Classroom Strategies Blackline Master Page 193 IV - 13

Are Spinners Really Random?

12

3 4

13

4 5

2

1

2

3

4 6

5

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Num

ber of Coins

Type of Coin

25

10

Spin to Win!

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Spin to Win!You are going to conduct an experiment in which you will spin both spinners and recordthe value spun, for example, if you spin a two and a dime, you will record $0.20.

1. What are the possible outcomes? What is the probability of each outcome?

2. Now conduct the experiment 36 times and record your results in the table below.

Trial# Coin Number Value Trial # Coin Number Value Trial # Coin Number Value

123456789101112

131415161718192021222324

252627282930313233343536

3. How do your results compare with the theoretical probability?

4. Now make a pie chart of your results. Show the number of times you gotexactly 50 cents, more than 50 cents, and less than 50 cents.

5. Calculate the probability of getting exactly 50 cents, less than 50 cents,more than 50 cents. How does this compare with your pie chart?

6. Suppose this were a carnival game. You must pay 55 cents to play it, andyou win what you spin. Discuss the fairness of this game and the wisdomof playing it or running it.

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Application Contingency Table

The table above shows the ages and gender of candidates who applied for the space colony. Use the information to answer the questions below.

1. There were 240 applicants. If all the applications are put in a barrel and one is drawn, what is the probability of drawing the application of someone from 40-49 years of age?

2. What is the probability of drawing the application of a woman?

3. What is the probability of drawing the application of a man 40-49 years old?

4. Susan picked an application from the barrel and said “I have the application of someone over 50.” What is the probability that she had the application of a woman?

5. What is the probability of drawing an application of someone at least 40 years old?

6. Susan made a Venn Diagram as shown below. Indicate the number of applicantsIn each section of the diagram. How many are be in each section?

Women Ages of 40-49

Age Range Men Women Totals20-29 30 18 4830-39 24 24 4840-49 80 40 12050 and over 6 18 24

Totals 140 100 240

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Space Race

In 1957 the USSR launched the first satellite,Sputnik, into space. This started a space racebetween the USSR and the USA. Start your ownspace race below.

Roll a pair of dice. Each time you roll the dice, make an X in one of

the boxes above the number That represents the sum of the numbers on the dice you rolled.

Which space capsule will reach the Moon first? Which would you want to be riding on?

Run the race three times if you have time.

1 2 3 4 5 6 7 8 9 10 11 12

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Mini Review - Probability

A class has access to these random number generators: some regular six-sided dice, some 12-sided dice, a spinner marked 1-10, and fair coins.

1. Someone in your class believes that if you toss heads on a coin, then the next tossis more likely to be tails than heads. Describe how you would design an experimentto test this. Carry out the experiment and describe the results.

2. Someone in your class wants to know the probability that when five people meet, at least two of them will be born in the same month. Describe how you would designan experiment to test this. Carry out the experiment and describe the results.

3. The Bubble Chew company puts 10 different Action Man cards in its packs - … one card per pack. What is the probability that you will have to buy fewer than 20 packs of gumto get the entire set? How would you design an experiment to test this? Carry out this experiment and describe the results.

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Mini Review – Probability (cont.)

Answer each question below.

4. If a coin is fair, how many times can you expect to toss heads out of 50 tries?

5. If you roll a fair die, what is the probability of rolling a three?

If you roll this die 600 times, how many times can you expect to roll a three?

If you roll this die six times, how many times can you expect to roll a three?

6., On Saturday afternoons, at a movie theater, there is an equal probability that the customers are male or female. Which is more likely, A or B?

A When the 200 seats fill up, 100 customers are male and 100 are female. B When the first two customers come in, one is male and one is female.

Explain your answer.

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Matrix Logic

Sam, May, Arthur, and Tom play in the school band and each of them playsa different instrument. The instruments they play are the trumpet, flute, drums, and oboe. These students also play on different athletic teams. One plays basketball, one golfs, one runs track, and one plays tennis. Three of these students are related to each other. Use the clues below to determine who plays which sport and which instrument.

