Lesson Plan: Review of Mixed Numbers

Lesson Summary

This 50-minute lesson focuses on reviewing the concept of mixed numbers, converting between mixed numbers and improper fractions, and comparing and ordering mixed numbers. Students will use multimedia resources from Media4Math.com to enhance their understanding. Activities include interactive demonstrations, hands-on exercises, and real-world applications. The lesson concludes with a 10-question quiz and an answer key.

Lesson Objectives

  • Understand the concept of mixed numbers.
  • Convert between mixed numbers and improper fractions.
  • Compare and order mixed numbers.

Common Core Standards

  • CCSS.Math.Content.4.NF.B.3.c: Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Prerequisite Skills

  • Understanding of fractions and improper fractions.
  • Basic arithmetic with whole numbers.

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.

  • Have students use calculators to convert between mixed numbers and improper fractions.
  •  Provide an example, such as converting \( 3 \frac{1}{2} \) to an improper fraction \( \frac{7}{2} \) and vice versa.

 

Fractions

 

Fraction Bars Activity

Use fraction bars to represent mixed numbers and improper fractions. For example \( 1 \frac{1}{2} \) is shown as both a mixed number and an improper fraction.

 

FractionsFractions

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

\( \frac{3}{2} \)

 

Number Line Activity

Use number lines to represent mixed numbers and proper fractions. For example \( 1 \frac{1}{3} \) is represented both ways on a number line. 

 

Fractions

 

\( 1 \frac{1}{3} \)

Fractions

\( \frac{4}{3} \)

 

 

Teach

In this lesson, students will focus on three main concepts: 

  • understanding mixed numbers, 
  • converting between mixed numbers and improper fractions, and 
  • comparing mixed numbers

Start by reviewing the definition of a mixed number and its two components: the whole number part and the fractional part. Emphasize how mixed numbers can be visualized using fraction bars or circles, which combine whole parts and fractions into a single representation.

Next, explain how mixed numbers and improper fractions are related, highlighting that any mixed number can be expressed as an improper fraction. Use step-by-step demonstrations to clarify this process, showing how the whole number part is converted to fraction form and added to the fractional part. Similarly, illustrate how improper fractions can be broken down into their mixed number equivalents.

Finally, introduce the concept of comparing mixed numbers. Explain that this often involves converting them to improper fractions or finding a common denominator. Use visual aids such as number lines to help students grasp the comparison process. This foundational understanding will prepare students to engage with the examples that follow.

Example 1: Converting a Mixed Number to an Improper Fraction

Convert \( 2 \frac{3}{4} \) to an improper fraction.

  • Multiply the whole number (\( 2 \)) by the denominator (\( 4 \)): \( 2 \times 4 = 8 \).
  • \( 2 \frac{3}{4} \) = \(\frac{8}{4} \) + \(\frac{3}{4} \)
  • Add the numerators: \( 8 + 3 = 11 \).
  • Place the result over the original denominator: \( \frac{11}{4} \).

Conclude: \( 2 \frac{3}{4} = \frac{11}{4} \).

Example 2: Converting an Improper Fraction to a Mixed Number

Convert \( \frac{11}{4} \) to a mixed number.

  • Divide the numerator by the denominator: \( 11 \div 4 = 2 R3 \).
  • Write the following:
    • The whole number part of the quotient: (\2\), 
    • The remainder as the numerator: (\3\), and 
    • The divisor as the denominator (\4\).

Conclude: \( \frac{11}{4} = 2 \frac{3}{4} \).

Example 3: Comparing Mixed Numbers

Compare \( 2 \frac{3}{4} \) and \( 2 \frac{1}{2} \).

  • Since the whole number parts are the same, compare the fractional parts.
  • We know that \(\frac{3}{4} \) > \(\frac{1}{2} \).

So \( 2 \frac{3}{4} > 2 \frac{1}{2} \).

Example 4: Mixing Ingredients

You are making a recipe that calls for \( 1 \frac{1}{2} \) cups of flour and \( 3 \frac{1}{4} \) cups of sugar. How much total flour and sugar is needed?

  • Convert both mixed numbers to improper fractions: \( 1 \frac{1}{2} = \frac{3}{2} \) and \( 3 \frac{1}{4} = \frac{13}{4} \).
  • Find a common denominator: \( \frac{3}{2} = \frac{6}{4} \) and \( \frac{13}{4} = \frac{13}{4} \).
  • Add the fractions: \( \frac{6}{4} + \frac{13}{4} = \frac{19}{4} \).
  • Convert back to a mixed number: \( \frac{19}{4} = 4 \frac{3}{4} \).

