Lesson Plan: Adding Mixed Numbers

Lesson Plan: Adding Mixed Numbers

Lesson Summary

In this 50-minute lesson, students will learn how to add mixed numbers with both like and unlike denominators, with an emphasis on solving real-world problems. The lesson incorporates multimedia resources from Media4Math.com, including visual aids, interactive examples, and practice exercises to enhance comprehension. A 10-question quiz with an answer key is included to assess student understanding.

Lesson Objectives

  • Add mixed numbers with like and unlike denominators.
  • Solve real-world problems involving the addition of mixed numbers.
  • Understand and apply strategies for finding common denominators when necessary.

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 mixed numbers.
  • Adding fractions with like and unlike denominators.

Key Vocabulary

Multimedia Resources

 

 

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. 

  • Estimate the sum of two mixed numbers using the fraction calculator. 
  • With the Desmos calculator, use the round() formula.
  • Note the two ways of estimating the mixed number sums.

 

fractions

 

Have students try other combinations of mixed numbers.

Multimedia Slide Show

Use Media4Math’s Fraction Definitions Slide Show https://www.media4math.com/library/slideshow/fraction-definitions to introduce or review key fraction concepts.

Pizza Fractions Activity

Provide pizza fractions that model mixed numbers and ask students how to find the sum.

 

Fractions

Fractions

 

To see the collection of pizza fraction clip art images, go to this collection: https://www.media4math.com/MathClipArtCollection--EquivalentFractionModelsPizzaSlices

 

 

Teach

Concept Overview

Adding mixed numbers involves working with both whole numbers and fractions. When the fractions have like denominators, addition is straightforward—students simply add the whole numbers and then the fractions. However, when the fractions have unlike denominators, the process requires finding a common denominator. This step ensures that the fractions are expressed in equivalent forms with the same denominator, enabling addition. Understanding equivalent fractions and how to find a least common denominator (LCD) are foundational skills for success in this lesson. Real-world contexts, such as measurements in recipes or travel distances, help students connect abstract math concepts to practical applications.

Example 1: Adding Mixed Numbers with Like Denominators

Problem: \( 2 \frac{1}{4} + 3 \frac{2}{4} \)

  1. Add the whole numbers: \( 2 + 3 = 5 \).
  2. Add the fractions: \( \frac{1}{4} + \frac{2}{4} = \frac{3}{4} \).
  3. Combine: \( 5 + \frac{3}{4} = 5 \frac{3}{4} \).

Example 2: Adding Mixed Numbers with Unlike Denominators

Problem: \( 3 \frac{2}{5} + 2 \frac{1}{3} \)

  1. Find the least common denominator: The LCM of 5 and 3 is 15.
  2. Rewrite fractions: \( \frac{2}{5} = \frac{6}{15} \) and \( \frac{1}{3} = \frac{5}{15} \).
  3. Add the fractions: \( \frac{6}{15} + \frac{5}{15} = \frac{11}{15} \).
  4. Add the whole numbers: \( 3 + 2 = 5 \).
  5. Combine: \( 5 \frac{11}{15} \).

Example 3: Real-World Application: Distance Traveled

A hiker travels \( 4 \frac{1}{2} \) miles in the morning and \( 3 \frac{3}{4} \) miles in the afternoon. How far did they travel in total?

  1. Convert to fractions with a common denominator: \( 4 \frac{1}{2} = 4 \frac{2}{4} \), \( 3 \frac{3}{4} = 3 \frac{3}{4} \).
  2. Add the whole numbers: \( 4 + 3 = 7 \).
  3. Add the fractions: \( \frac{2}{4} + \frac{3}{4} = \frac{5}{4} = 1 \frac{1}{4} \).
  4. Combine: \( 7 + 1 \frac{1}{4} = 8 \frac{1}{4} \).

Example 4: Real-World Application: Landscaping

A landscaper spreads \( 5 \frac{2}{3} \) cubic yards of mulch in one garden and \( 4 \frac{5}{8} \) cubic yards in another. How much mulch did they use in total?

  1. Find the LCM of the denominators. The LCM of 3 and 8 is 24.
  2. Convert fractions to a common denominator: \( 5 \frac{2}{3} = 5 \frac{16}{24} \), \( 4 \frac{5}{8} = 4 \frac{15}{24} \).
  3. Add the whole numbers: \( 5 + 4 = 9 \).
  4. Add the fractions: \( \frac{16}{24} + \frac{15}{24} = \frac{31}{24} = 1 \frac{7}{24}\).
  5. Combine: \( 9 + 1 \frac{7}{24} = 10 \frac{7}{24} \).

