Lesson Plan: Finding Common Denominators

Lesson Summary

This 50-minute lesson focuses on finding common denominators and using them to create equivalent fractions, addressing CCSS.Math.Content.5.NF.A.1. Students will explore strategies to find common denominators through hands-on activities, visual aids, and real-world applications. Multimedia resources from Media4Math.com are integrated into the lesson, including video tutorials and slide shows. The lesson concludes with a 10-question quiz and an answer key for assessment.

Lesson Objectives

  • Find common denominators for pairs of fractions.
  • Use common denominators to create equivalent fractions.

Common Core Standards

CCSS.Math.Content.5.NF.A.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

Prerequisite Skills

  • Understanding of equivalent fractions.
  • Multiplication of whole numbers.
  • Least common multiple (LCM).

Key Vocabulary

  • Common denominator
    A common multiple of the denominators of two or more fractions.
  • Least common denominator (LCD)
    The smallest common denominator for a set of fractions.

Multimedia Resources 

 

 

Warm Up Activities

Choose from one or more of these activities.

Spreadsheet Activity

Use a spreadsheet to generate multiples. Here is a model of what you can use to create a template.

 

Fractions

 

  • Ask them to calculate and list the multiples of two given numbers, such as 6 and 8. Here is the spreadsheet data using the template above.

 

Multiples

 

  • Have students circle the smallest common multiple from their lists. 
  • Continue with other multiple pairs.
  • Afterward, facilitate a class discussion to explore patterns in the multiples and emphasize the importance of finding the least common multiple (LCM) when working with fractions.

Multimedia Slide Show

Present a slide show with images of fraction bars and number lines to visually demonstrate how fractions with different denominators can be represented. Pause after each slide to ask students questions, such as, “What would the common denominator be for these fractions?” or “How could we rewrite these fractions?” Use this activity to connect visual representations to abstract concepts.

 

FractionsFractions

 

Refer to this booklet for printable fraction bars:

https://www.media4math.com/library/76897/asset-preview

 

Hands-On Activity

Distribute sets of fraction strips to pairs of students. Assign them to work collaboratively to match pairs of fractions with different denominators (e.g., \( \frac{1}{3} \) and \( \frac{1}{4} \)). Encourage them to overlap the fraction strips to identify a common length (denominator) visually. Once they’ve matched several pairs, hold a group discussion where students share their findings and methods for determining the common denominators.

 

Teach

In this section, students will dive deeper into the process of finding common denominators and their importance in adding or subtracting fractions with unlike denominators. Begin by explaining the concept of denominators and why they need to be common for accurate fraction operations. Use diagrams, visual aids, and real-world examples to make these concepts relatable and engaging.

Additional Instructional Content:

  • Using Visual Models: Start with a review of fraction bars and area models to show how fractions can be partitioned into equal parts. Emphasize that equivalent fractions represent the same value but have different numerators and denominators.
  • Interactive Number Line Activity: Demonstrate on a number line how fractions with different denominators can be scaled to have a common denominator. Show the fractions \( \frac{1}{3} \) and \( \frac{1}{4} \) on a number line, and then plot their equivalents \( \frac{4}{12} \) and \( \frac{3}{12} \).
  • Importance of the Least Common Denominator (LCD): Explain how the LCD simplifies the process of fraction operations by minimizing the complexity of calculations. Use examples to show why finding the smallest shared denominator is more efficient.
  • Real-Life Connection: Relate the concept of common denominators to real-life scenarios, such as measuring ingredients in cooking or splitting bills among friends with different contributions.

Key Concepts:

  1. Common denominators allow fractions to be rewritten as equivalent fractions with the same denominator.
  2. The LCD is the smallest shared denominator that simplifies calculations.

Example 1: Common Denominators Using Fraction Bars

Find a common denominator for \( \frac{1}{3} \) and \( \frac{1}{4} \). 

  • Visualize fraction bars for \( \frac{1}{3} \) and \( \frac{1}{4} \). 

 

Fractions

 

  • You can pare this solution with listing multiples of 3 and 4:
    • 3: 3, 6, 9, 12
    • 4: 4, 8, 12
  • Identify 12 as the smallest common multiple and have students count the number of fractional amounts in the twelfths fraction bar. 
  • Rewrite fractions as \( \frac{4}{12} \) and \( \frac{3}{12} \).

Example 2: Common Denominators Using Number Lines

Find the common denominator for \( \frac{1}{5} \) and \( \frac{1}{2} \). 

  • Graph each fraction on a separate number line.

 

Fractions

 

  • Identify a number line that can acommodate both fractions.

 

Fractions

 

  •  Rewrite fractions as \( \frac{2}{10} \) and \( \frac{5}{10} \).

Example 3: Finding the LCD for Two Fractions

Find the common denominator for \( \frac{2}{5} \) and \( \frac{3}{6} \). 

