
• Math Video Definitions Collection: Fractions https://www.media4math.com/MathVideoCollection--FractionsVocabulary
• Slideshow: Fraction Definitions https://www.media4math.com/library/slideshow/fraction-definitions

Warm Up Activities

Choose from one or more activities.

Activity 1: Estimating Whole Numbers

Look at the number line below. Without counting tick marks, estimate the whole number represented by the red point.

Write your estimate as a whole number and then compare with a partner. Explain how you arrived at your answer.

Activity 2: Fill in the Missing Numbers

The number line below has some tick marks. Fill in the blanks with the correct whole numbers:

Now repeat with this number line.

Discuss your answers with a partner and explain how you determined the missing numbers.

Activity 3: Number line modeling activity

• Use this slide show to demonstrate different fraction number lines: https://www.media4math.com/library/slideshow/fraction-number-lines
• Show them a blank number line and ask them to divide the number line into equal parts (e.g., halves, thirds, fourths).
• Have students label the fractions on the number line.

Teach

Relating Fractions to the Number Line Model

• Start by showing whole number being graphed on a number line. Use this slide show: https://www.media4math.com/library/slideshow/graphing-whole-numbers-number-line
• Explain that a number line is for graphing numbers.
• Since fractions can be graphed on a number line, reinforce that fractions are another type of number (different from whole numbers, but still numbers).
• Show how fractions can be represented on a number line by dividing the line into equal parts. Refer back to the fraction number lines shown earlier: https://www.media4math.com/library/slideshow/fraction-number-lines

Plotting Fractions on Number Lines

• Use this slide show to present graphing whole numbers on a number line and how fractions are graphed: https://www.media4math.com/library/slideshow/fractions-and-whole-numbers-number-line
• Model how to plot fractions on a number line by counting the number of parts indicated by the numerator and marking the corresponding point on the line.
• Provide examples with different denominators (e.g., halves, thirds, fourths) and have students plot the fractions on their own number lines.

Example 1: Plotting a Fraction on a Number Line

Let’s plot $\frac{3}{4}$ on a number line.

1. Draw a number line and mark the whole numbers 0 and 1.
2. Divide the segment between 0 and 1 into four equal parts because the denominator is 4.
3. Count three parts from 0 and place a point at $\frac{3}{4}$.

Example 2: Plotting an Improper Fraction

Now, let’s graph $\frac{4}{3}$.

1. Since 7 is greater than 3, convert it to a mixed number: $\frac{4}{3} = 1 \frac{1}{3}$.
2. Draw a number line and mark whole numbers 0, 1, and 2.
3. Divide each whole number segment into three equal parts (denominator = 3).
4. Count seven parts from 0 and mark the point at $\frac{4}{3}$, which is one-third past 1.

Example 3: Comparing Two Fractions on a Number Line

Let’s compare $\frac{2}{5}$ and $\frac{3}{5}$ by plotting them.

1. Draw a number line and label 0 to 1.
2. Divide the segment into five equal parts.
3. Mark $\frac{2}{5}$ by counting two parts and $\frac{3}{5}$ by counting three parts.
4. Since $\frac{3}{5}$ is to the right of $\frac{2}{5}$, we see that $\frac{3}{5}$ is larger.

Example 4: Real-World Example – Measuring with a Ruler

A carpenter needs to cut a piece of wood that is $\frac{5}{8}$ of a foot long. Let’s plot $\frac{5}{8}$ on a number line.

1. Draw a number line from 0 to 1 (representing 1 foot).
2. Divide the segment into eight equal parts (since inches are often divided into eighths).
3. Count five parts from 0 and place a mark at $\frac{5}{8}$.
4. This shows the correct measurement for the cut.

Example 5: Real-World Example – Sharing a Pizza

A pizza is cut into six equal slices. If you eat four slices, what fraction of the pizza have you eaten?

1. Since the pizza is divided into 6 slices, the fraction is $\frac{4}{6}$, which simplifies to $\frac{2}{3}$.
2. Draw a number line from 0 to 1, representing a whole pizza.
3. Divide it into six equal sections.
4. Count four parts from 0 and mark the point at $\frac{4}{6}$ (or $\frac{2}{3}$).
5. This shows that you ate more than half of the pizza!

Review

Practice identifying fractions on a number line:

• Display a number line with various fractions plotted. Use this slide show: https://www.media4math.com/library/slideshow/fractions-number-lines
• Ask students to identify the fractions represented by different points on the line.
• Encourage students to explain their reasoning.

Example 1: Graphing a Fraction Less Than 1

Let’s review how to graph $\frac{4}{5}$ on a number line.

1. Draw a number line from 0 to 1.
2. Divide the space between 0 and 1 into five equal parts since the denominator is 5.
3. Count four parts from 0 and mark the point at $\frac{4}{5}$.

Example 2: Real-World Example – Filling a Water Bottle

A water bottle holds 1 liter when full. If you fill it up to $\frac{3}{4}$ of its capacity, where would that be on a number line?

1. Draw a number line from 0 to 1, representing the full bottle.
2. Divide it into four equal parts, since the denominator is 4.
3. Count three parts from 0 and place a mark at $\frac{3}{4}$.
4. This shows that the bottle is three-quarters full.

Example 3: Real-World Example – Running a Race

Emma is running a 1-mile race. She has completed $\frac{5}{8}$ of a mile. Let’s plot this on a number line.

1. Draw a number line from 0 to 1, representing the full mile.
2. Divide the section into eight equal parts, since the denominator is 8.
3. Count five parts from 0 and place a mark at $\frac{5}{8}$.
4. This shows that Emma has run more than half of the race.

Quiz

10-question quiz

1. Plot $\frac{1}{2}$ on the number line.
   
2. Plot $\frac{3}{4}$ on the number line.
   
3. Plot $\frac{2}{3}$ on the number line.
   
4. Identify the fraction represented by the point on the number line.
   
5. Identify the fraction represented by the point on the number line.
   
6. Plot $\frac{5}{6}$ on the number line.
   
7. Plot $\frac{1}{3}$ on the number line.
   
8. Plot $\frac{3}{5}$ on the number line.
   
9. Identify the fraction represented by the point on the number line.
   
10. Identify the fraction represented by the point on the number line.
    

Answers:

1. 1/2 should be plotted at the midpoint of the number line.
2. 3/4 should be plotted at the 3/4 mark on the number line.
3. 2/3 should be plotted at the 2/3 mark on the number line.
4. 1/4
5. 3/6 or 1/2
6. 5/6 should be plotted at the 5/6 mark on the number line.
7. 1/3 should be plotted at the 1/3 mark on the number line.
8. 3/5 should be plotted at the 3/5 mark on the number line.
9. 5/8
10. 4/6 or 2/3

Purchase the lesson plan bundle. Click here.