Lesson Plan: Adding Fractions with Like Denominators

Lesson Plan: Adding Fractions with Like Denominators

 

Lesson Summary

In this lesson, students will learn how to add fractions with like denominators and apply this knowledge to solve word problems. The lesson will include hands-on activities, multimedia resources from Media4Math.com, and guided examples to reinforce understanding. A 10-question quiz with an answer key will assess students’ comprehension.

Lesson Objectives

  • Add fractions with like denominators
  • Solve word problems involving addition of fractions with like denominators

Common Core Standards

  • CCSS.Math.Content.4.NF.3.a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Prerequisite Skills

  • Understanding of basic fractions and numerators/denominators
  • Ability to add whole numbers

Key Vocabulary

Multimedia Resources from Media4Math.com

 

 

Warm Up Activities

Choose from one or more of these activities:

Calculator Activity

Use any fraction calculator for this activity. Desmos.com has a freely available calculator.

  1. Distribute calculators to each student.
  2. Provide a set of simple fraction addition problems with like denominators, such as \(\frac{1}{4} + \frac{2}{4}\) and \(\frac{1}{3} + \frac{1}{3}\). Pick fractions whose sums are already in simplest form.
  3. Students calculate the sum of the numerators and confirm the results using the calculators.
  4. Facilitate a brief discussion about why only the numerators are added while the denominator stays the same. Emphasize that the denominator represents the size of the parts.
  5. Then have students add fractions whose sums are in simplest form. Have them account for the sum using the notion of common factors.
Fractions

 

Multimedia Slide Show

  • Display a slide show from Media4Math.com showing visual models of fraction addition using fraction bars and fraction circles. For example use this collection of pizza slice images: 

https://www.media4math.com/MathClipArtCollection--FractionModelsPizzaSlices

  • Pause after each slide to ask guiding questions like, “What do you notice about the denominators?” or “How do the numerators change?”
  • Encourage students to explain in their own words why the denominators remain consistent.

 

FractionsFractionsFractions

\(\frac{1}{4}\)

\(\frac{1}{4}\)

\(\frac{2}{4}\) = \(\frac{1}{2}\)

 

Hands-On Activity

  1. Provide each pair of students with a set of fraction circles or fraction bars.
  2. Assign problems such as \(\frac{1}{4} + \frac{2}{4}\) or \(\frac{1}{8} + \frac{5}{8}\).
  3. Have students physically combine the fractions using the manipulatives, aligning the pieces to ensure they represent a single whole.
  4. Conclude by having a few pairs share their solutions and explain their process.

 

Fraction BarsFractions

\(\frac{1}{4} + \frac{2}{4}\ = \frac{3}{4}\)

\(\frac{1}{4} + \frac{1}{2}\ = \frac{3}{4}\)

 

 

Teach

Introduction: Explain that adding fractions with like denominators is similar to adding whole numbers, as long as the denominators remain the same. Use fraction bars and a number line to demonstrate how fractional parts add up.

Key Concepts:

  • Fractions with the same denominators can be added by adding their numerators while keeping the denominator unchanged.
  • This method works because the fractions represent parts of the same whole.

Here is the step-by-step procedure for adding fractions with like denominators:

  • Step 1: Write the fractions being added, ensuring that they have the same denominator.
  • Step 2: Add the numerators (the top numbers) together.
  • Step 3: Keep the denominator the same (do not add or change it).
  • Step 4: Simplify the fraction if possible (e.g., divide the numerator and denominator by their greatest common factor).
  • Step 5: If the result is an improper fraction, decide whether to leave it as is or convert it to a mixed number as needed.

 

Example 1: Adding Simple Fractions

Problem: Add \(\frac{2}{6} + \frac{3}{6}\).

  1. Write the fractions: \(\frac{2}{6} + \frac{3}{6}\).
  2. Because the denominators are the same, add the numerators: \(2 + 3 = 5\).
  3. The denominator remains the same: \(6\).
  4. Final answer: \(\frac{5}{6}\).

In this example, the fractions have the same denominator and the sum is a fraction in simplest form. 

Example 2: Adding Fractions and Simplifying

Problem: Add \(\frac{1}{4} + \frac{2}{4}\).

  1. Write the fractions: \(\frac{1}{8} + \frac{3}{8}\).
  2. Because the denominators are the same, add the numerators: \(1 + 3 = 4\).
  3. The denominator remains the same: \(8\).
  4. Sum: \(\frac{4}{8}\). This is not in simplest form.
  5. Simplify: \(\frac{1}{2}\)

In this example, the fractions have the same denominate and the sum is further simplified.

Example 3: Real-World Application

Problem: Combine \(\frac{1}{4}\) cup of oil with \(\frac{3}{4}\) cup of milk for a recipe.

 

FRACTIONS

 

  1. Write the fractions: \(\frac{1}{4} + \frac{3}{4}\).
  2. Because the denominators are the same, add the numerators: \(1 + 3 = 4\).
  3. The denominator remains the same: \(4\).
  4. Sum: \(\frac{4}{4}\). This is not in simplest form.
  5. Simplify: 1 cup

Example 4: Adding Pizza Slices

Problem: You and your friend each have leftover pizza slices. You have \(\frac{5}{6}\) of a pizza, and your friend has \(\frac{4}{6}\) of a pizza. If you combine your leftovers, how much pizza do you have in total?

