# Heads Up! A c t i v i t y 5. The Problem. Name Date

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1 . Name Date A c t i v i t y 5 Heads Up! In this activity, you will study some important concepts in a branch of mathematics known as probability. You are using probability when you say things like: It is impossible for me to meet you after school, I am certain that our book reports are due next Monday, or It is not likely that my parents will let me go to the game. Probability is used on the television or in the newspaper with statements like The chance of rain tomorrow is 60% or The chance of selecting a winning ticket for the lottery jackpot is 1 in 10,700,000. In all of these situations, a statement is being made about how sure we are that a particular event will or will not occur. The Problem You and a partner are going to toss a coin ten times, keep a record of the results of each toss, and write down the number of times that heads came up during the ten tosses. Decide which of you will toss the coin and which will keep record of the results. Before you begin tossing the coin, decide how many heads you think you will see over the ten coin tosses and how certain you are of your prediction. Answer #1 through #4 in the Questions section. You may want to spend some time discussing the statements listed above and others that the students generate. To help develop a probability sense, you may want to focus on benchmark probabilities of 0 (impossible), 50% or ½ (likely or possible), and 100% (certain). The common terms students will place with given probabilities are interesting; for example, It is not likely my parents will let me go to the game. What probability would your students assign to the phrase not likely. A 20% chance, a 50% chance? What is their probability sense?

7 Activity 5: Heads Up! Did the fractional part of the coins coming up heads get closer to ½ as more coins were tossed? Explain how you know. Is that what you expected to happen? How are the students determining that the fractions in L3, 14/20, 23/40, and so on, are close to ½? This is a good time to practice equivalent or benchmark fraction ideas. ) Return to page 43, Displaying a Graph.

8 48 Graphing Calculator Activities for Enriching Middle School Mathematics Problems for Additional Exploration 1. If a paper cup is dropped onto a flat surface it will land either on its bottom, its top, or its side. Bottom Side Top A fifth grade student tossed a paper cup several times and made a bar graph of the results. 15 Frequency of Outcomes trials of tossing the cup were carried out. Based upon these trials: P(Cup lands on Bottom) 5/30 = 1/6 P(Cup lands on Side) 15/30 = 1/2 P(Cup lands on Top) 10/30 = 1/3 These probabilities sum to 1. a. How many trials of the experiment did the student carry out? b. Based upon this student s experiment, what are the estimates for each of the following probabilities (where P equals Probability): P (Cup lands on Bottom): P (Cup lands on Side): P (Cup lands on Top): c. What is the sum of the three probabilities from part b?

9 Activity 5: Heads Up! 49 d. If another student were to toss a similar cup 120 times, about how many times would you expect the cup to land on its bottom? On its side? On its top? If 120 tosses were done, you would expect 20 to land on the bottom, 60 to land on the side, and 40 to land on the top. 2. If a thumbtack is dropped onto a hard flat surface, it will land either point up or point down. Point up Point down What probabilities do you think should be assigned to each of theses outcomes? Make a guess. Then design an experiment to approximate the experimental probability that a thumbtack will land point up. Results will vary depending upon the type of thumbtack used. The outcomes are not equally likely. For example, using a standard small-head thumbtack, we estimated the probability of the tack landing point up to be 0.7 (to the nearest tenth).

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