Author: Angela Han
School/Organization:
S. Weir Mitchell Elementary School
Year: 2011
Seminar: Math Concepts in the Classroom
Grade Level: 14
Keywords: chance, Everyday Math, games, probability
School Subject(s): Math
The goal of this curriculum unit is to develop students’ understanding of probability and chance. It is designed to develop the students’ vocabulary related to probability, and allow students to become comfortable with talking about chance events. It will introduce many probability expressions such as sure, certain, probably, 5050 chance, not likely, impossible, and others. In addition, the students will explore how probability affects various situations by performing probability experiments, and they will learn to represent the data from chance events explorations in graphs and tables. Through continual use of this vocabulary in explorations, the students will progressively make them part of their repertoire. Students will be able to: Make informal comparisons between the chances of arious outcomes of an event.Make predictions by comparing the likelihood of two possible outcomes. Explore equally likely outcome events through experimentation. This unit is intended to complement the School District of Philadelphia’s preexisting curriculum Everyday Math. The allotted time for this unit is 15 days spread throughout the year. Its audience is third grade students in a low to midincome urban neighborhood.
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The goal of this curriculum unit is to develop students’ understanding of probability and chance. It is designed to develop the students’ vocabulary related to probability, and allow students to become comfortable with talking about chance events. It will introduce many probability expressions such as sure, certain, probably, 5050 chance, not likely, impossible, and others. In addition, the students will explore how probability affects various situations by performing probability experiments, and they will learn to represent the data from chance events explorations in graphs and tables. Through continual use of this vocabulary in explorations, the students will progressively make them part of their repertoire. Students will be able to:
This unit is intended to complement the School District of Philadelphia’s preexisting curriculum (Everyday Math). The allotted time for this unit is 15 days spread throughout the year. Its audience is third grade students in a low to midincome urban neighborhood.
Probability is one of the most important subjects to be taught because of its pervasiveness in our society. It is used every day, in almost every capacity of daily existence. We are faced daily with situations where a proper understanding of probability is crucial, such as weather reports, investments, and our health. We do not act blindly to get what we want. Our actions also depend on how likely the desired outcome is (Schlottmann 2001). When we make decisions on if we should spend an extra $100 on a warranty for a washer, we use our knowledge of how likely the washer will breakdown to form our decision.
Young children need to explore the process of probability. The study of probability in the early grades provides a stronger foundation for high school students (NCTM, 2000). By studying probability, children make sense of experiences involving chance. Beginning in the elementary grades, students should be taught experimental probability concepts, yet that does not always happen. Even though probability is rich in class participatory activity material and the amount is infinite, as a class progresses through the school system, and content delivery for examinations becomes a priority, this kind of activity tends to be held back. This is truly disappointing as it can actually enrich and motivate a child’s learning (Fisher 2005).
The School District of Philadelphia (SDP) uses Everyday Math as their math curriculum, which is a spiral curriculum that begins with fundamentals that children already have learned and builds upon them by adding more complex and subtle categories and methods. Even though probability is such a major part of our daily lives, SDP only dedicates a few lessons sporadically throughout the school year in their 3^{rd} grade’s Planning and Scheduling Timeline, briefly grazing the topic. Thus, teachers need to supplement the curriculum with more opportunities to help students develop the necessary skills.
The objectives of this probability unit include the following:
The strategies that are the most conducive to a third grade classroom are: examination, exploration, and application. These strategies will be a springboard for the critical thinking that is the emphasis of this unit. They can be explained as follows:
Students examine how probability affects everyday situations in their lives and in read alouds (It’s A Penny by Loreen Leedy, A Million Fish…More or Less by Patricia C. McKissack, A Very Improbable Story: A Math Adventure by Edward Einhorn, and Probably Pistacho by Stewart J. Murphy).
Students discover how probability affects various circumstances by conducting probability experiments and collect, organize, and display data using tables, charts and graphs.
Students apply what they have learned by using basic probability terms in everyday situations and designing probability games.
Note: Each lesson is a 45 minute period.
Objectives:
With 80% accuracy, students will learn:
PA Mathematics Standards:
Materials:
Plans:
Note: Add to these lists throughout the unit.
Objectives:
With 80% accuracy, students will learn:
PA Mathematics Standards:
Materials:
Plans:
Note: Have the chart paper labeled “Probability – Class Chart” and marker ready to write down students’ predictions.
Objectives:
With 80% accuracy, students will learn:
PA Mathematics Standards:
Materials:
Plans:
Objectives:
With 80% accuracy, students will learn:
PA Mathematics Standards:
Materials:
Plans:
Fisher, Ian. “Maths Resource Good Luck?” Mathematics in School. Jan. 2005.
National Council of Teachers of Mathematics (NCTM). Principle and standards
for school mathematics. Reston, VA: NCTM, 2000.
Pennsylvania Department of Education. “Academic Standards for Mathematics.” 22 Pennsylvania Code, Chapter 4, Web. 30 June 2011.
Scholottmann, Anne. “Children’s Probability intuitions: Understanding the Expected Value of Complex Gambles.” Child Development, Jan/Feb 2001.
Resources:
Basic concepts of Certain, Probable, Unlikely, Impossible #1:
http://www.freetrainingtutorial.com/mathgames/probabilitybasics.html?1&
Basic concepts of Certain, Probable, Unlikely, Impossible #2: http://www.kidsmathgamesonline.com/numbers/probability.html
Coin Toss: http://pbskids.org/cyberchase/games/probability/cointoss.html
Fish Tank:http://www.freetrainingtutorial.com/mathgames/probabilityfishtank.html?1&
Marble Mania: http://www.sciencenetlinks.com/interactives/marble/marblemania.html
Probability Quiz: http://www.newbedford.k12.ma.us/elementary/gomes/stjohn/Subjects/Math/Probability/Probability1.html
Appendix 1
Vocabulary for Chance Events
sure will happen 
for sure, unavoidable, absolutely, must

