A Coin-Toss Experiment

Transcription

1 A Coin-Toss Experiment Objective To guide children as they develop intuition equally likely events. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Record the results of a coin-toss experiment. [Data and Chance Goal 1] Analyze results of a coin-toss experiment and draw conclusions equally likely results. [Data and Chance Goal ] Use the terms equally likely and fair to summarize the results of a coin-toss experiment. [Data and Chance Goal 3] Predict the outcome of a coin-toss experiment and test the prediction using coins. [Data and Chance Goal ] Key Activities Children perform a coin-toss experiment to confirm that some outcomes are equally likely. Ongoing Assessment: Recognizing Student Achievement Use journal page 98. [Data and Chance Goal 1] Key Vocabulary heads tails fair equally likely Materials Math Journal 1, p. 98 Home Link 9 Class Data Pad (optional) per partnership: 10 coins, carpet squares or blotters (optional) calculator half-sheet of paper Practicing Measuring Line Segments Math Journal 1, p. 99 ruler Children measure the line segments to the nearest 1_ inch, 1_ inch, and 1_ 8 inch. Math Boxes 10 Math Journal 1, p. 100 Children practice and maintain skills through Math Box problems. Home Link 10 Math Masters, p. 113 Children practice and maintain skills through Home Link activities. ENRICHMENT Making Predictions Rolling Dice Math Masters, p. 11 per partnership: 1 six-sided die Children roll a die to explore equally likely outcomes. ELL SUPPORT Building a Math Word Bank Differentiation Handbook, p. 13 Children add the term fair to their Math Word Banks. EXTRA PRACTICE Drawing a Scaled Bar Graph Math Journal 1, p. 98 Math Masters, p. 118A Children represent their coin-toss data on a scaled bar graph. Advance Preparation You may wish to gather carpet squares or blotters to reduce noise and bounce for the coin toss. Teacher s Reference Manual, Grades 1 3 pp. 116, 117, 10, 11 9 Unit Multiplication and Division

2 Getting Started Mathematical Practices SMP, SMP3, SMP6, SMP8 Content Standards 3.MD.3 Mental Math and Reflexes Pose multiplication facts. Suggestions: Math Message Maria and Joe toss a coin to decide who goes first when they play a game. Is this a fair way to decide? Explain why or why not on a half-sheet of paper. Home Link 9 Follow-Up Review answers and strategies. Point out that for many of the comparisons, it is not necessary to use the map scale to get a measurement. For example, in Problem 1 the scale is 1 inch = 300 miles. So, 1,000 miles is a little more than 3 inches. On the map, the distance from New York to Los Angeles is much more than 3 inches. Also, the distance from New York to Los Angeles is greater than the distance from Chicago to Dallas. 1 Teaching the Lesson Math Message Follow-Up WHOLE-CLASS Ask children whether they have seen a coin toss used to decide the order of play for games. Remind them that a coin has two different sides heads and tails. Have a volunteer demonstrate how to toss a coin to decide the order of play. 1. A player or official tosses a coin into the air.. Another player calls out either heads or tails while the coin is in the air. 3. If the player correctly calls the side that is faceup after the toss, then that player, or that player s team, wins the toss. If the player calls incorrectly, then the other player or team wins the toss.. The player or team that wins the toss chooses the order of play; for example, to play first or second, to serve or receive. Use the following questions to prepare children for the coin-toss experiment. What are all of the possible outcomes of tossing a coin? It will land either heads up or tails up. How likely is a coin to land heads up? To land tails up? Most children will say that heads and tails are equally likely or that each of these outcomes has the same chance. One objective of this lesson is to collect coin-tossing results that should convince children that heads and tails are equally likely outcomes. Lesson 10 9

3 Date 10 Coin-Toss Experiment Work with a partner. You need 10 coins. 1. You will each toss all 10 coins times. For each toss you make, record the number of HEADS and the number of TAILS in the table. Toss Record Toss HEADS TAILS (10 coins). Use the information in both your partner s and your tables to fill in the blanks below. My total: HEADS TAILS My partner s total: HEADS TAILS Our partnership total: HEADS TAILS 3. Record the number of HEADS and the number of TAILS for the whole class. Number of HEADS: Number of TAILS:. Suppose a jar contains 1,000 pennies. The jar is turned over. The pennies are dumped onto a table and spread out. Write your best guess for the number of HEADS and TAILS. Time Sample answers: Number of HEADS: 00 Number of TAILS: 00 Math Journal 1, p. 98 Student Page 1 3 Total Is tossing a coin a fair way to determine the order of play? Possible responses: The person who calls heads or tails does it when the coin is in the air, so he or she can t know how it will land. It is fair. The coin lands heads up as often as it lands tails up. So, the one who calls it will be right half the time. That s fair. I ve seen them toss like this to start football games. They wouldn t do it this way if it were not fair to both sides. NOTE Fair means that each player has an equal chance of winning. Sometimes children misinterpret fair to mean that one player has a better chance of winning. Conducting and Analyzing a Coin-Toss Experiment (Math Journal 1, p. 98) PARTNER PROBLEM SOLVING Tell children that they are going to conduct a coin-toss experiment to determine whether heads and tails are equally likely. Partners share 10 coins. They take turns tossing all 10 coins times. For each turn, they shake 10 coins and drop them one foot above a surface. (A carpet sample or blotter is an ideal surface for this activity.) Children count the number of coins landing heads up and the number landing tails up. They each record the results of their own coin tosses in the table at the top of journal page 98. Children calculate the total number landing heads up from all five tosses and the total number landing tails up. Ask them to check their calculations by adding the two totals: (total heads up) + (total tails up) should equal 0. Finally, partnerships combine totals for heads and tails. The combined number should equal 100. Ongoing Assessment: Recognizing Student Achievement Journal Page 98 Problem 1 Use journal page 98 Problem 1 to assess children s progress toward collecting and organizing data. Children are making adequate progress if they are able to complete the Toss Record chart. Some children may be able to draw conclusions from their own and their partner s tables. [Data and Chance Goal 1] 96 Unit Multiplication and Division

