---

 Lesson Plan: Comparing Fractions

---

 

Lesson Objectives:

• Students will be able to compare fractions with the same numerator or denominator by reasoning about their size.
• Students will be able to compare fractions with different numerators and denominators by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2.

Common Core Standards

• 3.NF.A.3.D - Compare two fractions with the same numerator or the same denominator by reasoning about their size.
• 4.NF.A.2 - Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2.

Prerequisite Skills

• Understanding fractions
• Familiarity with equivalence
• Modeling fractions visually

Key Vocabulary

• Comparing Fractions: Determining if one fraction is greater, less than, or equal to another fraction.
  • Multimedia Resource: https://www.media4math.com/library/43576/asset-preview
  • Multimedia Resource: https://www.media4math.com/library/74762/asset-preview
• Ordering Fractions: Arranging a set of fraction in order from least to greatest or greatest to least. 
  • Multimedia Resource: https://www.media4math.com/library/43581/asset-preview
  • Multimedia Resource: https://www.media4math.com/library/74784/asset-preview

Multimedia Resources

• Math Definitions Collection: Fractions https://www.media4math.com/Definitions--Fractions

 

---

 

Warm Up Activities

Activity 1: Number Line Comparisons

Place these fractions on a number line: $\frac{1}{4}$, $\frac{3}{4}$, $\frac{1}{2}$, $\frac{5}{8}$.

Discuss:

• Which fraction is larger?
• How does placement on the number line affect its value?

Activity 2: Balance Scale Model

Compare the fractions using a balance scale:

Which side is heavier when comparing $\frac{1}{3}$ and $\frac{1}{2}$?

Repeat with:

• $\frac{2}{5}$ vs. $\frac{1}{2}$
• $\frac{3}{8}$ vs. $\frac{5}{8}$

Activity 3: Desmos Fraction Calculator

Use the Desmos Calculator to compare fractions. We'll use $\frac{1}{2}$ as a benchmark fraction.

• Compare $\frac{3}{9}$ vs. $\frac{1}{2}$. How can you tell $\frac{3}{9}$ is less than $\frac{1}{2}$?
• Repeat with $\frac{4}{6}$ vs. $\frac{1}{2}$. 

 

 

---

 

Teach

Equivalent and Unit Fractions

Briefly review the concept of equivalent fractions and how to create equivalent fractions by multiplying or dividing the numerator and denominator by the same number.

Use this slideshow to review equivalent fractions.

https://www.media4math.com/library/slideshow/equivalent-fractions

Start by comparing unit fractions. Use this resource:

https://www.media4math.com/library/43519/asset-preview

Methods for Comparing

Introduce three methods for comparing fractions:

1. Visual Models: Show these examples of using number lines to compare fractions. Use this slideshow.
    https://www.media4math.com/library/slideshow/comparing-fractions-number-line-math-examples
2. Benchmark Fractions: Compare fractions to benchmark fractions like 1/2 or 1/4 to determine which is greater or less. Use this resource:
   https://www.media4math.com/library/43534/asset-preview
3. Common Denominators: Find a common denominator for the fractions and compare their numerators.
   1. Start by defining common denominators by using this video definition: https://www.media4math.com/library/74761/asset-preview
   2. Generate equivalent fractions to find the common denominator. Use this resource to review this technique: a href="https://www.media4math.com/library/slideshow/examples-generating-equivalent-fractions">https://www.media4math.com/library/slideshow/examples-generating-equivalent-fractions

Use this resource to show different strategies for comparing fractions:

https://www.media4math.com/library/64363/asset-preview

Example 1: Greater Than Comparison

Compare: $\frac{5}{6}$ and $\frac{3}{8}$

Step 1: Find the LCD

• The denominators are 6 and 8.
• Multiples of 6: 6, 12, 18, 24, 30, 36, ...
• Multiples of 8: 8, 16, 24, 32, 40, ...
• LCM(6,8) = 24, so the LCD = 24.

Step 2: Convert to Equivalent Fractions

• $\frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}$
• $\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}$

Step 3: Compare Numerators

Since $20 > 9$, we conclude:

$$\frac{5}{6} > \frac{3}{8}$$

Example 2: Less Than Comparison

Compare: $\frac{2}{7}$ and $\frac{3}{5}$

Step 1: Find the LCD

• The denominators are 7 and 5.
• Multiples of 7: 7, 14, 21, 28, 35, 42, ...
• Multiples of 5: 5, 10, 15, 20, 25, 30, 35, ...
• LCM(7,5) = 35, so the LCD = 35.

Step 2: Convert to Equivalent Fractions

• $\frac{2}{7} = \frac{2 \times 5}{7 \times 5} = \frac{10}{35}$
• $\frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35}$

Step 3: Compare Numerators

Since $10 < 21$, we conclude:

$$\frac{2}{7} < \frac{3}{5}$$

Example 3: Equal Fractions

Compare: $\frac{4}{9}$ and $\frac{8}{18}$

Step 1: Find the LCD

• The denominators are 9 and 18.
• Multiples of 9: 9, 18, 27, ...
• Multiples of 18: 18, 36, 54, ...
• LCM(9,18) = 18, so the LCD = 18.

