Author: Jason M. Bui
School/Organization:
S. Weir Mitchell Elementary School
Year: 2011
Seminar: Math Concepts in the Classroom
Grade Level: 3
Keywords: Everyday Math, probability, self contained
School Subject(s): Math
This unit is designed for a selfcontained third grade classroom that is following the
School District of Philadelphia’s Core Curriculum with Everyday Mathematics. The unit
is intended to reinforce the Pennsylvania state mathematics probability and prediction
standards already covered in Kindergarten through second grade and provide the students
with a more solid base of understanding for the standards that will be covered in third
grade and beyond.
Probability is not covered in detail in the third grade Everyday Mathematics curiculum
until the end of the year. It touches on probability concepts here and there throughout the
year one lesson at a time. As a result the students have a difficult time connecting the
different probability concepts they are taught. The students also have a difficult time
connecting the idea of probability to their own lives. This unit will cover probability
concepts once a week for six to eight weeks. This will give the students time to master
and connect the different probability concepts and skills taught to them previously and
also help them to master the probability concepts and skills that will be taught to them in
the future.
The goal is that at the end of the unit the studneys will be able to design a fair game of
their own to demonstrate their knowledge of probabilty.
Download Unit: 11.02.02.pdf
This unit it designed to help students develop a better understanding of probability and chance. The unit focuses on the concepts of fair and unfair and logic as they relate to the rules of games. The unit will explore the skills of counting possible outcomes, determining if the outcomes are equally likely or not, calculating the probability of each outcome, and finally using probability to determine if the rules are fair and make sense.
This unit is designed for a selfcontained third grade classroom that is following the School District of Philadelphia’s Core Curriculum with Everyday Mathematics. The unit is intended to reinforce the Pennsylvania state mathematics probability and prediction standards already covered in Kindergarten through second grade and provide the students with a more solid base of understanding for the standards that will be covered in third grade and beyond.
Probability is a concept that the Everyday Mathematics curriculum touches on here and there throughout the year. It’s not a concept however, that the curriculum spends a significant amount of time on. As a result the students have a difficult time connecting the different probability concepts they are taught. They also have a difficult time connecting the idea of probability to their lives. This unit will cover the concept of probability once a week for six to eight weeks, which will give the students time to master and connect the different probability concepts and skills taught to them previously and also help them to master the probability concepts and skills that will be taught to them in the future.
The unit will teach the students strategies they can use to count possible outcomes of an experiment.
It can often be difficult to connect third grade mathematics to the real lives of third graders from lower socioeconomic backgrounds. The concept of fair versus unfair is very real and important to third graders however. Students often get upset and declare that “It’s not fair!” when they lose at something.
This unit will take place within the confines of the Core Curriculum. Lessons in this unit will be taught once a week on Fridays for six to eight weeks. Most Fridays in the Core Curriculum are used for playing Everyday Mathematics games and review. The lessons in this are not meant to replace the math games and review. The lessons will incorporate the math games into the unit by having the students analyze the rules of the games to determine A) if the games are fair and B) if the rules make sense. The lessons will also save time throughout the year when the Friday review would be about probability. Students will construct an understanding of basic probability concepts in this unit, so less time is required for formal review of them.
The following probability terms are important to know and understand to teach this unit; sample space, outcomes, event, experiment, and probability. A sample space is the set of things that could happen. Outcomes are the basic things that could happen i.e. the elements of the sample space. An event is a set or collection of outcomes. The probability of an event is the chance that the event will happen expressed as a percentage or a number between 0 and 1.
This unit seeks to give students a thorough understanding of how to determine if a game or activity is fair and whether the rules of the game are logical. The unit will examine fairness through the use of probability.
The unit will break down the understanding of probability and fairness into three basic questions: How many possible outcomes are there for the experiment of playing one’s turn? Are all of the outcomes equally likely? And if not, does the unequal probability give an advantage to one of the players?
The students will understand what an experiment and an outcome are. The experiments in this unit will be playing one’s turn. They will learn to use the FourStep Method and a table or an organized list (see Strategies below) to count the possible outcomes of an experiment.
The students will be taught the following strategies during this unit.
The FourStep Method (The Problem Solver 3)
Find Out: The first step of the FourStep Method is to understand what the problem is about. The students will have to comprehend the words and phrases used in the problem. They will have to be able to identify the question in the problem.
Choose a Strategy: The second step of the FourStep Method is choosing an appropriate strategy that will help you solve the problem. The students should realize that there is usually more than one way to solve a problem however certain strategies are more helpful for particular problems.
Solve It: The third step of the FourStep Method is solving the problem. The students will need to be able to use their strategies to work through the problem.
Look Back: The fourth step of the FourStep Method is to check your work. The students should reread the problem and make sure their answer makes sense.
Use or Make a Table (The Problem Solver 3)
One example of using the fourstep method is making a table. A table is a way to organize data. Tables help students “keep track of data, spot missing data, and identify data that is asked for in a problem.” Making a table doesn’t directly relate to probabilitiy.
Example:
Problem 35 from The Problem Solver 3: The guards of Clock Castle open the two gates at the same time every hour to let visitors go into the castle. The guards keep track of how many people they let in through their gates. This is what they wrote today.