  • Start by listing the multiples of 5 and 6:
    • 5: 5, 10, 15, 20, 25, 30
    • 6: 6, 12, 18, 24, 30
  • The LCM is 30. This becomes the LCD for a common denominator.
  • Rewrite \( \frac{2}{5} \) as \( \frac{12}{30} \) and \( \frac{3}{6} \) as \( \frac{15}{30} \).

Example 4: Finding the LCD for Three Fractions

Find a common denominator for \( \frac{1}{2} \), \( \frac{1}{3} \), and \( \frac{1}{4} \). 

  • List the multiples of 2, 3, and 4:
    • 2: 2, 4, 6, 8, 10, 12)
    • 3: 3, 6, 9, 12
    • 4: 4, 8, 12
  • The LCM is 12. This becomes the LCD for a common denominator.
  • Rewrite \( \frac{1}{2} \) as \( \frac{6}{12} \), \( \frac{1}{3} \) as \( \frac{4}{12} \), and \( \frac{1}{4} \) as \( \frac{3}{12} \).

Example 5: Real-world Application: Recipes

A recipe calls for \( \frac{1}{3} \) cup sugar and \( \frac{1}{4} \) cup honey. Find a common denominator to combine measurements. 

  • Identify the LCD of 3 and 4 (12). 
  • Rewrite as \( \frac{4}{12} \) and \( \frac{3}{12} \), respectively. 
  • The total is \( \frac{7}{12} \).

Summary of Teach section: Students learned to find common denominators using fraction bars, area models, and real-world contexts. They practiced rewriting fractions as equivalent fractions with common denominators.

Multimedia Resources 

 

 

Review

In this section, we will consolidate the key ideas from the lesson and revisit the techniques used to find common denominators. Finding the least common denominator (LCD) is critical for adding or subtracting fractions with unlike denominators. By identifying the least common multiple (LCM) of the denominators, we ensure that fractions are represented with equivalent values, making operations straightforward. Throughout the lesson, students practiced using number lines, area models, and real-world applications to reinforce their understanding of equivalent fractions and the importance of common denominators in mathematical reasoning. This review ties together those concepts and prepares students to apply them independently.

Let’s also take a moment to revisit the vocabulary terms essential to this topic. Understanding these terms strengthens conceptual knowledge and ensures precision when discussing fraction operations.

Review key vocabulary:

  • Common denominator: A common multiple of the denominators of two or more fractions.
  • Least common denominator (LCD): The smallest common denominator for a set of fractions.

Example 1: Finding the LCM

Compare \( \frac{3}{8} \) and \( \frac{1}{6} \) by finding the least common multiple (LCM) of their denominators. 

  • List the multiples of 8 and 6:
    • 8: 8, 16, 24, 32
    • 6: 6, 12, 18, 24 
  • The LCM is 24, which becomes the least common denominator (LCD). 
  • Rewrite \( \frac{3}{8} \) as \( \frac{9}{24} \) and \( \frac{1}{6} \) as \( \frac{4}{24} \). 

Example 2: Using area models for visual understanding

Compare \( \frac{2}{5} \) and \( \frac{1}{2} \) by finding the least common multiple (LCM) of their denominators. 

  • List the multiples of 5 and 2: 
    • 5: 5, 10, 15
    • 2: 2, 4, 6, 8, 10
  • The LCM is 10, which becomes the least common denominator (LCD). 
  • Rewrite \( \frac{2}{5} \) as \( \frac{4}{10} \) and \( \frac{1}{2} \) as \( \frac{5}{10} \). Draw two area models, dividing one into 5 parts and the other into 2 parts, then further partition each into 10 equal parts. Shade \( \frac{4}{10} \) and \( \frac{5}{10} \) to visually confirm equivalency and their relationship to the LCD.

Multimedia Resources 

 

 

Quiz

Directions: Write your answers on the lines provided. Show all work.

  1. Find a common denominator for \( \frac{1}{3} \) and \( \frac{1}{5} \).
  2. Rewrite \( \frac{3}{4} \) and \( \frac{2}{5} \) with a common denominator.
  3. Identify the least common multiple of 6 and 8.
  4. Use fraction strips to find a common denominator for \( \frac{2}{7} \) and \( \frac{3}{9} \).
  5. Rewrite \( \frac{5}{6} \) and \( \frac{7}{10} \) as fractions with the same denominator.
  6. What is the LCD of \( \frac{1}{8} \) and \( \frac{1}{12} \)?
  7. Compare \( \frac{3}{10} \) and \( \frac{4}{15} \) by finding a common denominator.
  8. Rewrite \( \frac{4}{9} \) and \( \frac{5}{12} \) as fractions with a common denominator.
  9. Real-world: Combine \( \frac{1}{3} \) cup sugar and \( \frac{1}{4} \) cup honey. What is the total?
  10. Find the common denominator for \( \frac{1}{2} \), \( \frac{1}{3} \), and \( \frac{1}{4} \).

Answer Key

  1. 15
  2. 15/20 and 8/20
  3. 24
  4. 63
  5. 50/60 and 42/60
  6. 24
  7. 9/30 and 8/30
  8. 48/108 and 45/108
  9. 7/12
  10. 12