LESSON PLAN
Grade Level/Course: Grade 6 Mathematics
Teacher(s): Ms. Green & Mr. Nielsen
Unit: Probability Lesson 6
Date: Summer 2008
Topic(s): Playing Carnival Games
Resources:
Transparencies: _________________________________________________________________________
Worksheets:
Everyday Mathematics MM p.218-219
Technology:
Smart Board, Projector, & Document Camera
Manipulatives:
Calculators, coins, dice, dry erase boards, and markers
Other Supplies: Probability chart
Assessments:
Classwork:
Booth 4
Assignment Options:
__________________________________________________________________
Project/Performance Task: __________________________________________________________________
Quiz/Test:
___ Objective Items
___ Short Answer with Work Shown
___ Extended Response
Individual or Group Presentation: Share group results with class
Notebook/Portfolio:
Record Vocabulary
Journal/Exit Slips:
__________________________________________________________________
Observation(s): _________________________________________________________________________
2007 MN Math Standards and Benchmarks
____ Number & Operations
X
Data Analysis and Probability
_____ Geometry & Measurement
_____ Problem Solving
____ Algebra
Instructional Strategies
Launch:
___ Questioning
___ Inquiry
___ Accessing Prior Knowledge
X Brainstorming
___ Setting Objectives/Goals
___ Recording Information
___ Demonstration
___ Reinforcing Effort
___ Graphic Organizers & Other Non-LRs
X Cooperative Learning
___ Problem Solving
___Problem-based Learning
___ Instructional Technology
___ Compare and Contrast
X Simulations and Modeling
___ Graphic Organizers & Other Non-LRs
Summarize:
___ Questioning
X Written or Oral Summaries
___ Providing Feedback
___ Cooperative Learning
X Compare and Contrast
___Discuss
___ Reinforcing Effort
___Graphic Organizers & Other Non-LRs
X Analyze
Apply:
___ Questioning
___ Presentations and Exhibitions
___ Research
X Project Design
___ Problem Solving
___ Connections to Other Disciplines
Explore:
___ Questioning
___Presentations/Sharing
___ Guided Practice
___ Reinforcing Effort
The Plan:
Objective: Simulate carnival games and predict which
game has the best chance of winning a prize. Find the
outcomes for each booth and the probability of winning a
carnival prize.
Notes/Reflections/Vocabulary:
5 minutes
Vocabulary
*Simple Probability
*Chance
*Outcome
*Equally likely
*Event
*Favorable Outcomes
*Possible Outcomes
*Trial
EXPLORE (Investigation(s))(Making, Investigating, Finding . . .)
35 minutes
LAUNCH (Introducing)
Create a list of games played at carnivals. Discuss the odds
of winning a prize at these games. What is the purpose of
Carnival games?
The students will visit six carnival booths. They will record Carnival Booths
1. Two in a Row 50.0%
the results of 10 games and describe strategies for winning
2. Odd Tail Toss 25.0%
the greatest number of prize coupons. Have students find
3. Roll It Up 41.7%
the possible outcomes using tables. Teach students that the
4. 10 or More 11.1%
probability of an event is favorable outcomes / possible
5. Make the Call 16.7%
outcomes. Model using the table method to produce the
6. 7 or More 58.3%
possible outcomes and probability for booth 6. With the
students, complete the outcomes and probability for booths
1 and 5. Have the students work with partners to practice
with booths 2 and 3. Have students work individually to
complete booth 4.
SUMMARIZE (Wrapping the Lesson) (Discussing, Writing . . .)
Bring the group together to share their booths’ probability.
The teacher will add the probabilities to the class chart.
Have a class discussion about the predicted easiest game
and the game with the greatest probability of winning a
prize coupon.
Extension
Objective: Make a connection between the experimental
probability and theoretical probability of an event. Have
students conduct the experimental probability for the booth
of their choice.
Homework
Create a Carnival Game using dice and or coins. Find the
outcomes using a table and determine the probability of
winning the game.
Resources
Modified from Everyday Mathematics Grade 6 Unit 7, Lesson 7.1
10 minutes
Carnival Games
At the carnival, you play 10 games and will try to
win as many prize coupons as possible. You must
visit at least three different booths.
Booth 1
Booth 2
Two in a Row
Flip a coin twice. If the
coin lands on the same side
both times, you win a prize
coupon.
Booth 3
Odd Tail Toss
Flip a coin once and roll a
die once. If you get Tails
and an odd number, you
win a prize coupon.
Booth 4
Roll It Up
10 or More
Roll a die twice. If the
second roll is a greater
number than the first, you
win a piece coupon.
Roll a die twice. If you get
5 or greater both times,
you win a prize coupon.
Booth 5
Make the Call
Predict the roll of a die. If
that number comes up,
you win a prize coupon.
Booth 6
7 or More
Roll a die twice. If the total
of the rolls is 7 or greater,
you win a prize coupon.