Example 5: Real-World Application: Painting

A painter uses \( 2 \frac{3}{4} \) gallons of paint for one room and \( 3 \frac{2}{5} \) gallons for another. How much paint did they use in total?

  1. Find the LCM of 4 and 5: 20.
  2. Convert fractions to a common denominator: \( 2 \frac{3}{4} = 2 \frac{15}{20} \), \( 3 \frac{2}{5} = 3 \frac{8}{20} \).
  3. Add the whole numbers: \( 2 + 3 = 5 \).
  4. Add the fractions: \( \frac{15}{20} + \frac{8}{20} = \frac{23}{20} = 1 \frac{3}{20} \).
  5. Combine: \( 5 + 1 \frac{3}{20} = 6 \frac{3}{20} \).

Multimedia Resources

Here are some tutorial videos that provide additional examples: 

 

 

Review

Concept Overview

Reviewing the addition of mixed numbers reinforces the steps students learned during instruction. Focus on summarizing the process: add whole numbers, convert fractions to equivalent forms with a common denominator, add the fractions, and combine the results. Highlight the importance of simplifying fractions in the final answer. Real-world examples help students see the practical relevance of this skill, such as combining ingredient amounts in recipes or calculating total distances traveled.

Example 1: Adding Mixed Numbers

Problem: \( 5 \frac{3}{8} + 2 \frac{7}{8} \)

  1. Add the whole numbers: \( 5 + 2 = 7 \).
  2. Add the fractions: \( \frac{3}{8} + \frac{7}{8} = \frac{10}{8} = 1 \frac{2}{8} = 1 \frac{1}{4} \).
  3. Combine: \( 7 + 1 \frac{1}{4} = 8 \frac{1}{4} \).

 Example 2: Real-World Application: Gardening

A gardener combines \( 3 \frac{1}{4} \) pounds of soil with \( 5 \frac{2}{3} \) pounds of compost. How much total material is added?

  1. Convert fractions to a common denominator: \( 3 \frac{1}{4} = 3 \frac{3}{12} \), \( 5 \frac{2}{3} = 5 \frac{8}{12} \).
  2. Add the whole numbers: \( 3 + 5 = 8 \).
  3. Add the fractions: \( \frac{3}{12} + \frac{8}{12} = \frac{11}{12} \).
  4. Combine: \( 8 + \frac{11}{12} = 8 \frac{11}{12} \).

Example 3: Real-World Application: Cooking

A chef uses \( 1 \frac{3}{5} \) cups of cream for one recipe and \( 2 \frac{2}{3} \) cups of cream for another. How much cream is used in total?

  1. Convert fractions to a common denominator: \( 1 \frac{3}{5} = 1 \frac{9}{15} \), \( 2 \frac{2}{3} = 2 \frac{10}{15} \).
  2. Add the whole numbers: \( 1 + 2 = 3 \).
  3. Add the fractions: \( \frac{9}{15} + \frac{10}{15} = \frac{19}{15} = 1 \frac{4}{15} \).
  4. Combine: \( 3 + 1 \frac{4}{15} = 4 \frac{4}{15} \).

Multimedia Resources

 

 

Quiz

Directions: Solve each problem. Simplify your answers. Show your work.

  1. \( 1 \frac{2}{5} + 2 \frac{1}{5} \)
  2. \( 3 \frac{1}{6} + 4 \frac{5}{6} \)
  3. \( 5 \frac{2}{3} + 2 \frac{1}{2} \)
  4. \( 2 \frac{3}{4} + 3 \frac{1}{2} \)
  5. \( 7 \frac{5}{8} + 3 \frac{3}{8} \)
  6. \( 4 \frac{1}{3} + 5 \frac{2}{9} \)
  7. \( 6 \frac{1}{4} + 3 \frac{3}{4} \)
  8. \( 8 \frac{2}{5} + 2 \frac{1}{10} \)
  9. \( 5 \frac{1}{7} + 3 \frac{6}{7} \)
  10. A baker uses \( 2 \frac{1}{2} \) cups of flour for one recipe and \( 1 \frac{3}{4} \) cups for another. How much flour does the baker use in total?

Answer Key

  1. \( 3 \frac{3}{5} \)
  2. \( 7 \frac{1}{6} \)
  3. \( 7 \frac{5}{6} \)
  4. \( 6 \frac{1}{4} \)
  5. \( 11 \)
  6. \( 9 \frac{5}{9} \)
  7. \( 10 \)
  8. \( 10 \frac{1}{2} \)
  9. \( 8 \)
  10. \( 4 \frac{1}{4} \)