Lesson 5.2.6 Day 2 – Teacher Notes Standard: 7.SP.C.8a and b Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event. Full mastery of the standard can be expected by the end of the chapter. Lesson Focus: The focus of today is for students to wrap up all material learned about probability to this point. This emphasizes uniform and non-uniform probability. A supplemental sheet can be used in Day 2 of this lesson to provide students with more practice of finding probability when “or/and” problems are given. (5-81) I can find probabilities of compound events using organized lists, tables, tree diagrams, etc. and analyze the outcomes. Calculator: Yes Literacy/Teaching Strategy: Think-Pair-Share (5-79); Pairs Check (5-82)

Bell Work

Day 2 (same introduction) In Lesson 5.2.5, you used systematic lists, probability tables, and probability trees to organize the outcomes of different probability situations.  Today you will use a probability table to help organize events when one outcome is more likely than another.

5-79. SPINNING ODDS AND EVENS — PART 1 Your team is going to play against your teacher in a game with two hidden spinners.  Spinner A has the numbers 2, 3, and 4 on it.  Spinner B has the numbers 6, 7, and 8 on it.   The rules are: Spin each spinner. Add the results. If the sum is even, one team gets a point.  If the sum is odd, the other team gets a point. The first team to earn 10 points wins. a. Should you choose the odd or even numbers in order to win?  Discuss the choices with your team and decide which side to take.  Be prepared to justify your choice with mathematics. 

5-79 cont. b. Play the game at least three times with your teacher.  Your teacher will spin the spinners and announce the results.  Record the results of each spin and their sum.  Is the result odd or even most often?  Does this match with your prediction?  c. Make a probability table and determine the theoretical probability for this game.

5-80. SPINNING ODDS AND EVENS — PART 2 Now that you have played the game several times, obtain a Lesson 5.2.6 Resource Page from your teacher and take a close look at the hidden spinners. a. Are the spinners different from what you expected? How? Be as specific as you can. Do you still think you made the correct choice of odd or even numbers? b. What assumption about the spinners did you make in part (c) of problem 5‑79?  c. What is the probability of spinning each outcome on Spinner A?  On Spinner B?   

5-81.  Raul had imagined that the spinners were divided into equal parts before he saw them.  He created the probability table at right to organize the outcomes.  “I thought there would be a  1 3  chance of spinning a 3 on Spinner A.  But now that I see the spinners, I know that is not true.  I need to make a new rectangle in order to find the probability.” a. Create a new rectangle.  Label the top row and left column with the numbers on each spinner and their probabilities.  b. Write a multiplication problem to show the probability of spinning a 3 and a 7. Calculate P(3 and 7).    

5-81 cont. c. Complete the table to show each possible sum and its probability.  d. What is the probability of spinning an odd sum?  What is the probability of spinning an even sum?  e. Did you make the right choice of an odd or even number in problem 5-80?  Explain your reasoning.

Additional Practice Create your own AND problem now that you have a better understanding of what an AND problem is. You must have the following: AT LEAST 8 final number of options Three questions that you would ask someone to answer NO SPINNERS WITH NUMBERS (Be creative)