Sample Unit

Probability Unit Overview

Students will learn about probability. We will compare and contrast both theoretical probability and experimental probability through a variety of rich learning experiences.

Learning Expectations:

  • Determine the theoretical probability of an outcome in a probability experiment, and use it to predict the frequency of the outcome.
  • Demonstrate an understanding of relationships involving percent.
  • Represent the probability of an event using a value from the range 0 to 1.
  • Predict the frequency of an outcome of a simple probability experiment or game, by calculating and using the theoretical probability of that outcome.
  • Estimate quantities using benchmarks of  10%, 25%, 50%, 75%, and 100%.

Prepare a flexible plan sequencing learning experiences:

1. Introductory Lesson: Explore – What is probability? Students play Lucky 7 and begin to calculate the probability of winning for each player. Pg’s 388 – 389.2. Pg’s 390 – 391. Activity – Which game are you more likely to win?

Students are offered a choice of two games. They are asked which game they are more likely   to win.

3. Pg’s 392 – 393. Activity – Coin Flipping, students forming circles, spinning bottles and determining probability of bottle landing on either a girl or boy.

4. Pg’s 394 – 397. Maze Activity. Create a maze with paths leading to each desk grouping using masking tape. Either prizes or a performance activity will be waiting at each grouping. -What is the probability of winning a prize in this maze?

5. Pg’s 400 – 401. Activity – Game with dice. Students choose which player they would like to be in order to win this game of probability.

6. Pg’s 402 – 403. Activity – Drawing Tree Diagrams.

Culminating Lesson: Pg’s 404 – 405. Dance Activity. Students create Board Game for culminating task.

Decide how you will organize your space:

Desk groupings around the room.

Decide how you will adapt and modify your plans for specific students:

Students working at the grade 5 level will use their Math Quest 5 books for any textbook work. Students needing an extra challenge will be assigned corresponding lesson questions from the Skills and Problem Banks (407 – 410)

Decide on homework tasks:

*Any work assigned that is not completed in class.

*Culminating Task (Create a Board Game)

Decide how you will communicate with parents:

Through signed planners. Phone calls home if necessary.

Decide how you will celebrate the learning:

We will celebrate the learning by having the students play each others board games.

Board Game Culminating Task

Your Name: _______________________

Group Member Names

  1. _______________________
  2. _______________________
  3. _______________________
  4. _______________________

Your task is to design a Board Game.

As a Group you will hand in the following:

[ ] Completed Board Game

[ ] Good copy of Instructions/ Rules

[ ] Good copy of your probability question with Tree Diagram, Experiment,  and all questions answered.

[ ] Individual copies of Board Game Culminating Task Sheet.

Draw a rough sketch of Board:

What kind of Dice will you use? (Choose one)

[ ] Standard

[ ] Make our own

What is the title of your Game? ___________________________________

How many players can play your game? ____________

How do you know who wins the game?

______________________________________________________________________________________________________________________________________________

Instruction/ Rules

Write a rough draft of the rules to your game:

Pose a question of probability (example: Player A is 3 spots behind Player B. If both players get one more roll each, what is the probability of Player A passing Player B?)

or

(Player A is 12 spots away from the finish line. What is the probability of Player A getting the finish line in 2 rolls of the dice?)

Question:

a) Determine the Theoretical probability using a Tree Diagram. Represent the probability using a fraction and a percentage.

b) Determine an Experimental probability by conducting an experiment. Represent the probability using a fraction and a percentage.

I contributed to my group by: ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Introductory Lesson to Probability

Goal: Begin to understand the concept of Probability.

Body:

Pose Question: What is Probability? (7 minutes)

30 seconds to discuss with your group.

Probability is the likelihood that an event will happen.

Coin

Raise your hand if you have ever flipped a coin to decide on something.

If I flip this coin, what are chances it will land on Heads?

If I flip this coin, what is the probability of it landing the Heads?

If I flip this coin twice, what is the probability of its landing on heads both times?

Dice

What are the chances that I will roll a 3?

What is the probability that I will roll an even number?

