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 Lesson Plan: What Is a Fraction?

 

Lesson Objectives

  • Define and identify fractions as equal parts of a whole
  • Understand the meaning of numerator and denominator
  • Represent fractions using visual models
  • Partition shapes into equal parts and express the area of each part as a unit fraction

Common Core Standards Addressed

  • 3.NF.A.1 - Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
  • 3.G.A.2 - Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.

Prerequisite Skills

  • Understanding of whole numbers
  • Ability to partition shapes into equal parts

Key Vocabulary

Multimedia Resources

 

 

Warm Up Activities

Choose from one ore more activities.

Activity 1: Pizza Fraction Activity

Objective: Explore fractional amounts.

1.Display an unsliced pizza and various ways of slicing it. 

 

FractionsFractionsFractionsFractions

 

2. Use this slideshow: https://www.media4math.com/library/slideshow/slicing-pizzas

3. Divide the class into small groups of 3-4 students.

4. Ask the students to discuss how they would divide the pizza into equal slices so that everyone in the group gets a fair share.

5. Discuss as a class the challenges they faced in ensuring equal parts and the importance of fractions in fair sharing.

Activity 2: Fraction Number Line Hop

Objective: Introduce students to fractions on a number line through a physical movement game.

Instructions:

 

Fractions

 

  • Draw a large number line on the board or floor, labeling it from 0 to 1.
  • Divide sections between whole numbers into equal parts (e.g., \( \frac{1}{2} \), \( \frac{1}{3} \), \( \frac{1}{4} \)).
  • Call out a fraction (e.g., "Jump to 1/2!") and have students move to the correct location.
  • Discuss how fractions are positioned between whole numbers.

Activity 3: Fraction Hunt

Objective: Help students recognize fractions in everyday life.

Instructions:

  • Ask students to look around the classroom and find objects that can be divided into equal parts.
  • Examples include a pizza diagram, a set of books on a shelf, or the windows in the classroom.
  • Have students describe the objects using fractions. For example, "The window has 4 panes, so each pane is \( \frac{1}{4} \) of the whole window."
  • Discuss how fractions are used to describe parts of a whole.

Activity 4: Fishing for Fractions

This interactive game has students finding fish with equivalent fractions. Use this game for students who are already familiar with equivalent fractions.

https://www.media4math.com/library/4845/asset-preview

 

 

Teach

Defining Fractions

Modeling Fractions

  • Draw a circle on the board and divide it into equal parts (e.g., halves, thirds, fourths).
  • Label each part with the appropriate fraction (e.g., \( \frac{1}{2} \), \( \frac{1}{3} \), \( \frac{1}{4} \)).
  • Use the slide show from the previous section: https://www.media4math.com/library/slideshow/fraction-basics
  • Repeat the process with different shapes (e.g., rectangles, squares) to reinforce the concept.
  • Encourage students to identify and label the fractions represented by the shaded parts.
  • Review these fraction circle models and have students identify the denominator represented by each fractional part: https://www.media4math.com/library/slideshow/fraction-circles

Example 1: Understanding Fractions as Parts of a Whole

Scenario: You have a pizza with 8 slices. If you eat 3 slices, what fraction of the pizza have you eaten?

Solution:

  • The total number of slices is 8 (denominator).
  • The number of slices eaten is 3 (numerator).
  • The fraction of the pizza eaten is \( \frac{3}{8} \).
  • The remaining pizza fraction is \( \frac{5}{8} \).

Key Takeaway: Fractions represent a part of a whole, with the denominator showing the total number of parts and the numerator showing how many parts are considered.

Example 2: Fractions on a Number Line

Scenario: Mark the fraction \( \frac{3}{4} \) on a number line between 0 and 1.

Solution:

  • Divide the section between 0 and 1 into 4 equal parts.
  • Each part represents \( \frac{1}{4} \).
  • Starting from 0, count three parts to reach \( \frac{3}{4} \).

Key Takeaway: A fraction represents a point on a number line, showing its relative position between whole numbers.

Example 3: Equivalent Fractions

Scenario: Show that \( \frac{1}{2} \) is the same as \( \frac{2}{4} \) and \( \frac{3}{6} \).

Solution:

  • Start with a visual representation of \( \frac{1}{2} \) (e.g., shading half a circle or rectangle).
  • Divide the same shape into 4 equal parts and shade 2 of them: \( \frac{2}{4} \).
  • Divide it into 6 equal parts and shade 3 of them: \( \frac{3}{6} \).
  • Since all representations cover the same area, \( \frac{1}{2} \) = \( \frac{2}{4} \) = \( \frac{3}{6} \).

Key Takeaway: Equivalent fractions represent the same value, even if the numerator and denominator are different.

