Math Concept Reader
Fun and Games Math Concept Reader ca37os_lay_070105ac_cr.indd 1 1/9/07 9:51:58 PM DIGITAL FINAL PROOF Fun and Games ca37os_lay_070105ac_cr.indd 2 1/9/07 9:51:58 PM DIGITAL FINAL PROOF Copyright © Gareth Stevens, Inc. All rights reserved. Developed for Harcourt, Inc., by Gareth Stevens, Inc. This edition published by Harcourt, Inc., by agreement with Gareth Stevens, Inc. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the copyright holder. Requests for permission to make copies of any part of the work should be addressed to Permissions Department, Gareth Stevens, Inc., 330 West Olive Street, Suite 100, Milwaukee, Wisconsin 53212. Fax: 414-332-3567. HARCOURT and the Harcourt Logo are trademarks of Harcourt, Inc., registered in the United States of America and/or other jurisdictions. Printed in the United States of America ISBN 13: 978-0-15-360185-9 ISBN 10: 0-15-360185-X 1 2 3 4 5 6 7 8 9 10 179 16 15 14 13 12 11 10 09 08 07 Fun and Games by Linda Bussell Math Concept Reader ca37os_lay_070105ac_cr.indd 1 1/9/07 9:51:59 PM DIGITAL FINAL PROOF Thursday is Game Day at Valley Elementary School. On game day, students play games, such as board games, after school. There are many different games to play. Each student finds a game to play. Sometimes players toss a coin to decide who takes the first turn. Some games use number cubes to decide game moves, while other games use spinners. Aaron and Natalie use number cubes in math class. They use coins and spinners, too. They use them for probability experiments. Aaron wonders whether the result of any toss or spin is as likely as any other. Chapter 1: Likely or Unlikely? ca37os_lay_070105ac_cr.indd 2 1/9/07 9:51:59 PM DIGITAL FINAL PROOF Natalie did an experiment in class this week. She tossed a coin and recorded which side landed face up. She repeated the experiment. She made a tally table of the results. The result of a toss or spin is called an outcome. A coin toss has two possible outcomes, heads and tails. Heads and tails are equally likely to occur, so they have the same probability. A fair coin is equally likely to land on heads or tails. The probability of heads is one out of two times. The probability of tails is also one out of two. Chapter 1: Likely or Unlikely? Valley Elementary students play games after school. ca37os_lay_070105ac_cr.indd 3 1/9/07 9:52:01 PM DIGITAL FINAL PROOF Experiment Results for 100 Two-color Counter Tosses Heads Tails Aaron says, “I did an experiment with a two-color counter. The coin toss is just like that.” He pulls a sheet of paper from his backpack. On the paper is a table that he made to record the results of the two-color counter experiment. Natalie agrees. The possible outcomes for the coin and counter are the same. Some students are about to play a game. Aaron and Natalie join them. “Are you ready to play?” asks Natalie. “I will toss a coin to see who goes first.” Chapter 2: More Likely A two-color counter has two possible outcomes. ca37os_lay_070105ac_cr.indd 4 1/9/07 9:52:03 PM DIGITAL FINAL PROOF Sometimes players toss number cubes to determine game moves. There is a number on each face of the cube that tells the players how many spaces to move a game piece. Some games use one number cube while other games use two. Tyler, Tanisha, and Austin play a game that uses one number cube. The outcome is the number of spaces a player moves a game piece. A cube has six sides that are each numbered. The possible outcomes are 1, 2, 3, 4, 5, and 6. There are no other possible outcomes. Chapter 2: More Likely ca37os_lay_070105ac_cr.indd 5 1/9/07 9:52:03 PM DIGITAL FINAL PROOF Experiment Results for Tossing One Number Cube 100 Times Outcome Tally Total 16 15 18 17 16 18 1 2 3 4 5 6 If the number cube is fair, the likelihood of any one outcome is equal to any other. There are six numbers on each cube. The likelihood of tossing any number is 1 out of 6. Austin says, “Let’s toss the number cube 100 times.” Tanisha draws a tally table. Tyler tosses the number cube, and it lands on the number 4. Tanisha makes a tally mark in the row for outcomes of 4. Tyler tosses the number cube again. Tanisha makes a tally mark in the row for outcomes of 1. They do this over and over again. Tanisha makes a tally table to record outcomes. ca37os_lay_070105ac_cr.indd 6 1/9/07 9:52:05 PM DIGITAL FINAL PROOF Austin says, “Look at the number of tallies for each outcome. The numbers are not equal. They are about the same.” Other students watch. They are interested in Austin’s experiment. Now they have more questions about probability. Mariela and Abigail play a game that uses two number cubes. Mariela wonders about the probability of tossing 2 sixes. “Figuring the possible outcomes for one number cube is easy,” Mariela says. “I can just count the number of sides. Figuring the possible outcomes with two number cubes is different. I cannot just count the number of sides.” Figuring out the possible outcomes of tosses using two number cubes is different than figuring out the outcomes of tosses using one number cube. ca37os_lay_070105ac_cr.indd 7 1/9/07 9:52:06 PM DIGITAL FINAL PROOF Experiment Results for Tossing Two Number Cubes 200 Times Outcome Tally Total 6 10 16 24 26 36 26 24 16 10 6 2 3 4 5 6 7 8 9 10 11 12 Abigail says, “Let’s do an experiment. We can toss two number cubes, and record the outcomes in a tally table.” The table will help us decide whether all possible outcomes are equally likely. “The outcome for two number cubes is the sum of the result for each cube. The possible outcomes are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12,” Mariela says. Abigail tosses the number cubes and Mariela records the toss outcomes. Abigail tosses and tosses. Mariela writes and writes. Abigail tosses the number cubes 200 times! Mariela records the outcomes of tosses using two number cubes. ca37os_lay_070105ac_cr.indd 8 1/9/07 9:52:07 PM DIGITAL FINAL PROOF [...]