Lesson #20 Probability

Transcription

1 Math Buddies Grade Lesson #20 Probability Goals: Record data from experiments and determine the probability that an event will happen. Read questions and determine if probability is needed to solve them. Draw tree diagrams to determine all possible combinations. Vocabulary: Outcome - a possible event that can happen. For example heads and tails are two possible outcomes for flipping a coin. Probability the chance that an event will happen. Impossible event an event that cannot happen. Probability is 0. Unlikely event the event that should happen less than any other event. Likely event the event that should happen more than any other event. Certain event an event that will definitely happen. Probability is 1. Related SOL: 4.19 The student will a) predict the likelihood of outcomes of a simple event, using the terms certain, likely, unlikely, impossible; and b) determine the probability of a given simple event, using concrete materials 5.17 The student will a) solve problems involving the probability of a simple event by using tree diagrams or by consulting a sample space representing all possible results; b) predict the probability of outcomes of simple experiments, representing it with fractions or decimals from 0 to 1, and test the prediction; and c) create a problem statement involving probability and based on information from a given problem situation. Students will not be required to solve the created problem statement. Materials: A bag containing 6 red, 1 blue, and 3 green tiles (Note: Do Not let students open this bag until the experiment is complete) A spinner with the number teddy bear counters in each color: red, green, and blue 6 fruit counters of each type: apples, grapes, and strawberries

2 Math Buddies Grade Goal 1: Record Data From Experiments And Determine The Probability That An Event Will Occur. Activity1.1: What s in the Bag? (5-8 minutes) 1. Take out Lesson #20, Student Activity Sheet #1: What s in the Bag? You will share the same recording sheet. Take out the bag. The bag contains different colored color tiles. You are going to do an experiment and then try to guess what colors are in the bag without looking in the bag. 2. You will take turns. You will withdraw a tile; record the color, then place the tile back in the bag. Record the colors with tally marks. (For example, after withdrawing 5 red tiles, the students will have five tallies ( ) recorded on red.) Each person will do this 10 times. Allow students to play the game as you watch and coach. 3. How many times did you draw a red tile? How many times did you draw a blue tile? How many times did you draw a green tile? 4. Which color occurred the most often? (It should have been red.) Which color occurred the least often? (Yellow. No yellow were drawn.) Did you ever draw a yellow tile? (No.) 5. Tell the students to open the bag and sort the color tiles by color. How many red tiles were in the bag? (6) How many blue tiles were in the bag? (1) How many green tiles were in the bag? (3) How many total tiles were in the bag? (10) 6. Since there were 6 red tiles and 10 total tiles, the probability of drawing a red tile is 6/10. What is the probability of drawing a blue tile from the bag? (1/10) What is the probability of drawing a green tile from the bag? (3/10) 7. We say that it was impossible to draw a yellow tile. Why? (Because there were no yellow tiles in the bag.) What is the probability of drawing a yellow tile? (0/10) If the probability is 1, we say the event is certain to occur. Activity 1.2: What Could Be Drawn? (3-5 minutes): 1. Take out Lesson #20, Student Activity Sheet #2: What Could Be Drawn? Bag #1 contains pictures of animals. What possible animal pictures can be drawn from the bag? (bee and butterfly) 2. What is the probability of drawing a picture of a bee? (3/4)

3 Math Buddies Grade What is the probability of drawing a picture of a butterfly? (1/4) 3. Which animal is the most likely to be drawn? (bee) Why? (There are more bees than butterflies.) Which animal is the least likely to be drawn? (butterfly) Why? (There is only 1 butterfly.) 4. Bag #2 contains different pictures. What possible pictures can be drawn from the bag? (bicycle, police car, and ambulance) 5. What is the probability of drawing a picture of a bicycle? (3/6) What is the probability of drawing a picture of a police car? (1/6) What is the probability of drawing a picture of an ambulance? (2/6) 6. Which picture is the most likely to be drawn? (bicycles) Why? (There are more cars than police cars and ambulances.) Which picture is the least likely to be drawn? (police car) Why? (There is only 1 police car.) 7. What is the probability of drawing a truck from Bag #2? (0/6) Why? (Bag #2 does not have pictures of trucks.) Activity 1.3: Spinners (5-8 minutes) 1. Take out Lesson #20, Student Activity Sheet #3: Spinners. You will share the same recording sheet. Take out the spinner. You will do an experiment with the spinner to try to determine which color is most likely to occur. 2. You will take turns. You will spin the spinner then record the color the arrow lands on with tally marks. Each person will do this 10 times. Allow students to play the game as you watch and coach. 3. How many times did the spinner land on 1? How many times did the spinner land on 2? How many times did the spinner land on 3? How many times did the spinner land on 4? How many times did the spinner land on 5? 4. Since 1/5 of the spinner is 1 the probability that it will land on 1 is 1/5. What is the probability that it will land on 2? (1/5) What is the probability that it will land on 3? (1/5) What is the probability that it will land on 4? (1/5) What is the probability that it will land on 5? (1/5) What is the probability that it will land on a number larger than 3? (2/5) Why? (There are 2 numbers (4 and 5) on the spinner larger than 3.) What is the probability that it will land on a number smaller than 4? (3/5) Why? (There are 3 numbers (1,2, and3) on the spinner smaller than 4.) What is the probability that it will land on a number smaller than 6? (5/5 or 1) Why? (All five numbers on the spinner are smaller than 6.)