Carnival Games Records
Below, record the number of each booth you visit. Make a tally
mark for each prize coupon you win during your 10 games.
Booth Number
Number of Prize Coupons Won
Total Number of Prize Coupons Won
1. Describe a strategy for winning the greatest number of prize coupons in 10 games
if you must visit at least 3 different booths.
2. At which booths does it seem easy to win?
3. Describe how you would change the rules of one game to make it easier to win.
Carnival Games
Booth
Number of
Favorable Outcomes
Number of
Favorable Outcomes Probability
Possible Outcomes Possible Outcomes of Winning
1
2
3
4
5
6
Carnival Games
Booth
Number of
Favorable Outcomes
1
2
3
4
5
6
2
3
15
4
1
21
Number of
Favorable Outcomes Probability
Possible Outcomes Possible Outcomes of Winning
4
12
36
36
6
36
2/4 or ½
50.0%
3/12 or ¼
25.0%
15/36 or 5/12 41.7%
4/36 or 1/9
11.1%
1/6
16.7%
21/36 or 7/12 58.3%
Booth 1
Flip 1
Flip 2
Heads
Heads
Tails
Heads
Tails
Tails
Heads
Tails
Booth 2
Heads
Tails
1
2
3
4
5
6
Heads Odd
Heads Even
Heads Odd
Heads Even
Heads Odd
Heads Even
Tails Odd
Tails Even
Tails Odd
Tails Even
Tails Odd
Tails Even
Booth 3
1
2
3
4
5
6
1
1,1
1,2
1,3
1,4
1,5
1,6
2
2,1
2,2
2,3
2,4
2,5
2,6
3
3,1
3,2
3,3
3,4
3,5
3,6
4
4,1
4,2
4,3
4,4
4,5
4,6
5
5,1
5,2
5,3
5,4
5,5
5,6
6
6,1
6,2
6,3
6,4
6,5
6,6
Booth 4
1
2
3
4
5
6
1
1,1
1,2
1,3
1,4
1,5
1,6
2
2,1
2,2
2,3
2,4
2,5
2,6
3
3,1
3,2
3,3
3,4
3,5
3,6
4
4,1
4,2
4,3
4,4
4,5
4,6
5
5,1
5,2
5,3
5,4
5,5
5,6
6
6,1
6,2
6,3
6,4
6,5
6,6
Booth 5
1
2
3
4
5
6
Booth 6
1
2
3
4
5
6
1
1,1
1,2
1,3
1,4
1,5
1,6
2
2,1
2,2
2,3
2,4
2,5
2,6
3
3,1
3,2
3,3
3,4
3,5
3,6
4
4,1
4,2
4,3
4,4
4,5
4,6
5
5,1
5,2
5,3
5,4
5,5
5,6
6
6,1
6,2
6,3
6,4
6,5
6,6
LESSON PLAN
Grade Level/Course: Grade 6 Mathematics
Teacher(s): Ms. Green & Mr. Nielsen
Unit: Probability Lesson 7
Date: Summer 2008
Topic(s): Experimental Probability & Coin Flipping
Resources:
Transparencies: _________________________________________________________________________
Worksheets:
Coin Flipping Experiment Handout
Technology:
Smart Board, Projector, & Document Camera
Manipulatives:
Calculators, coins, dry erase boards, and markers
Other Supplies: Probability chart
Assessments:
Classwork:
Assignment Options:
__________________________________________________________________
Project/Performance Task: __________________________________________________________________
Quiz/Test:
___ Objective Items
___ Short Answer with Work Shown
___ Extended Response
Individual or Group Presentation: Share group results with class
Notebook/Portfolio:
Record Vocabulary
Journal/Exit Slips:
__________________________________________________________________
Observation(s): _________________________________________________________________________
2007 MN Math Standards and Benchmarks
____ Number & Operations
X
Data Analysis and Probability
_____ Geometry & Measurement
_____ Problem Solving
____ Algebra
Instructional Strategies
Launch:
___ Questioning
___ Inquiry
___ Accessing Prior Knowledge
X Brainstorming
___ Setting Objectives/Goals
___ Recording Information
___ Demonstration
___ Reinforcing Effort
___ Graphic Organizers & Other Non-LRs
X Cooperative Learning
___ Problem Solving
___Problem-based Learning
___ Instructional Technology
___ Compare and Contrast
X Simulations and Modeling
___ Graphic Organizers & Other Non-LRs
Summarize:
___ Questioning
X Written or Oral Summaries
___ Providing Feedback
___ Cooperative Learning
X Compare and Contrast
___Discuss
___ Reinforcing Effort
___Graphic Organizers & Other Non-LRs
X Analyze
Apply:
___ Questioning
___ Presentations and Exhibitions
___ Research
X Project Design
___ Problem Solving
___ Connections to Other Disciplines
Explore:
___ Questioning
___Presentations/Sharing
___ Guided Practice
___ Reinforcing Effort
The Plan:
Notes/Reflections/Vocabulary:
10 minutes
Vocabulary
Revisit probability tree diagrams using the Carnival Game
booths. Ask students how they would go about create a tree *Tree diagram
*Law of large numbers
LAUNCH (Introducing)
diagram for booth 1. Guide students through a tree diagram
for booth 2.
