AIM: How can we assess our understanding of probability?
HW: Prepare for NYS Assessment
Please clear your desk of everything except for a pencil, calculator, and scantron.
AIM: How can we practice probability problems?
Announcements: Probability Assessment Monday, March 27, 2017
Theoretical, Experimental, Sample space, tree diagram, compound events, expected outcomes
HW: Prepare for Monday's Probability Assessment
The city bus is scheduled arrive at Evie's stop at 7:20 a.m. each morning. The table below shows the actual arrival times randomly taken from the past few months.
7:21 7:21 7:19 7:20 7:23
7:22 7:20 7:18 7:20 7:18
7:21 7:20 7:19 7:17 7:25
7:20 7:20 7:18 7:19 7:24
According to the table, what is the probability that Evie's bus will come before 7:20 a.m. tomorrow?
Station learning took place in class today. There were 8 probability questions hung up around the classroom. Students worked with selected groups to solve questions around the classroom. When they determined an answer, they wrote it on their sheet, put the answer on a post-it and stuck it to the chart paper. When a group completed all of the questions, they came to me to verify answers. Groups that had incorrect responses were sent back to the respective centers to retry.
AIM: How can we practice probability problems?
HW: Probability Packet #16-28
How can we determine probability of rolling an even number on a number cube and a blue on the spinner? P(even, blue):
Students worked in their collaborative partnerships to solve probability problems. Responses to questions were collected using Plickers. The responses will be used for feedback tomorrow before students conduct the probability picture/comment walk.
We also had a discussion in which we applied probability to the lottery. At first, students were asked to raise their hands when asked "Do you think you will win a multi-million dollar jackpot in your life?" Many students raised their hands. After our discussion accompanied by infographics, students' opinions changed dramatically.
AIM: How can we find the probability of compound events?
HW: Probability Packet #1-15
Giselle has 2 pairs of sneakers, 3 pairs of jeans, and 4 tops. How many different outfits can she make with her options?
After reviewing how sample spaces are used to find the total outcomes in a situation, students looked at a faster way to find the probability of a compound event. Students learned that if you want to find the total probability of two events, you must find the probability of the first event, and multiply it by the probability of the second event. Students then worked on tasks involving compound events.
Please use the resources below to help with your understanding of today's lesson.
Probability Quiz - http://www.thatquiz.org/tq-d/math/probability/
AIM: How can we determine the probability of a compound event?
HW: Sample Space Worksheet (downloadable copy found in the resource section)
Michelle was rolling a number cube. She recorded the results in the following table. What was her experimental probability of rolling an even number?
Number | 1 | 2 | 3 | 4 | 5 | 6 |
Frequency | 2 | 3 | 6 | 3 | 5 | 1 |
In previous lessons, we learned to find the probability of one event--such as rolling a number cube, or spinning a spinner, or flipping a coin, or picking colored tiles from a container. Today we looked at how probability works when there is a compound event, which is when two or more events happen at once. Examples of compound events include finding the probabilty of flipping a coin and getting a heads AND drawing a heart from a deck of cards. We use sample spaces to organize all of the possible outcomes that can happen. From there, we can determine probabilities of compound events. The sample spaces that we will be working with are: tree diagrams, lists, and area models.
AIM: How can you determine the relative frequency of an outcome?
HW: What Do You Expect: p.18 #9-10
Kalvin decides to use tiles with the letters A - Z to help choose his cereal each morning. If vowels represent Cocoa Blast and consonants represent Healthy Nut Flakes, should he expect to eat both cereals an equal amount in a month? Explain.
Classwork: Still working within the context of Kalvin and his cereal, the class looked at another situation where Kalvin decided to toss two coins. If the coins matched (two heads or two tails), then Kalvin got his cereal. If the coins did not match, then he needed to eat his mother's cereal. Students worked with their desk partners to find the relative frequency of each outcome. We then looked at the class results and saw that the probabilities hovered around 50%.
AIM: How does modeling with an experiment help determine the likelihood of each outcome?
Announcements: The end of the 4th marking period is today. Late assignments can no longer be submitted, without special circumstances and prior approval.
HW: What Do You Expect textbook pp. 17-18, #7-8, p.21, #21-23
Kalvin flipped heads 3 out of the first 4 days in a week. Should he expect this trend to continue for the rest of the month? Explain.
Classwork: Kalvin wants to find another way of choosing a cereal every morning that will give him a better chance of eating his favorite cereal than flipping a coin. He needs to create a new experiment that will favor his getting to eat Cocoa Blast more days out of the month. His mother approves of this idea, but will get suspicious if Kalvin is never eating Healthy Nut Flakes.
A. Creating the experiment.
With your group members create an experiment that you will be able to complete 30 times in 5 minutes from the materials in your tub. Before you may begin running your experiment you must write the following in your notes...
1. Describe how your experiment works.
2. Why you believe it will let Kalvin eat Cocoa Blast more than half of the days in June.
3. Which result represents Cocoa Blast and which represents Health Nut Flakes.
B. Running Your Experiment
1. Run your experiment 30 times or for 5 minutes (whichever happens first). Keep a running total of your results by recording them in a table.
2. For the month of June, what fraction of days will Kalvin be eating Cocoa Blast?
3. What percentage of days in June will Kalvin be eating Cocoa Blast?
C. Analyzing the results.
1. Was your experiment successful? If Kalvin uses your experiment will he be eating Cocoa Blast more than half the days?
If your experiment was successful: Describe what about the experiment that you designed made it successful.
If Unsuccessful: How could you change your experiment so that you would get the results that you wanted?
Design and test an experiment that will result in Kalvin getting to eat Cocoa blast more than half of the days in the month of June.
- Playing cards- 5 colored cubes - Three number cubes- Two Index Cards - Plastic Cup- Two Coins
- If you have another idea feel free to use it. Please check ?with me first though.