Step 2: Convert to Equivalent Fractions

• $\frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{8}{18}$

Step 3: Compare Numerators

Since both fractions are equal, we conclude:

$$\frac{4}{9} = \frac{8}{18}$$

Example 4: Real-World Benchmark Fractions (Recipe Adjustment)

A recipe calls for $\frac{5}{8}$ cup of flour. Jamie only has a $\frac{1}{4}$ cup measuring tool. Can she measure exactly $\frac{5}{8}$ cup?

Step 1: Find the LCD

• The denominators are 8 and 4.
• Multiples of 8: 8, 16, 24, ...
• Multiples of 4: 4, 8, 12, 16, 20, ...
• LCM(8,4) = 8, so the LCD = 8.

Step 2: Convert to Equivalent Fractions

• $\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}$

Step 3: Use the Measuring Cup

• Jamie can use $\frac{1}{4}$ cup twice (which is $\frac{4}{8}$).
• Then add half of $\frac{1}{4}$ cup (which is $\frac{1}{8}$).

Since $\frac{4}{8} + \frac{1}{8} = \frac{5}{8}$, Jamie can measure exactly $\frac{5}{8}$ cup.

Example 5: Real-World Benchmark Fractions (Comparison Only)

Leo drank $\frac{5}{9}$ of his juice, while Mia drank $\frac{3}{7}$. Who drank more?

Step 1: Find the LCD

• The denominators are 9 and 7.
• Multiples of 9: 9, 18, 27, 36, 45, 54, 63, ...
• Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, ...
• LCM(9,7) = 63, so the LCD = 63.

Step 2: Convert to Equivalent Fractions

• $\frac{5}{9} = \frac{5 \times 7}{9 \times 7} = \frac{35}{63}$
• $\frac{3}{7} = \frac{3 \times 9}{7 \times 9} = \frac{27}{63}$

Step 3: Compare Numerators

Since $35 > 27$, we conclude:

$$\frac{5}{9} > \frac{3}{7}$$

Leo drank more juice than Mia.

 

---

 

Review

Introduce this game to review comparing fractions:

https://www.media4math.com/library/43544/asset-preview

Use this Quizlet Flash Card set to review comparing and ordering fractions:

https://www.media4math.com/library/26746/asset-preview

Example 1: Comparing Greater and Lesser Fractions

Compare: $\frac{7}{12}$ and $\frac{5}{9}$

Step 1: Find the LCD

• The denominators are 12 and 9.
• Multiples of 12: 12, 24, 36, 48, ...
• Multiples of 9: 9, 18, 27, 36, 45, ...
• LCM(12,9) = 36, so the LCD = 36.

Step 2: Convert to Equivalent Fractions

• $\frac{7}{12} = \frac{7 \times 3}{12 \times 3} = \frac{21}{36}$
• $\frac{5}{9} = \frac{5 \times 4}{9 \times 4} = \frac{20}{36}$

Step 3: Compare Numerators

Since $21 > 20$, we conclude:

$$\frac{7}{12} > \frac{5}{9}$$

Review Example 2: Equal Fractions

Compare: $\frac{9}{15}$ and $\frac{3}{5}$

Step 1: Find the LCD

• The denominators are 15 and 5.
• Multiples of 15: 15, 30, 45, ...
• Multiples of 5: 5, 10, 15, 20, 25, 30, ...
• LCM(15,5) = 15, so the LCD = 15.

Step 2: Convert to Equivalent Fractions

• $\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}$

Step 3: Compare Numerators

Since both numerators are equal, we conclude:

$$\frac{9}{15} = \frac{3}{5}$$

Review Example 3: Real-World Benchmark Fraction Comparison

Ava and Noah are reading books. Ava has read $\frac{3}{7}$ of her book, while Noah has read $\frac{4}{9}$ of his book. Who has read more?

Step 1: Find the LCD

• The denominators are 7 and 9.
• Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, ...
• Multiples of 9: 9, 18, 27, 36, 45, 54, 63, ...
• LCM(7,9) = 63, so the LCD = 63.

Step 2: Convert to Equivalent Fractions

• $\frac{3}{7} = \frac{3 \times 9}{7 \times 9} = \frac{27}{63}$
• $\frac{4}{9} = \frac{4 \times 7}{9 \times 7} = \frac{28}{63}$

Step 3: Compare Numerators

Since $28 > 27$, we conclude:

$$\frac{4}{9} > \frac{3}{7}$$

Noah has read more of his book than Ava.

 

---

 

Quiz

Answer the following questions.

1. Which fraction is greater, 1/3 or 1/4?
2. Compare 5/8 and 3/4 using a visual model.
3. Use a benchmark fraction to determine which is greater, 7/10 or 3/5.
4. Find a common denominator to compare 2/3 and 5/6.
5. Which fraction is less, 1/2 or 3/4?
6. Compare 7/9 and 5/9 by reasoning about their size.
7. Use a visual model to compare 1/6 and 1/3.
8. Find a common denominator to compare 3/8 and 5/12.
9. Which fraction is greater, 2/5 or 1/3?
10. Compare 7/13 and 6/17 using a benchmark fraction.

Answer Key

1. 1/3
2. 5/8 is less than 3/4
3. 7/10 is greater than 3/5
4. 8/12 and 10/12, so 5/6 is greater than 2/3
5. 3/4
6. 5/9 is less than 7/9
7. 1/3 is greater than 1/6
8. 9/24 and 10/24, so 5/12 is greater than 3/8
9. 2/5
10. 7/13 is greater than 6/17

Purchase the lesson plan bundle. Click here.