4 Each partnership calls out the numbers of heads and tails for their 100 tosses, and you record the results on the board or Class Data Pad. You and the children use calculators to find the total number of heads and the total number of tails for the entire class. Children record the class totals in Problem 3 on the journal page. Date 10 Use your ruler to measure each line segment. 1 Measure to the nearest inch. 1. inches Student Page Time Measuring Line Segments Heads Total: 86 Tails Total: 1. 1 inches 3. 1 inches Try This 1 Measure to the nearest inch inches. 3 inches Measure to the nearest 1 8 inch inches Sample class data The class totals should show nearly equal numbers of heads and tails, confirming children s intuition that these results are equally likely. Help them summarize the results. Use language such as, We got nearly equal numbers of heads and tails, Heads and tails are equally likely, and You get heads on 1 out of tosses if you toss a lot. Math Journal 1, p. 99 Ongoing Learning & Practice Practicing Measuring Line Segments (Math Journal 1, p. 99) INDEPENDENT Children measure the line segments on journal page 99. This page reviews content covered in Lesson 3-3. Lesson 10 97

5 Date 10 Math Boxes marbles are shared equally. Each child gets marbles. How many children are sharing? Use counters to solve. (unit) How many marbles are left over? 3. What is the perimeter of the rectangle? 1 in. 3 children 3 marbles in. The perimeter is 68 in.. (unit). Write the number that has hundreds 7 thousands 8 ones tens ten-thousands 7,8 Read it to a partner. Student Page (unit) 73 Time. Is a 6-sided die more likely to land on an odd number or on an even number? Explain. Sample answer: Neither. A 6-sided die has 3 even and 3 odd numbers. There is an equal chance of landing on either.. Complete the Fact Triangle. Write the fact family. 6 6, Use,, or.,001 1,00,001 1,00,001,100 0,10 0,10 Math Boxes 10 (Math Journal 1, p. 100) INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson -8. The skills in Problems and 6 preview Unit content. Home Link 10 (Math Masters, p. 113) INDEPENDENT Home Connection Children play the game Rock, Paper, Scissors with someone at home. They tally wins and losses and tell whether they think the game is fair. Remind children that fair means that all players have an equal chance of winning Math Journal 1, p. 100 Home Link Master Name Date Time HOME LINK 10 A Fair Game? Family Family The class Note is exploring text probability. Play Rock, Paper, Scissors with your child. After 0 rounds, Note Please have your return child this decide Home Link whether to school the game tomorrow. is fair and tell you why or why not. (A game is fair if all players have an equal chance of winning or losing.) Please return this Home Link to school tomorrow. Play the game Rock, Paper, Scissors with someone at home. Play at least 0 times. Keep a tally of wins and losses. Rock, Paper, Scissors Materials players hands Players Object of the Game To choose a hand position that beats your partner s choice. rock paper scissors Directions 1. Each player hides one hand behind his or her back and puts it in the rock, paper, or scissors position.. One player counts, One, two, three. 3. On three, both players show their hand positions.. Players choose the winner according to these rules. py g g p Rock dents scissors. Paper covers rock. Rock wins. Paper wins. If both players show the same position, no one wins. Scissors cut paper. Scissors wins. 1. Is this a fair game? (Fair means each player has the same chance of winning.) yes. On the back of this paper, explain why or why not. Math Masters, p Unit Multiplication and Division

6 3 Differentiation Options ENRICHMENT Making Predictions Rolling Dice (Math Masters, p. 11) PARTNER 1 Min To apply children s knowledge of equally likely results, have them explore the outcomes of rolling a die. Begin by discussing what it means to say that a die is fair. The die is equally likely to land on any side for each roll. Have children complete Math Masters, page 11. When they have finished the page, discuss their predictions and their results. ELL SUPPORT SMALL-GROUP Building a Math Word Bank (Differentiation Handbook, p. 13) 1 Min Name Date Time 10 Making Predictions Rolling Dice Think how you would know that a die is fair. Sample answers: 1. Make predictions. If you roll the die 30 times, which number will come up the most? How many times might you roll a? Explain how you made your predictions. Answers vary. I might roll it times. Since there are 6 numbers on the die, each one might come up times in 30 rolls.. Roll a die 30 times. Use tally marks to record your results in the table below. Number Times Rolled 1 Answers vary Compare your results with your predictions. Answers vary.. Do you think your die is fair? Teaching Master Explain. Sample answer: Yes, each number has an equal chance of being rolled. Math Masters, p. 11 To provide language support for probability, have children use the Word Bank template found on Differentiation Handbook, page 13. Ask children to write fair, draw a picture representing the term, and write other related words. See the Differentiation Handbook for more information. EXTRA PRACTICE Drawing a Scaled Bar Graph (Math Journal 1, p. 98; Math Masters, p. 118A) PARTNER 1 Min To provide experience with creating graphs, have children use Math Masters, page 118A to draw scaled bar graphs representing their coin-toss data. They may select either the heads data or the tails data from the Toss Record on journal page 98. Remind children to label the vertical axis with intervals of. Name Date Time 10 Graphing a Data Set Make a bar graph for your set of data. Title: Teaching Master Sample answer: Number of Heads for Each Toss Number of Heads Toss Number Math Masters, p. 118A Lesson 10 99

7 Name Date Time 10 Graphing a Data Set Make a bar graph for your set of data. Title: Copyright Wright Group/McGraw-Hill 118A