Total flour and sugar needed is \( 4 \frac{3}{4} \) cups.

Example 5: Distance Traveled

A person walks \( 2 \frac{2}{5} \) miles in the morning and \( 3 \frac{3}{5} \) miles in the evening. How many miles did they walk in total?

  • Convert both mixed numbers to improper fractions: \( 2 \frac{2}{5} = \frac{12}{5} \) and \( 3 \frac{3}{5} = \frac{18}{5} \).
  • Add the fractions: \( \frac{12}{5} + \frac{18}{5} = \frac{30}{5} \).
  • Simplify the fraction: \( \frac{30}{5} = 6 \).

Total distance walked is 6 miles.

Multimedia Resources

Here are some tutorial videos that provide additional examples: 

 

 

Review

Summary of Key Concepts:

  • A mixed number consists of a whole number and a fraction.
  • Mixed numbers can be converted to improper fractions by multiplying the whole number by the denominator, adding the numerator, and placing the result over the original denominator.
  • Improper fractions can be converted to mixed numbers by dividing the numerator by the denominator.

Key Vocabulary:

  • Mixed number: A number that includes both a whole number and a fraction.
  • Improper fraction: A fraction where the numerator is greater than or equal to the denominator.

Example 1: Converting an Improper Fraction

Convert \( \frac{17}{5} \) to a mixed number.

  • Divide the numerator by the denominator: \( 17 \div 5 = 3 R2\).
  • Write the quotient as the whole number (3), the remainder as the numerator (2), and the denominator unchanged (5).

Conclude: \( \frac{17}{5} = 3 \frac{2}{5} \).

Example 2: Converting a Mixed Number

Convert \( 4 \frac{1}{6} \) to an improper fraction.

  • Multiply the whole number (4) by the denominator (6): \( 4 \times 6 = 24 \).
  • Add the numerator (1): \( 24 + 1 = 25 \).
  • Place the result over the original denominator: \( \frac{25}{6} \).

Conclude: \( 4 \frac{1}{6} = \frac{25}{6} \).

Example 3: Real-World Problem

A runner completes \( 5 \frac{2}{3} \) miles on Monday and \( 4 \frac{1}{4} \) miles on Tuesday. How far did they run in total?

  • Convert both mixed numbers to improper fractions: \( 5 \frac{2}{3} = \frac{17}{3} \), \( 4 \frac{1}{4} = \frac{17}{4} \).
  • Find a common denominator: \( \frac{17}{3} = \frac{68}{12} \), \( \frac{17}{4} = \frac{51}{12} \).
  • Add the fractions: \( \frac{68}{12} + \frac{51}{12} = \frac{119}{12} \).
  • Convert to a mixed number: \( \frac{119}{12} = 9 \frac{11}{12} \).

Conclude: The runner ran \( 9 \frac{11}{12} \) miles in total.

Multimedia Resources

 

 

Quiz

Directions: Convert, compare, or analyze each of the following problems. Show all work.

  1. Convert \( 3 \frac{1}{4} \) to an improper fraction.
  2. Convert \( \frac{17}{5} \) to a mixed number.
  3. Compare \( 2 \frac{2}{3} \) and \( 3 \frac{1}{6} \). Write \( < \), \( > \), or \( = \).
  4. Convert \( 5 \frac{7}{8} \) to an improper fraction.
  5. Convert \( \frac{29}{6} \) to a mixed number.
  6. Compare \( 4 \frac{2}{5} \) and \( 4 \frac{3}{10} \). Write \( < \), \( > \), or \( = \).
  7. Convert \( 6 \frac{1}{3} \) to an improper fraction.
  8. Convert \( \frac{25}{8} \) to a mixed number.
  9. Compare \( 3 \frac{4}{9} \) and \( 3 \frac{5}{12} \). Write \( < \), \( > \), or \( = \).
  10. Convert \( 9 \frac{3}{7} \) to an improper fraction.

Answer Key

  1. \( \frac{13}{4} \)
  2. \( 3 \frac{2}{5} \)
  3. \( 2 \frac{2}{3} > 3 \frac{1}{6} \)
  4. \( \frac{47}{8} \)
  5. \( 4 \frac{5}{6} \)
  6. \( 4 \frac{2}{5} > 4 \frac{3}{10} \)
  7. \( \frac{19}{3} \)
  8. \( 3 \frac{1}{8} \)
  9. \( 3 \frac{4}{9} < 3 \frac{5}{12} \)
  10. \( \frac{66}{7} \)