4 Math Buddies Grade What is the probability that it will land on a number larger than 6? (0/6 or 0) Why? (There are no numbers larger than 6 on the spinner.) Goal 2: Read Questions And Determine If Probability Is Needed To Solve Them. Activity 2.1: Which is Probability? (5-8 minutes) 1. Take out Lesson #20, Student Activity Sheet #4: Which is probability? We have been studying probability throughout today s lessons. Probability is about determining the chance that an event will occur. 2. Toby has a bag of marbles. There are 6 questions about the marbles. Determine which questions are probability questions and circle them. 1. How many marbles are in the bag? This is not probability. The question does not involve chance just counting the marbles. 2. If Toby picks one marble from the bag without looking, which color will it most likely be? This is probability. Drawing a marble without looking and determining what color it might be involves chance. 3. Are there more black marbles or white marbles in the bag? This is not probability. The question does not involve chance only comparing the number of each color marble. 4. If Toby picks one marble from the bag without looking, which color will it be least likely to be? This is probability. Drawing a marble without looking and determining what color it might be involves chance. 5. Will Toby more likely choose a black marble or a white marble from the bag, if he picks a marble from the bag? This is probability. Determining what color it might be involves chance. 6. If Toby picks one marble from the bag how many marbles will be left in the bag? This is not probability. The question asked what was left in the bag, not what came out of the bag. This only involves subtraction. Goal 3: Draw Tree Diagrams To Determine All Possible Combinations. Activity3.1: How Many Choices? (5-8 minutes) 1. Take out Lesson #20, Student Activity Sheet #5: How Many Choices? Take out the teddy bears (, Blue and ) and the fruit counters (Apple, Grapes, Strawberry). (Note: Some student pages may say Banana, Grapes, Orange please have the students change these to Apple, Grapes, Strawberry.) 2. Jamal can choose one teddy bear and one piece of fruit. There are three different colored teddy bears:, Blue and and there are three types of fruit: Apple, Grapes, Strawberry. Record all the possible ways Jamal can

5 Math Buddies Grade choose a bear and a piece of fruit. How many different ways can Jamal choose a bear and a piece of fruit? (9) 3. All the possible combinations are: red bear and apple red bear and grapes red bear and strawberry blue bear and apple blue bear and grapes blue bear and strawberry green bear and apple green bear and grapes green bear and strawberry Activity 3.2: Tree Diagrams (5-8 minutes) 1. Take out Lesson #20, Student Activity Sheet #6: Tree Diagrams. (Note: Some student pages may say Banana, Grapes, Orange please have the students change these to Apple, Grapes, Strawberry.) 2. Instead of using the counters to determine the possible combinations of bears and fruit, you could have used a tree diagram. To draw a tree diagram, you begin with your first choice. For Jamal, that would be choosing a bear. He has 3 choices: red, blue, and green. After Jamal chooses a bear, he must choose fruit. If he chooses a red bear, he can choose an apple, grapes, or a strawberry. Each choice is connected to the red bear. If he chooses a blue bear, he can choose an apple, grapes, or a strawberry. Each choice is connected to the blue bear. Draw in Jamal s fruit choices for the green bear on the tree diagram. The student will write in an apple, grapes, or a strawberry. 3. Make a tree diagram to show all possible combinations for Shannon. Black White Black Purple White Black White Black Yellow White Lesson #20: Assessing Student Learning (5-10 minutes) 1. Take out Lesson #20, Student Assessments. 2. Have students complete the four multiple-choice assessment items independently. 3. Discuss and correct the items the student answered incorrectly. Answer Key: 1. C (2 out of 10 candles are striped.) 2. G (The spinner could land on 6, 7, or 8.) 3. B (This is the only question that involves chance.) 4. J (The notepad can be yellow or blue. The ruler can be orange, pink or green.) Lesson #20: Student Activity Sheet #1 What s in the Bag?

