Math Background

Lesson: Probability
Introducing the Concept

Materials: 12 cardboard cards with the following letters: 4 with an A, 2 with an E, 2 with an I, 3 with an O, and 1 with a U

Prerequisite Skills and Concepts: Students should be able to simplify fractions.

  • Say: You have learned how to list all possible outcomes. Now you will learn how to express probability as a fraction.
  • Say: We have 12 cards, all the same size and shape, with the following letters printed on them: 4 with an A, 2 with an E, 2 with an I, 3 with an O, and 1 with a U. We will shuffle the cards and choose one at random.
    Write the following on the board to clarify the numbers for the students:
    A = 4
    E = 2
    I = 2
    O = 3
    U = 1.
  • Say: We will try to find the probability of choosing an E.
  • Ask: How many cards are there altogether? (12)
  • Ask: To write the probability as a fraction, what denominator do we use and why?
    Students should say “12,” because it represents the total number of outcomes or cards we could choose.
  • Ask: Out of 12 possible outcomes, how many favorable outcomes are there for “E?”
    Students should respond that there are 2 cards marked E and thus there are 2 favorable outcomes.
  • Say: So the numerator of the fraction is 2.
  • Say: The definition of probability is “the likelihood of an event occurring.” This is shown as the ratio of the number of favorable outcomes to the number of possible outcomes.
    Write the following on the board.
    probability equation
  • Ask: What fraction should we write for the probability of drawing an E? Students should respond with two-twelfths, or one-sixth. Remind students that when we express probability as a fraction, we write the fraction in simplest form.
  • Ask: If we shuffle all 12 cards again, what is the probability that we will draw a card with an O?
    Students should respond three-twelfths, or one-fourth.
  • Ask: What is the probability of drawing a card with a consonant on it?
    Students should respond that the probability is zero (zero-twelfths = 0), since the cards list only vowels. Therefore, it is impossible to draw a card with a consonant on it.
  • Ask: What is the probability of drawing a card with a vowel on it?
    Students should reply that the probability is 1, since all cards have vowels. (twelve-twelfths = 1) This is a certain event.
  • Ask: Is the probability of drawing an A or an E likely, unlikely, or equally likely?
    Students should respond that the drawing of an A or an E is equally likely. The number of favorable outcomes is 4 + 2, or 6, with a probability of 6 out of 12, or six-twelfths, which is one-half.

    Have students use a number cube marked 1, 3, 5, 7, 9, and 11. Have them find the probability of rolling the cube and having the following land faceup. Solutions are provided.

    1. 3—one-sixth
    2. number less than 10—five-sixths
    3. number between 2 and 6—one-third
    4. number less than 34—1
    5. number greater than 4 and less than 11—one-half

Houghton Mifflin Math Grade 5