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INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING Lesson Goals: Determine the probability of simple and compound events. (Q.8.b) Interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. (CCSS.Math.Content.HSS.CP.A.4)CCSS.Math.Content.HSS.CP.A.4.

INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING 4 What you will do in this lesson: Think & work alone Think, Pair, Share Cooperative Learning in Small Groups

Basics of Probability Video h.aspx?a=activity23 5

INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING 6 What does finding the probability that an event will occur mean to you? How many different ways can probability be represented mathematically? What are they? Would the probability ever be zero? Justify your answer. Would the probability ever be one? Justify your answer. If the event is “flipping a heads” on a coin, what is the “complement” of that event? What would be true about adding the probability of an event and its complement? In your own words…

INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING Probability Facts 7 Probability can be expressed as a fraction, decimal, ratio, or percent between 0 and 1, inclusive. If it is impossible for the event to happen, the probability is 0. If it is certain that the event will happen, the probability is 1. If two events are equally likely to happen, the probability is ½,.5, or 50%. The sum of an event and its complement is 1. Probability = number of desired outcomes total number of possible outcomes

INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING Independent vs. Dependent 8 Suppose we wanted to choose a 4-digit pin number where the numbers could be repeated; how many different pin numbers could we choose from? _____ x _____ x _____ x _____ = _____ Should we replace the first post-it note in the box after we draw it and before we draw the second number? Should we continue to replace the number we draw into the box before we draw the next number? Answer: 10 x 10 x 10 x 10 = 10 4 = 10,000

INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING Independent vs. Dependent 9 Suppose we wanted to choose a 4-digit pin number where the numbers could NOT be repeated; how many different pin numbers could we choose from? _____ x _____ x _____ x _____ = _____ Should we replace the first post-it note in the box after we draw it and before we draw the second number? How about on the subsequent draws? Answer: 10 x 9 x 8 x 7 = 5040

INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVINGDefinitions 10 Independent event – the probability of a second event does not depend on the first event Dependent event – the probability of a second event does depend on the first event

INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING The SOLVE method… 11 S tudy the problem (What am I trying to find?) O rganize the facts (What do I know?) L ine up a plan (What steps will I take?) V erify your plan with action (How will I carry out my plan?) E xamine the results (Does my answer make sense? If not, rework.) Always double check!

INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING S – Study the problem. 12 What is the problem asking me to do? Find the question. Find the probability of spinning a red section twice. A spinner has 6 equal sections. Two sections are red, 3 sections are blue, and 1 section is green. What is the probability of spinning a red section twice? p. 23 in the GED Test Exercise Book / Common Core Achieve / Mathematics by McGraw Hill Education, #8

INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING O – Organize the facts. 13 What do I know? Spinner has 6 equal sections Spinner has 6 equal sections 2 red, 3 blue, 1 green A spinner has 6 equal sections. Two sections are red, 3 sections are blue, and 1 section is green. What is the probability of spinning a red section twice?

INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING L – Line up a plan. 14 Since the second spin does not depend on the outcome of the first spin, these are independent events. We need to: Find the probability that we would get a red on the first spin Find the probability that we get a red on the second spin (which is the same as the first) Multiply the two probabilities together since it is a compound event

INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING V – Verify your plan with action V – Verify your plan with action. 15 P(R) = 2/6 = 1/3, thus the probability of getting a red on each spin is ⅓. P(R, R) = ⅓ x ⅓ = 1/9

INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING E – Examine the results. 16 Does my answer make sense? It does make sense in that it should be smaller for getting a red spin two times in a row as opposed to getting it just on one spin alone. Thus, the answer is choice A, 1/9.

INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING Using the SOLVE method 17 P. 23 in the GED Test Exercise Book / Common Core Achieve / Mathematics by McGraw Hill Education, #9 A bag has 5 red marbles and 4 white marbles. Aaron draws a marble, sets it aside, and draws a second marble. What is the probability that Aaron will draw a white marble on both draws ?

INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING S – Study the problem. 18 What is the problem asking me to do? Find the question. Find the number of red and yellow cell-phone covers purchased in the last 25 sales. The table below shows the last 25 cell-phone cover purchases at Cell Phone Hut. The best prediction for the number of red covers sold of the next 100 sales is 40. Complete the table. p. 23 in the GED Test Exercise Book / Common Core Achieve / Mathematics by McGraw Hill Education, #7 ColorNumber Red Yellow Blue8

INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING O – Organize the facts. 19 What do I know? 8 blue covers sold in the last 25 sales They predict that the # of red that will sell out of the next 100 sales will be 40. The table below shows the last 25 cell- phone cover purchases at Cell Phone Hut. The best prediction for the number of red covers sold of the next 100 sales is 40. Complete the table. ColorNumber Red Yellow Blue8

INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING L – Line up a plan. 20 Find the probability for selling a red cover for the next 100 sales. Work backwards to determine how many red covers were sold in the last 25 sales for this probability to be true. Once we get the number of red, we can add it to the number of blue and then subtract that total from 25 to get the number of yellow.

INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING V – Verify your plan with action. 21 P(R) = 40/100 = 10/25, thus 10 of the last 25 covers sold had to be red. 25 = R + Y + B 25 = 10 + Y = 18 + Y = Y 7 = Y

INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING E – Examine the results. 22 Does my answer make sense? It does, since = 25 and for this sample date, we can now verify that the P(R) = 10/25 = 40/100 or 40%.

INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING Using Probability to Interpret Data 23 The manager of the pizza shop wanted to know what kind of pizza slices customers order during lunch. She collected this data during one lunch session. Suppose 200 slices are expected to be sold in one week. Use the data to estimate how many cheese slices will be ordered in a week. PizzasSlices Ordered Pepperoni25 Sausage10 Cheese50 Mushroom15