Lesson Plan for Probability with a Random Drawing

written by: Glynessa Cress, Gcress98@aol.com, Spring 2001
graphics, editing, & formatting by: Dr. Beth McCulloch Vinson

Subject: Probability with a random drawing

Grade: Three

I. Behavioral Objectives:

After a teacher-directed math lesson, the students of Mrs. Cress' third-grade class will: define probability; predict, record, and discuss outcomes from a random drawing; and identify most likely and least likely outcomes. Each student will conduct a random drawing; record the data on a data chart; analyze the data; and graph the data. Each student will report his or her data with an accuracy rate of at least 90%.

II. Instruction/Method:

A. Anticipatory Set:

1. Explain that today they will learn about probability.

2. Define probability as a mathematical term for chance. (The chance that something will happen.)

3. Brainstorm ideas of probability in everyday life, such as the weather forecast (chance of rain), decisions we make that depend on the chance of the outcome (Should I take an umbrella with me?), the chance of winning the lottery, and playing games (chance of winning).

4. Share the book Cloudy with a Chance of Meatballs by Judi Barrett and weather forecasts from the newspaper or the television.

5. Review ways to collect and organize data. First, review ways to collect data. Then, review how to organize data in a chart. Remind the students that tally marks are always made in groups of five. Show them an example of a data chart with information recorded with tally marks (one that the students have made in a previous lesson would be great). Last, review the pictograph, circle graph, and bar graph and show examples of each on the overhead projector.

B. Statement of Objective:

"When we finish today you will be able to predict, record, and discuss outcomes using a random drawing experiment and identify most likely and least likely outcomes."

C. Instructional Input:

1. Review the definition of probability (chance).

2. Discuss the following definitions to ensure understanding: "likely," "more likely," "less likely," and "equally likely."

3. Use the weather forecast, an everyday example of probability in use, to help the students understand these new terms. Compare the weather forecasts for several days using the terms. For example, if the forecast states that there is a 20% chance of rain on Monday and a 90% chance on Tuesday, ask the students which day it is more likely to rain, which day it is least likely to rain, and so on.

4. Discuss what a random drawing is by example of the lottery. Give each student a numbered ticket and put a duplicate of each student's ticket in a clear bowl. Mix the numbers as you explain to the students that they all have an equal chance to win the class lottery because they each have only one ticket. However, in other lotteries, many people buy more than one ticket in order to increase their chance of winning. Ask the students, "If I gave one student two tickets, would his or her chance of winning increase or decrease?". Have the students put their thumbs up for increase and thumbs down for decrease. This way you can see who needs further explanation. Continue to explain a random drawing by showing the students that you draw a ticket out of the bowl without looking and thus it is a random pick of the winner. Reward the winner with a homework pass. Explain to the class how to express each student's chance of winning in terms of numbers (1 out of total in class).

D. Modeling:

1. Explain to the students that they are now going to conduct several experiments in which they will learn more about probability.

2. Show the students a paper bag, in which you have secretly put five blocks (two reds, two blues, one yellow). Tell the students, "There are five colored blocks in the bag. As a class, we are going to predict and identify the colors of the blocks, and how many of each color are in the bag."

3. Have the students form a single line. The first student then draws a block from the bag and the color of the block is recorded on the board. The student replaces the block and then goes to the back of the line.

4. After the first ten students have drawn out a block, stop and make predictions. First, ask the students to identify the colors of the blocks. Next, have them predict how many of each color are in the bag.

5. Continue the drawings, adding the rest of the class' colors to the first ten. After everyone has had a turn, ask the students to reevaluate their guesses and make new predictions if necessary. The drawings will continue until the predictions are correct.

6. Discuss how the students decided how many blocks of each color were in the bag.

7. Discuss the activity further using the new terms. Ask the students which color was most likely to be picked, which color was least likely to be picked, how many of each color would need to be added for the chances to be equal, and so on.

E. Checking for Understanding:

1. Show the students a new number of yellow, red, and blue blocks. Have them record which colored block is most likely to be chosen, which colored block is least likely to be chosen, and how many of each colored block would need to be added in order for the chances to be equal.

2. Discuss their answers.

F. Guided Practice:

1. This will be a good time to start the book Charlie and the Chocolate Factory by Roald Dahl. It will need to be read up to chapter five, which talks about the golden tickets and Charlie's small chance of getting a gold ticket. If your class has read Charlie and the Chocolate Factory retell the story and reread chapter five.

2. Discuss what a small chance Charlie had to win a golden ticket and how he must have felt about having such a small chance.

3. Divide the class into heterogeneous groups of four. Give each group a paper bag with one golden Hershey Kiss and three silver Hershey Kisses inside.