 

 

Review

Key Takeaways

  • A fraction represents a part of a whole.
  • The denominator tells how many equal parts make up the whole.
  • The numerator tells how many parts are being considered.
  • Fractions can be represented in different ways: as part of a shape, on a number line, or in real-world situations.
  • Equivalent fractions have the same value but different numerators and denominators.

Key Vocabulary

  • Fraction: A number that represents a part of a whole, written as a numerator over a denominator (e.g., \( \frac{3}{4} \)).
  • Numerator: The top number in a fraction that tells how many parts are being counted.
  • Denominator: The bottom number in a fraction that tells how many equal parts make up the whole.
  • Equivalent Fractions: Fractions that have different numerators and denominators but represent the same value (e.g., \( \frac{1}{2} \) = \( \frac{2}{4} \) = \( \frac{3}{6} \)).
  • Improper Fraction: A fraction where the numerator is greater than or equal to the denominator (e.g., \( \frac{9}{4} \)).
  • Mixed Number: A whole number combined with a fraction (e.g., 2 \( \frac{1}{2} \)).

Example 1: Comparing Fractions

Scenario: Which fraction is greater: \( \frac{3}{4} \) or \( \frac{2}{3} \)?

Solution:

  • Find a common denominator. The least common denominator of 4 and 3 is 12.
  • Convert the fractions:

    • \( \frac{3}{4} \) = \( \frac{9}{12} \)

    • \( \frac{2}{3} \) = \( \frac{8}{12} \)

  • Since \( \frac{9}{12} \) is greater than \( \frac{8}{12} \), we conclude that \( \frac{3}{4} \) is greater than \( \frac{2}{3} \).

Key Takeaway: To compare fractions, convert them to a common denominator and compare the numerators.

Example 2: Converting an Improper Fraction to a Mixed Number

Scenario: Convert \( \frac{7}{3} \) into a mixed number.

Solution:

  • Divide the numerator (7) by the denominator (3). The quotient is 2 with a remainder of 1.
  • The whole number part is 2.
  • The remainder 1 becomes the numerator, and the denominator stays the same.
  • So, 7/3 is equivalent to 2 \( \frac{1}{3} \).

Key Takeaway: To convert an improper fraction to a mixed number, divide the numerator by the denominator and express the remainder as a fraction.

Multimedia Resources

 

 

Quiz

Use the following quiz to assess students.

  1. What is a fraction?
    A. A fraction represents equal parts of a whole.
    B. A fraction is a whole number.
    C. A fraction is a type of measurement.
    D. A fraction is a type of shape.
  2. What does the numerator represent in a fraction?
    A. The total number of equal parts in the whole.
    B. The number of shaded parts.
    C. The number of equal parts being considered.
    D. The number of unshaded parts.
  3. What does the denominator represent in a fraction?
    A. The number of equal parts being considered.
    B. The total number of equal parts in the whole.
    C. The number of shaded parts.
    D. The number of unshaded parts.

  4. Which fraction represents the shaded portion of the circle below?

     

    Fractions

     

    A. \( \frac{1}{4} \)
     

    B. \( \frac{3}{4} \)
     

    C. \( \frac{1}{2} \)
     

    D. \( \frac{2}{4} \)

     

  5. If a rectangle is divided into 6 equal parts, and 3 parts are shaded, what fraction does it represent?


    A. \( \frac{3}{6} \)

    B. \( \frac{4}{6} \)

    C. \( \frac{2}{6} \)

    D. \( \frac{5}{6} \)
     
  6. Which of the following is NOT a fraction (or part of a whole)?

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

    B. \( \frac{5}{1} \)

    C. \( \frac{2}{5} \)

    D. \( \frac{7}{10} \)
     

  7. What fraction is represented by the shaded portion of the square below?
     

    Fraction

     

    A. \( \frac{5}{8} \)

    B. \( \frac{2}{8} \)

    C. \( \frac{3}{8} \)

    D. \( \frac{4}{8} \)
     

  8. If a circle is divided into 5 equal parts, and 2 parts are shaded, what fraction does it represent?

    A. \( \frac{1}{5} \)

    B. \( \frac{3}{5} \)

    C. \( \frac{4}{5} \)

    D. \( \frac{2}{5} \)
     

  9. Which of the following fractions represents the shaded portion of the rectangle below?
     

    Fractions

     

    A. \( \frac{4}{6} \)

    B. \( \frac{4}{8} \)

    C. \( \frac{4}{5} \)

    D. \( \frac{4}{7} \)
     

  10. If a square is divided into 10 equal parts, and 7 parts are shaded, what fraction does it represent?

    A. \( \frac{7}{10} \)

    B. \( \frac{3}{10} \)

    C. \( \frac{5}{10} \)

    D. \( \frac{8}{10} \)
     

Answer Key

  1. A
  2. C
  3. B
  4. D
  5. A
  6. B
  7. C
  8. D
  9. A
  10. A