Time  8:00  9:00  10:00  11:00  12:00  1:00  2:00  3:00 
Visitors through the King’s Gate  1  5  9  13  17  
Visitors through the Queen’s Gate  1  4  9  12  17 
The guards kept letting visitors go into the castle in the same way all day. How many visitors went through Queen’s Gate at the time that 33 visitors went through King’s Gate?
Solution: 33 visitors
Time  8:00  9:00  10:00  11:00  12:00  1:00  2:00  3:00  4:00 
Visitors through the King’s Gate  1  5  9  13  17  21  25  29  33 
Visitors through the Queen’s Gate  1  4  9  12  17  20  25  28  33 
Make an Organized List
An organized list helps students to keep their ideas about a problem organized. It is easier to look back and review the work that they already have done.
Example:
Problem 3 from The Problem Solver 3: The sign says: JULIO’S MAGIC SHOW. Julio is behind the curtain, getting ready for the show. He has to make up his mind what to put on. He will wear a cape or a coat. On his head he will wear a bright red wig or a hat. Then he will put on his black boots or his shoes with the pointy toes. What are the 8 different outfits Julio could wear for his magic show?
Solution:
Piece for Shoulders  Piece for Head  Pieces for Feet  
Outfit 1  coat  wig  boots 
Outfit 2  coat  wig  shoes 
Outfit 3  coat  hat  boots 
Outfit 4  coat  hat  shoes 
Outfit 5  cape  wig  boots 
Outfit 6  cape  wig  shoes 
Outfit 7  cape  hat  boots 
Outfit 8  cape  hat  shoes 
Duration: Two days (about 45 minutes per day)
Objectives:
The students will be able to count the number of possible outcomes of an experiment. They will be able to organize the outcomes in an organized list or a table. Students will understand that making an organized list or table will help them keep track of outcomes, spot missing outcomes and identify outcomes. They will also understand that organized lists and tables make it easier to discover patterns.
PA Mathematics Standards:
2.7C. List or graph the possible results of an experiment.
Materials:
The Problem Solver 3: Problem # 3
A spinner with four equal sections for each group
A regular sixsided die for each group
Varioussided dice
Duration: Two days (about 45 minutes per day)
Objectives:
The students will be able to count the number of possible outcomes of an experiment. They will be able to determine if all of the possible outcomes are equally likely or not.
PA Mathematics Standards:
2.7.A. Predict and measure the likelihood of an outcomes and recognize that the results of an experiment may not match predicted outcomes.
Materials:
A spinner with four equal sections for each group
A regular sixsided die for each group
Various – spinners
Quarters (real or from the Everyday Mathematics kit)
Worksheet 2A
1.Warm Up (5 minutes)
1.Warm Up (5 minutes)
Duration: Two days (about 45 minutes per day)
Objectives:
PA Mathematics Standards:
2.7A. Predict and measure the likelihood of experiments and recognize that the results of an experiment may not match predicted outcomes.
2.7C. List or graph the possible results of an experiment.
2.7D. Analyze data using the concepts of largest, smallest, most often, least often and middle.
Materials:
Baseball Multiplication boards (Many of the Everyday Mathematics games will work. Use a game that the class is familiar with.)
Dice (two different colors)
Counters
1.Warm Up (5 minutes)
1.Warm Up (5 minutes)
Duration: Two days (about 45 – 65 minutes per day)
Objectives:
Students will be able to design a fair and logical game.
PA Mathematics Standards:
2.7A. Predict and measure the likelihood of experiments and recognize that the results of an experiment may not match predicted outcomes.
2.7B. Design a fair and an unfair spinner.
2.7D. Analyze data using the concepts of largest, smallest, most often, least often and middle.
Materials:
Blank spinners
Dice
Cards
Poster board
Scissors
Glue
Crayons
1.Warm Up (5 minutes)
The Problem Solver 3: Activities for Learning ProblemSolving Strategies
School District of Philadelphia Core Curriculum Grade 3 Mathematics
Everyday Mathematics Teachers Edition
www.EdHelper.com/probability.html
www.freetrainingtutorial.com/probabilitygames.html
Pennsylvania State Mathematic Standards
2.7A. Predict and measure the likelihood of experiments and recognize that the results of an experiment may not match predicted outcomes.
2.7B. Design a fair and an unfair spinner.
2.7C. List or graph the possible results of an experiment.
2.7D. Analyze data using the concepts of largest, smallest, most often, least often and middle.
2A, Blank Spinner, Math Game Making Instructions
1) My spinner had _____ different sections.
2) When I spin the spinner there are _____ possible outcomes.
3) The possible outcomes are __________________________
________________________________________________.
4) The sections are all the same sizes or different sizes. Circle one.
Total ______
5) Are your results what you expected? Why or why not?
________________________________________________
________________________________________________
________________________________________________

Directions for making your own spinner
Pencil
Ruler
Paperclip
Protractor (optional)
Scoring Chart for Baseball Multiplication
36 = Home run
25 to 35 = Triple
16 – 24 = Single
5 or less = Out
Math Game Making Instructions
Today you are going to get to make your very own math game. Your game must show your understanding of the probability concepts we have been going over in class.
1) Your game must be fair. That means that all players have an equal chance of winning the game no matter when their turn is. 2) Your game can use spinners, dice, or coins. 3) Your game should be fun to play.