... chance of the pointer landing on any color is equally likely.” 10 ca37os_lay_070105ac_cr.indd 10 1/9/07 9:52:08 PM DIGITAL FINAL PROOF The probability of landing on blue with this spinner is 2 out of 4 Andrew has an idea He wants to make a new spinner to make the game more fun He draws a new spinner and divides it into four equal parts Andrew and Jared make two of the equal parts blue and none of the equal... red “We will be twice as likely to land on blue with this spinner,” says Andrew “The probability of landing on blue would be two out of four.” “Yes, and the probability of landing on red would be zero out of four since it is impossible to land on red,” says Jared 11 ca37os_lay_070105ac_cr.indd 11 1/9/07 9:52:08 PM DIGITAL FINAL PROOF The pointer is most likely to land on blue with this spinner Now Jared... idea He draws another spinner and colors the sections He makes the orange and yellow sections equal, but makes the blue section much larger than the other sections Jared asks Andrew, “Is it likely that the pointer will land in the blue section?” Andrew replies, “Yes! The blue section is larger than any other section It is most likely to land on blue It is less likely to land on yellow or orange.” “Yes,”... says, “Why don’t we make up our own games? We can use what we have learned about probability to make our games fair and fun! ” Jared says, “That’s a great idea, Mariela!” Austin says, “I want to make a spinner with numbers instead of colors It will have 12 equal spaces If the pointer lands on 2 through 12, the player’s piece moves that many spaces If the pointer lands on 1, the player has to start over!”... likely to land on yellow or orange.” “Yes,” says Jared, “but yellow and orange are equally likely because their areas are equal.” 12 ca37os_lay_070105ac_cr.indd 12 1/9/07 9:52:09 PM DIGITAL FINAL PROOF 1 Impossible 2 Likely 3 Certain 4 Unlikely The possible outcomes of landing on blue Jared and Andrew take turns drawing spinners They have fun designing new spinners for their game They work to decide whether... ca37os_lay_070105ac_cr.indd 9 1/9/07 9:52:08 PM DIGITAL FINAL PROOF Chapter 3: Fair Games Some of the games the students play use a spinner with a pointer on it The pointer determines where players can move their pieces on the game board Andrew and Jared play a game with a spinner that is divided into four equal parts Each part is a different color, and the colors match the spaces on the game board “This is a fair spinner... certain, likely, unlikely, or impossible for the pointer to land on orange? 3 Turn to page 13 Look at spinner number 4 If you were to spin the pointer 100 times, which color is it likely to land on most often? Why? Which color is the pointer likely to land on least often? Why? 4 Suppose you play a game with a spinner that 2 1 is 3 blue, and 3 yellow Are the outcomes equally likely? How could this spinner... that a given event will occur result data from conducting a survey or an experiment spinner a square or round base and pointer used in board games unlikely an outcome that does not have a good chance of happening 16 ca37os_lay_070105ac_cr.indd 16 1/9/07 9:52:13 PM DIGITAL FINAL PROOF Think and Respond 1 Suppose you have two number cubes Each cube has six faces numbered 1 through 6 What are the possible... to play math games! Next, Abigail tells everyone about her game idea It uses two number cubes “You get extra points for tossing 2 or 12 since those outcomes are the least likely,” she says Mariela says, “We can use the results from our experiment to decide how many points players should get for each toss The first player to score 100 points wins!” The students agree that this game sounds like fun! The...DIGITAL FINAL PROOF The girls see that some outcomes, like 6, 7, and 8, are more likely, while other outcomes, like 2 and 12, are less likely How can this be? Mariela says, “There is only one way to have an outcome of 12 The outcome of both number cubes must be 6.” Outcome of 12 Number Cube . Fun and Games Math Concept Reader ca37os_lay_070105ac_cr.indd 1 1/9/07 9:51:58 PM DIGITAL FINAL PROOF Fun and Games ca37os_lay_070105ac_cr.indd 2 1/9/07. parts. Andrew and Jared make two of the equal parts blue and none of the equal parts red. “We will be twice as likely to land on blue with this spinner,” says Andrew. “The probability of landing. of four.” “Yes, and the probability of landing on red would be zero out of four since it is impossible to land on red,” says Jared. 11 Chapter 3: Fair Games The probability of landing on blue