Class: Eighth Grade Math
Instructor: Marc Vogel
Unit: Probability
Period Length: 68 minutes
True Blue Probability Search
New Jersey Core Curriculum Content Standard
· 4.4.8 B.1. Interpret probabilities as ratios, percents, and decimals.
· 4.4.8 B.3. Explore the probabilities of conditional events.
· 4.4.8 B.4. Model situations involving probability with simulations and theoretical models.
· 4.5. A.1. Learn mathematics through problem solving, inquiry and discovery.
· 4.5. B.1. Use communication to organize and clarify one’s mathematical thinking.
· 4.5. B.2. Communicate one’s mathematical thinking coherently and clearly to peers, and others.
· 4.5. E.1. Create and use representations to organize, record, and communicate mathematical ideas.
Behavioral Objectives
SWBAT:
· Make predictions and draw conclusions on data by completing the True Blue Game.
· Investigate the relationship between theoretical and experimental probability by completing the True Blue Game and participating in the Closure activity.
· Make and test hypotheses by completing the True Blue Game.
· Calculate combined probability by completing the anticipatory set, the True Blue Game, and the Closure activity.
Timeline
Time
/Activity and Description
7 min. / · Anticipatory Set/Do Nowo What is probability?
o How do you calculate probability?
o What is the probability of getting heads if you flip a coin?
o What is the probability of getting heads two times in a row if you flip a coin two times?
30 min. / · True Blue Game Part One
o Put students in groups of two.
o Main Question: Trina wants to win a goldfish at the carnival. In order for her to win, she needs to pick two blue tiles out of the “True Blue Prize Bag,” without looking. If the prize bag contains three blue tiles and three red tiles, what is the probability of winning the game?
§ SET-UP
· Put three blue and three red Color Tiles in a bag.
· Rules - Draw two Color tiles. However, do not put the first tile back before drawing the second tile. If you draw two blue tiles then count this as a “win”.
§ PREDICTED PROBABILITY – Predict the number of wins you will get if you play the game forty times.
· Predicted probability = # of predicted wins / # of trials
§ EXPERIMENTAL PROBABILITY – Calculate it.
· Conduct forty trials.
· Record results
· Experimental probability = # of wins / # of trials
· Compare the experimental and predicted probabilities.
· Discussion
§ How did you make your prediction?
§ How did your prediction compare to the results of your experiment?
§ THEORETICAL PROBABILITY – Calculate it.
· Imagine picking the tiles one at a time. To find the theoretical probability that the first tile will be blue, write the ratio of the number of blue tiles to the total number of tiles in the bag.
· Imagine the first blue tile has been drawn. To find the theoretical probability that the second tile will be blue, write the ratio of the number of blue tiles remaining in the bag to the total number of tiles remaining.
· Multiply the theoretical probabilities to find the combined theoretical probability.
· Compare your experimental and theoretical probabilities.
§ COMBINE CLASS DATA
· Each team must add their data to the chart on the board.
· What came closer to the theoretical probability, the class data or your individual team data?
§ DISCUSSION QUESTION
· You based your theoretical probability on two separate draws. When finding probability, is there any difference between drawing two tiles at once and drawing them one at a time?
· To prove the answer to this question, have the teams perform forty trials again. However, this time require them to draw two tiles at one time.
§ Are the results the same? Explain.
25 min. / · True Blue Game Part 2
o Main Question: What if you wanted to change the game of True Blue so that Trina would have a 1 in 3 chance of winning the goldfish? How would you do this?
§ For this activity, each team can use up to 10 red and 10 blue tiles.
§ They must calculate the theoretical probability of drawing two blue tiles from the bag with the number of red and blue tiles that they chose.
§ Each team will adjust the numbers of red and blue tiles until the theoretical probability of drawing two blue tiles is 1 in 3.
§ Conduct ten trials. Record your results. Calculate the experimental probability.
§ Conduct ten more trials. Record your results. Calculate the experimental probability of all twenty trials.
§ Conduct ten more trials. Record your results. Calculate the experimental probability of all thirty trials.
§ Conduct then more trials. Record you results. Calculate the experimental probability of all forty trials.
§ Conduct ten more trials. Record your results. Calculate the experimental probability of all fifty trials.
o Follow-up Questions:
§ What methods and strategies did you use to make your work easier?
§ Did you organize your work in any special way?
§ How did the experimental probabilities compare to the theoretical probability?
§ Based on the results of your experimental probabilities, do you agree with the calculated theoretical probability?
5 min. / · Closure/Informal Assessment
o Describe the relationship between experimental probability and theoretical probability?
o What did you learn from this lesson?
1 min. / · Homework Assignment
o Complete the Calculating Probabilities Practice Worksheet
Materials: Color Tiles, True Blue Activity master, Calculating Probabilities Practice Worksheet
Reflection: Are the learners able to do the things listed in the objectives section of this plan? What went well during the lesson? What could be added or changed to make the lesson more effective?