Spinner

Two sections are blue, one is red, and one is green.

What are the chances I will spin on a blue?

Play Lucky 7 (25 minutes)

Distribute Materials, Explain the Game. (5 minutes)

Students play and record results on a piece of paper as outlined on page 388.

Students complete – Do You Remember? (Diagnostic) (20 minutes)

Page. 389

I will model questions 1 and 2. They have the rest of the period to complete the 6 questions.

Materials Needed:

-Large Dice

-Coin

-27 dice

-Counters

-Blank Paper for Lucky Seven and Do You Remember?

Lesson 2 – Conducting Probability Experiments

Goal: Compare probabilities in two experiments.

Body:

Review (2 minutes)

What is probability? What is a multiple?

Activity (25 minutes)– Which game are you more likely to win?

-Students are offered a choice of two games. They are asked which game they are more likely to win.

– Take a class vote. (1 minute)

– Each table will receive two dice and a box of counters.

– Referring to page 390, in their math notebooks each group will complete questions A to E on a large piece of paper, making a chart to record the results of each game.

Groups Present (10 minutes)

Groups will then present to the class which game they are more likely to win and why using probability language.

Visualizing Fractions on a Number Line (10 minutes)

Have students draw a number line in their notebooks while I draw one on the board.

Place finger on 0. This means the event is impossible, will never occur.

Place finger on 1. This means the event will always happen.

Place finger in the middle. This means the even has a 50 percent chance of    happening (heads and tails).

Where is 2/3’s on the number line?

Where is 1/4 on the number line?

Introduce terms: very unlikely, unlikely, likely, very likely.

Place the following fractions on the probability line. Tell which probability word or phrase best describes the probability.

a)     1/4

b)    4/5

c)     2/20

d)    5/16

Quiz on Number Line (10 minutes)

Materials Needed:

15 dice

Counters

Large sheets of Paper

Markers

Copies of Number Line Quiz

Lesson 3 – Using Percents to Describe Probabilities

Goal: Conduct experiments and use percent to describe probabilities.

Body:

Review (2 minutes)

How do you turn a fraction into a percentage?

Demonstrate (10 minutes)

Demonstrate how to use a percentage to describe probability.

Coin:

What is the probability of flipping Tails?

–       Draw a Number Line

–       Have a student place his finger on the line to show probability

–       Determine the fraction

–       Turn the fraction into a percentage

–       Answer: There is a 50% chance I will flip a tails.

Repeat: If all students in the classroom stood around a circle and we spun a bottle,   what is the probability of the bottle landing on a girl?

Independent Work (30 minutes)

Students complete Using Percents to Describe Probabilities Hand out

Materials Needed:

– 27 copies of ‘Using Percents to Describe Probabilities’ hand out. (Page 117)

– 27 dice

– Coin

– Bottle

Lesson 4 – Solving a Problem by Conducting an Experiment

Goal: Use an experiment as a problem solving strategy.

Body:

Maze Activity (35 minutes)

-Create a maze with paths leading to each desk grouping using masking tape.

-Each desk grouping contains a hidden prize or performance activity. (Dance for 30 seconds, Stick of Gum, Sing Twinkle Twinkle Little Star, Read a Poem etc)

-There are 6 desk groupings. 4 will be performance activities, 2 will contain small prizes.

-What is the probability of winning a prize in this maze? Make a class prediction.

-Class lines the perimeter of the Classroom.

-In pairs, students walk through the maze. Students on perimeter will flip a coin each time they come to a place in the path where they have to choose to go left or right. This way the choice is Random. – Vocabulary check.

Heads = Left

Tails = Right

-Eventually they will end up at a desk grouping and will uncover their prize or performance activity.

One student records results on the SMART Board.

1 toss 2nd toss 3rd toss 4th toss 5th toss Prize or Activity?
H H T P
T T H T A
T H H T H A

Independent Work (10 minutes)

In notebooks students answer the following questions:

  1. The probability of getting a prize in our maze is: (fraction)
  2. The probability of getting a prize in our maze is : (percentage)
  3. Was our prediction right?
  4. Why was a coin flip a good model to make the path choice random?
  5. Is an experiment a good way to solve this problem? Explain.