6 Math Buddies Grade DO NOT LOOK IN THE BAG UNTIL AFTER THE EXPERIMENT!!! 1. On your turn, draw a tile from the bag. 2. Record the color of the tile in the table below. 3. Place the tile back in the bag. 4. Alternate turns with your partner, and do this ten times each. Color Tile Blue Tile Tile Yellow Tile Number of Tiles Drawn 1. How many times did you draw a red tile? 2. How many times did you draw a blue tile? 3. How many times did you draw a green tile? 4. How many times did you draw a yellow tile? 5. Which color occurred the most often? 6. Which color occurred the least often? 7. Did you ever draw a yellow tile? Open the bag. Sort the tiles by color. What is the probability of drawing each color? Color Number of Tiles Probability Blue Yellow Lesson #20: Student Activity Sheet #2

7 Math Buddies Grade What Would You Draw? Bag #1 Animal Bee Probability Butterfly 1. Which animal is the most likely to be drawn? 2. Which animal is the least likely to be drawn? Bag #2 Picture Bicycle Probability Police Car Ambulance 3. Which picture is the most likely to be drawn? 4. Which picture is the least likely to be drawn?

8 Math Buddies Grade Lesson #20: Student Activity Sheet #3 Spinners 5 1. On your turn, spin the spinner. 2. Record the number that the arrow lands on. 3. Alternate turns with your partner. 4. Do this ten times each. Where the spinner landed Number of Trials Determine the probability of spinning the following numbers. Number 1 Probability Larger than 3 Smaller than 4 Smaller than 6 Larger than 6

9 Math Buddies Grade Lesson #20: Student Activity Sheet #4 Which is probability? Toby put the marbles in the bag above and shook the bag. Which of the following question could you use probability to solve? Circle the probability questions. 1. How many marbles are in the bag? 2. If Toby picks one marble from the bag without looking, which color will it most likely be? 3. Are there more black marbles or white marbles in the bag? 4. If Toby picks one marble from the bag without looking, which color will it be least likely to be? 5. Will Toby more likely choose a black marble or a white marble from the bag, if he picks a marble from the bag? 6. If Toby picks one marble from the bag how many marbles will be left in the bag?

10 Math Buddies Grade Lesson #20: Student Activity Sheet #5 How Many Choices? Jamal can choose one teddy bear and one piece of fruit. Teddy Bears Blue Fruit Apple Grapes Strawberry Determine all the possible ways Jamal can choose a bear and a piece of fruit. Teddy Bear Fruit Blue Blue Blue

11 Math Buddies Grade Lesson #20: Student Activity Sheet #6 Tree Diagrams Complete Jamal s choices as a tree diagram. Apple Grapes Strawberry Apple Blue Grapes Strawberry Shannon wants to buy a dress and a pair of shoes. Her choices are listed below. Dress Purple Yellow Shoes Black White Make a tree diagram to show all possible combinations for Shannon.

12 Math Buddies Grade Lesson #20: Student Assessments 1. Mitch bought a box of candles. 2. The spinner shown below is used to play a game. These are the candles that are in the box. What is the probability that the arrow will land on a number greater than 5? If Mitch takes out 1 candle without looking, what is the probability that it will be striped? A B F G H J C D

13 Math Buddies Grade These are the flags that will be carried in front of the marching band. 4. Each person attending a meeting will receive a notepad and a ruler. The table below shows the different colors of the notepads and the rulers. Which of the following tree diagrams shows all the different combinations of 1 notepad and 1 ruler. Which of the following questions about these flags could you use probability to solve? A How many more flags have trumpets on them than drums? B If Lionel picks a flag without looking, which kind of flag is he least likely to pick? C What kind of instrument is on exactly one-half of the flags? D If 5 people get to pick a flag before Amanda, how many will she have to choose from?