Objective: Gain additional practice with theoretical and
experimental probabilities by conducting a coin flipping
experiment.
EXPLORE (Investigation(s))(Making, Investigating, Finding . . .)
The students will complete A Coin-Flipping Experiment
handout in small groups. They will analyze the results and
answer questions about the experiment. After completing
the theoretical probability, student will conduct
experimental probability by flipping a coin 300 times and
recording the results.
SUMMARIZE (Wrapping the Lesson) (Discussing, Writing . . .)
Bring the group together to compare experimental and
theoretical probabilities.
Homework
Calculate the number of possible outcomes using a tree
diagram for choosing a dinner from 5 main courses, 3
vegetables, 2 salads, and 4 beverages.
Resources
Modified from Everyday Mathematics Grade 6 Unit 7, Lesson 7.5
30 minutes
The Law of Large Numbers
says that in repeated,
independent trials with the same
probability p of success in each
trial, the percentage of
successes is increasingly likely
to be close to the chance of
success as the number of trials
increases.
10 minutes
Extra Practice Unit 7 Name ___________________________________ Date _________________
A Coin-Flipping Experiment
1. Suppose you flip a coin 3 times.
What is the probability that the coin will land
a. HEADS 3 times?
b. HEADS 2 times and TAILS 1 time?
c. HEADS 1 time and TAILS 2 times?
d. TAILS 3 times?
e. With the same side up all 3 times (that is, all HEADS or all TAILS)?
Make a tree diagram to help you solve the problems.
2. One trial of an experiment consists of flipping a coin 3 times. Suppose you
perform 100 trials. For about how many trials would you expect to get HHH or
TTT?
What percent of the trials is that?
NCTM Standards
Data Analysis and Probability Standard for Grades 6–8
http://standards.nctm.org/document/chapter6/index.htm
Expectations
Instructional programs from
prekindergarten through grade 12
should enable all students to—
In grades 6–8 all students should—
Formulate questions that can be
addressed with data and collect,
organize, and display relevant data to
answer them
• formulate questions, design studies, and collect data about a
Select and use appropriate statistical
methods to analyze data
• find, use, and interpret measures of center and spread, including mean
characteristic shared by two populations or different characteristics
within one population;
• select, create, and use appropriate graphical representations of data,
including histograms, box plots, and scatterplots.
and interquartile range;
• discuss and understand the correspondence between data sets and
their graphical representations, especially histograms, stem-and-leaf
plots, box plots, and scatterplots.
Develop and evaluate inferences and
predictions that are based on data
• use observations about differences between two or more samples to
Understand and apply basic concepts
of probability
• understand and use appropriate terminology to describe complementary
make conjectures about the populations from which the samples were
taken;
• make conjectures about possible relationships between two
characteristics of a sample on the basis of scatterplots of the data and
approximate lines of fit;
• use conjectures to formulate new questions and plan new studies to
answer them.
and mutually exclusive events;
• use proportionality and a basic understanding of probability to make and
test conjectures about the results of experiments and simulations;
• compute probabilities for simple compound events, using such methods
as organized lists, tree diagrams, and area models.
MN State Standards
Grade: 6
Strand: Data Analysis & Probability
Standard: Use probabilities to solve real world and mathematical problems; represent
probabilities using fractions, decimals and percents.
Benchmarks
6.4.1.1
Determine the sample space (set of possible outcomes) for a given experiment and determine
which members of the sample space are related to certain events. Sample space may be
determined by the use of tree diagrams, tables or pictorial representations.
For example: A 6 ⋅ 6 table with entries such as (1,1), (1,2), (1,3), …, (6,6) can be used to represent the sample space
for the experiment of simultaneously rolling two number cubes.
6.4.1.2
Determine the probability of an event using the ratio between the size of the event and the size of
the sample space; represent probabilities as percents, fractions and decimals between 0 and 1
inclusive. Understand that probabilities measure likelihood.
For example: Each outcome for a balanced number cube has probability 1/6, and the probability of rolling an even
number is 1/2.
6.4.1.3
Perform experiments for situations in which the probabilities are known, compare the resulting
relative frequencies with the known probabilities; know that there may be differences.
For example: Heads and tails are equally likely when flipping a fair coin, but if several different
students flipped fair coins 10 times, it is likely that they will find a variety of relative frequencies of
heads and tails.
6.4.1.4
Calculate experimental probabilities from experiments; represent them as percents, fractions and
decimals between 0 and 1 inclusive. Use experimental probabilities to make predictions when
actual probabilities are unknown.
For example: Repeatedly draw colored chips with replacement from a bag with an unknown mixture of chips, record
relative frequencies, and use the results to make predictions about the contents of the bag.