uncertain, not sure 
very likely, almost surely, likely, good chance, probably, tossup, 5050 chance, possibly, not likely, poor chance, very unlikely

sure will not happen 
impossible, no way, can’t happen

Appendix 2
Name: Date:
Grade: /Room:
A Million Fish…More or Less
Directions: Listen to the story A Million Fish…More or Less. Circle the box that shows how likely each event in the book is.
very unlikely  unlikely  likely  very likely 
very unlikely  unlikely  likely  very likely 
very unlikely  unlikely  likely  very likely 
very unlikely  unlikely  likely  very likely 
very unlikely  unlikely  likely  very likely 
very unlikely  unlikely  likely  very likely 
Appendix 3
Name: Date:
Grade: /Room:
Likely and Unlikely Event
Directions: Tell whether each event below is sure to happen, sure not to happen, or may happen, but not sure. Circle the answer.
sure to happen  sure not to happen  may happen, but not sure 
sure to happen  sure not to happen  may happen, but not sure 
sure to happen  sure not to happen  may happen, but not sure 
sure to happen  sure not to happen  may happen, but not sure 
sure to happen  sure not to happen  may happen, but not sure 
Appendix 4
Name: Date:
Grade: /Room:
CoinToss Experiment
Directions: You will each toss all 10 coins 5 times. For each toss you make, record the number of “heads” and the number of “tails” in the table.
Toss Record  
Toss (10 coins)  Heads  Tails 
1  
2  
3  
4  
5  
Total 
Directions: Use the information in both your partner’s and your tables to fill in the blanks below.
My total: Heads: Tails:
My partner’s total: Heads: Tails:
Our partnership total: Heads: Tails:
Directions: Record the number of Heads and the number of Tails for the whole class.
Number of Heads: Number of Tails:
Appendix 5
Name: Date:
Grade: /Room:
Two Marbles
Directions: For this activity, you will use the interactive marble simulation on the computer to repeat the lesson’s first marble experiment that was conducted with only two marbles in the box. Follow these steps to repeat the experiment:
Results for oneintwo (or 50%) chance of picking the red marble or the blue marble
Number of Trials  % of Times Red is Picked  % of Times Blue is Picked 
10  
50  
100  
500 
What do you notice about the marble runs in which you do more trials?
What do you think would happen if you ran 1,000 trials?
Appendix 6
Name: Date:
Grade: /Room:
Probability
Directions: Answer each question.