 

FractionsFractions

 

Visually, you can see that these two fractional amounts will result in a fraction greater than 1.

  1. Write the fractions: \(\frac{5}{6} + \frac{4}{6}\).
  2. Because the denominators are the same, add the numerators: \(5 + 4 = 9\).
  3. The denominator remains the same: \(6\).
  4. Final answer: \(\frac{9}{6}\), which is an improper fraction, or a fraction greater than 1. 

Based on the illustrations, can you tell how to write the equivalent mixed number?

Example 5: Adding Juice

Problem: A recipe calls for \(\frac{7}{8}\) of a cup of orange juice and \(\frac{5}{8}\) of a cup of pineapple juice. If you mix the two juices, how much juice do you have in total?

 

Fractions

 

  1. Write the fractions: \(\frac{7}{8}\) + \(\frac{5}{8}\).
  2. Because the denominators are the same, add the numerators: \(7 + 5 = 12\).
  3. The denominator remains the same: \(8\).
  4. Final answer: \(\frac{12}{8}\), which is an improper fraction. It can also be written as the mixed number 1\(\frac{1}{2}\)

Additional Multimedia Resources

 

 

Review

Revisit key concepts:

Let’s begin by revisiting the key vocabulary and their definitions:

  • Like denominators: Fractions that have the same denominator, meaning the parts being added are of the same size.
  • Numerator: The top number of a fraction, representing how many parts are being considered.
  • Denominator: The bottom number of a fraction, representing the total number of equal parts in a whole.
  • Sum: The result of adding two or more numbers or fractions together.

Here is the step-by-step procedure for adding fractions with like denominators:

  1. Step 1: Write the fractions being added, ensuring that they have the same denominator.
  2. Step 2: Add the numerators (the top numbers) together.
  3. Step 3: Keep the denominator the same (do not add or change it).
  4. Step 4: Simplify the fraction if possible (e.g., divide the numerator and denominator by their greatest common factor).
  5. Step 5: If the result is an improper fraction, decide whether to leave it as is or convert it to a mixed number as needed.

 

Example 1: Adding Simple Fractions

Problem: Add \(\frac{2}{10} + \frac{5}{10}\).

  1. Write the fractions: \(\frac{2}{10} + \frac{5}{10}\).
  2. Because the numerators are the same, add the numerators: \(2 + 5 = 7\).
  3. The denominator is unchanged: \(10\).
  4. Final answer: \(\frac{7}{10}\).

This is an example in which the sum is already in simplest form.

Example 2: Adding Fractions

Problem: Add \(\frac{1}{6} + \frac{3}{6}\).

  1. Write the fractions: \(\frac{1}{6} + \frac{3}{6}\).
  2. Because the denominators are the same, add the numerators: \(1 + 3 = 4\).
  3. The denominator remains unchanged: \(6\).
  4. Final answer: \(\frac{4}{6}\) or \(\frac{2}{3}\).

This is an example in which the sum needs to be simplified.

Example 3: Adding Fractions

Problem: Add \(\frac{3}{8} + \frac{7}{8}\).

  1. Write the fractions: \(\frac{3}{8} + \frac{7}{8}\).
  2. Because the denominators are the same, add the numerators: \(3 + 7 = 10\).
  3. The denominator remains unchanged: \(8\).
  4. Final answer: \(\frac{10}{8}\), which is an improper fraction. This can also be written as the mixed number 1\(\frac{1}{4}\)

This is an example of a sum greater than 1, which can be written as an improper fraction or mixed number.

Additional Multimedia Resources 

 

 

Quiz

Directions: Add the following fractions. Simplify your answers when possible.

  1. \(\frac{1}{8} + \frac{3}{8}\)
  2. \(\frac{2}{5} + \frac{1}{5}\)
  3. \(\frac{4}{9} + \frac{5}{9}\)
  4. \(\frac{6}{12} + \frac{3}{12}\)
  5. \(\frac{7}{10} + \frac{2}{10}\)
  6. \(\frac{3}{8} + \frac{4}{8}\)
  7. \(\frac{3}{7} + \frac{2}{7}\)
  8. \(\frac{1}{6} + \frac{5}{6}\)
  9. \(\frac{2}{4} + \frac{2}{4}\)
  10. \(\frac{3}{10} + \frac{2}{10}\)

Answer Key

  1. \(\frac{4}{8}\) or \(\frac{1}{2}\)
  2. \(\frac{3}{5}\)
  3. \(\frac{9}{9}\) or \(1\)
  4. \(\frac{9}{12}\) or \(\frac{3}{4}\)
  5. \(\frac{9}{10}\)
  6. \(\frac{7}{8}\)
  7. \(\frac{5}{7}\)
  8. \(1\)
  9. \(\frac{4}{4}\) or \(1\)
  10. \(\frac{5}{10}\) or \(\frac{1}{2}\)