1. May walks to school with the trumpet player.2. The golfer likes to play golf with his father3. Sam is the brother of the oboe player.4. May’s cousin plays tennis and the drums.5. Tom uses a ball in his game.6. The basketball player lives next door to the flute player but he is not related to the others.7. May cannot play the flute8. The trumpet player plays basketball. 9. Tom does not play the drums.

Bask’tbl

Tennis

Track

Golf

Tom

Art

May

Sam

Bask’tblTennisTrackGolfTrumpetDrumOboeFlute

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http://kidsastronomy.Miningco.com/

Halley’s Comet

Edmund Halley studied the patterns of the visits of a certain comet. He noted that the comet

had appeared according to a pattern similar to the one below:

1454, 1530, 1605, 1682 . . .

Halley predicted when the comet would come again. When it showed up in the right year

(unfortunately Halley had died by then), the comet was named for him.

1. What year did Halley predict for the comet’s return?

2. Mark Twain was born in 1835, a year when Halley’s comet appeared. He predicted correctly

that he would die when the comet returned. In what year did he estimate he would die?

3. Halley’s comet last passed close to Earth in 1986. When will it return?

4. Approximately how many times will it return between the years 2000 and 3000?

NOTE: Halley actually based his observations on only three years: 1531, 1607, and 1682. The actual

orbital time for the comet varies from 74.4 to 79 years. The variations are due to the positionsof large planets that the comet passes.

There is more information available at:

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From Earth to Venus

Distance from Earth to Venus

-10

10

30

50

70

90

110

130

150

170

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52

Months

Dis

tan

ce (

millio

n

miles)

1. Estimate the shortest distance between Venus and Earth. Draw a picture of Earth and Venus in orbit when they are closest.

2. What is the greatest distance that occurs between Venus and Earth? Draw a picture of

Earth and Venus when they are farthest apart.

3. If the month labeled “1” is January, 2000, list two other months in which Earth and Venus are about

the same distance apart as they are in month “1”.

4. If Venus and Earth are very close to each other in July, 2001 (19th month), when will they be that

close again? When will be the next time after that, that they that close?

5. If the orbit of Earth is about 93 million miles from the sun, what is the approximate distance

of Venus from the sun?

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Planet Collector Cards

Captain Krypton cereal comes with a super-duper 3-d holographic planet picture card in each box.There are 10 cards in all, one for each planet, and one for the Asteroid Belt. You want tocollect them all. How many boxes of cereal will you need to buy? Do you think you could getthe entire set by buying only ten boxes? Do the experiment below to find out.

Use the spinner below to determine which card you get when you buy a box of Captain Krypton cereal. Each time you spin, put a tally mark by that planet’s name. When you get at least onemark for each of the cards, count how many times you had to spin. This is an experimental resultfor how many boxes of cereal you would have to buy to get the entire set.

Do the experiment three times. Result from trial 1: _____ 2: ______ 3: ________

Earth

Mercury

Venus

Mars

Asteroids

Jupiter

SaturnUranus

Neptune

Pluto

Mercury Venus Earth Mars Asteroids Jupiter Saturn Uranus Neptune Pluto

1)_______ ______ ______ _____ ______ ______ ______ ______ ______ ______

2)_______ ______ ______ _____ ______ ______ ______ ______ ______ ______

3)_______ ______ ______ ______ ______ ______ ______ ______ ______ ______

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Planet Collector Cards (cont.)

Combine your three trials with those of everyone else in the class.

What is the median number of boxes required?

What is the mean number of boxes required?

Is there a mode number of boxes required?

Complete the frequency distribution table below. If necessary,extend the chart.

Boxes bought How many different cards?10-14 ___________15-19 ___________20-24 ___________25-29 ___________30-34 ___________35-39 ___________40-44 ___________45-49 ___________

Make a statement about how many boxes you could expect to buy tocollect the entire set of cards.