4. Explain that the students are now going to perform their own random drawings for "gold tickets." Discuss how they are going to record their data in a data chart with tally marks. Discuss and draw together what the chart should look like and what information the chart should contain.

5. Instruct each group to take turns drawing a kiss out of the bag without looking (remind them that not looking is what makes it random). Record the color on their data chart, and then return the kiss to the bag. Each person will draw five times (total of 20 draws).

6. If necessary, assign each group member a number 1, 2, 3, or 4.

Student Number:

#1-Please draw a Kiss out of the bag without looking five times.

#2-Please record the color of the Kiss drawn each time on the data chart.

#3-Make sure the Kisses are returned to the bag after each draw and shake the bag before the next draw.

#4-Group leader: Make sure everyone is doing his or her job and that the group member drawing the Kiss from the bag is not looking.

After five draws, the members will change jobs until everyone has had a turn to draw five Kisses.

7. After ten drawings (or the first two students), have the students stop and make predictions about the number of silver Kisses, the number of gold Kisses, and the total number of Kisses.

8. Instruct the groups to record their results in a bar graph or pictograph to be shared with the class.

9. Walk to each group and observe who is working well in the group, who is following directions, and how well each student seems to understand the activity.

G. Independent Practice:

1. Give each student his or her own paper bag of Kisses with a new number of silver Kisses in each one.

2. Have the students perform his or her experiment with the same directions that applied to the guided practice, except they should draw twenty times on their own. Remind them to stop after ten drawings and make predictions.

3. Have these questions on the overhead for the students to answer about their experiment:

What color Kiss were you more likely to draw?
What color Kiss were you least likely to draw?
How many gold or silver Kisses need to be added to make your chances equal?
Graph your results in a pictograph, circle graph, or bar graph.

4. Enjoy your Kisses.

5. Oversee this activity in case someone needs help.

1. Strategies to use with Exceptional Children:

a. For enrichment, add more gold and silver Kisses and a new color Kiss to the gifted children's bags.

b. For remediation, do not change the number of Kisses in their bags and if necessary, allow them to work in pairs.

2. Activities which Value Cultural Diversity:

a. Children who speak English as a second language will make their charts and graphs in their native language.

b. Children from other cultures will tell about and show, if possible, candy related to their culture.

3. Activities which Foster Active Inquiry, Critical Thinking, and Problem Solving:

a. Send a note home to the parents explaining to them that we are learning about probability. Have them play a game with their child along with other family members and discuss the fairness of the game and what the child's chances are of winning. Children can also bring in the weather forecast for several weeks and chart how accurate the meteorologist is. Another idea would be for the child and parents to come up with a list of events that describe things that always happen, sometimes happen, and never happen.

b. The class will take a field trip to a local television station to ask the meteorologist how he or she predicts the weather. A guest speaker would also work.

H. Closure and Summary:

1. Bring the session to a close by having the children share their group graphs and then create a class graph about the combined data.

2. Have the children bring in examples of probability that they find at home like the weather forecast or lottery tickets.

3. Have the children write in their learning journals about what they learned from this lesson and at least one question they still have.

III. Assessment Techniques:

The students in Mrs. Cress' third-grade class will predict, record, and discuss outcomes using a random drawing experiment and identify most likely and least likely outcomes at an accuracy rate of at least 90%.

It must be determined whether a child understands and can analyze information collected, organize data, and display data through tally charts, pictographs, bar graphs, and circle graphs as prerequisite skills. In order to determine whether the children understand and can analyze information collected, the teacher could provide a graph of information and have the children answer questions about the graph. In order to determine whether the child can organize and display data through tally charts, pictographs, bar graphs, and circle graphs, the teacher could provide the children with the data and have them display it in these ways.

IV. Materials:

example of data chart, example of line graph, bar graph, and pictograph, weather forecast from newspaper or television, tickets, bowl, paper bag for each student, one for class activity, and one for each group, several bags of Hershey Kisses in silver, gold, and one other color, poster board for each group to record their graphs, and lineless paper for each student to record his or her graph.

Books:

Barrett, J. (1978). Cloudy with a Chance of Meatballs. Canada: Collier Macmillan Canada, Inc. (ISBN: 0-689-30647-4)

Dahl, R. (1964). Charlie and the Chocolate Factory. New York: Alfred A. Knopf.

Reference:

Hope, J., Lawerence, P., Martin, M., & Small, M. (1996). Mathematics and Children's Literature. Warren, NJ: Optical Data Corporation.

Predictions:

Number of Gold: ________

Number of Silver: ________

Total number of Kisses:_______

Color

Tally

Total

Silver

Gold