Materials Needed:

– 2 types of prizes (suckers, chocolate)

– 4 different Performance Activities

– Masking Tape

– SMART Board

– Coin

*Mid Chapter Review Students complete page 399 in text books.

Lesson 5 – Theoretical Probability

Goal: Create a list of all possible outcomes to determine a probability.

Body:

Review (2 minutes)

Experimental Probability.

Introduce Theoretical Probability (7 minutes)

-Choose a student to come to the front of the class. Introduce a game (page 400). Player 1 wins a point if they roll a 4. Player 2 wins a point if the sum of both Player 1 and 2’s rolls equal a 4. Ask the student to pick which player s/he would like to be.

-Before we play, we must figure out which player has the best chance of winning using Theoretical probability.

-On SMART Board, make a chart of all the possible outcomes. (See page 400 for chart)

-Once we have figured out each player’s probability of winning. The student may wish to re consider their choice of player.

-Play the game.

Ask students: (5 minutes)

  1. Why is the theoretical probability of Player 1 winning 6/36?
  2. How could we have predicted there would be 36 outcomes?
  3. How do we know that our chart includes all possible outcomes for the game?

Independent Practice (30 minutes)

Page 401 Questions 4 – 7.

Closer (3 minutes)

-Venn Diagram on SMART Board. Theoretical Probability vs Experimental Probability.

Materials Needed:

-Large foam dice

-SMART Board

Lesson 6 Tree Diagrams

Goal: Use a tree diagram to determine a theoretical probability

Body:

Review (3 minutes)

Review theoretical probability, display chart we used to figure out all of the different possibilities for the “Winning 4’s game”

Introduce Tree Diagrams (5 minutes)

Tree Diagrams are another way to figure out all of the possibilities. This is a way to count all combinations of events, using lines to form branches.

Tree Diagram for if you flip a coin twice.

Guided Practice (15 minutes)

Students open notebooks. They will draw a tree diagram along with me as I demonstrate on the SMART Board. We will be completing the tree diagram started on Page 401. We will complete A-C together.

Independent Practice (30 minutes)

Page 403 questions 3 and 4.

Closer (2 min)

How do you use the tree diagram to determine the denominator? The numerator?

Materials Needed:

SMART Board.

Lesson 7 Comparing Theoretical and Experimental Probability

Goal: Compare the theoretical probability of an event with the results of an experiment.

Body:

Review (10 minutes)

Questions from page 403

Class Activity (20 minutes)

We are going to compare the theoretical experimental probability and of pulling a red cube then a blue cube. The bag is filled with 4 cubes. 1 Blue, 1 Yellow, 2 Red. We will start by creating a Tree Diagram to determine the theoretical probability.

When we conduct our experiment, students will do a sequence of dance steps that correlate with the chosen color.

Red = Spin

Blue = Jazz Square

Yellow = Sunshine hands

Essentially the dance sequence we are looking for is a Spin then Jazz Square.

Each table grouping will now perform an experiment where they pull two cubes from the bag and record their results to find the experimental probability of pulling a red cube followed by a blue cube.

First Pull Second Pull
1 Y R
2 R R
3 R B

We will then compare our Theoretical Probability to our Experimental Probability.

Independent Work (20 minutes)

Student’s complete questions 4, 5, 6 on page 105

Introduce Culminating Task (10 minutes)

Students will work in groups of 4 or 5 and make a board game. They will each be given a Board Game Culminating Task sheet. This sheet will help them to get started and organize their project. It also has a space for them to let me know how they contributed to their group. Each student will hand in this sheet individually to me when they hand in and present their board game.

Closer (2 minutes)

Ask students: Which method do you prefer to use when determining probability? Experimental or Theoretical? Why?

Materials Needed:

Coloured Cubes

Paper bags

Dice

____________________________________________________________________________________________________________________________________________

Culminating Task Rubric – Board Game

4 3 2 1
Board Board very is creative.Board relates very well to the theme and rules of the game.Board is done in a very artful and thoughtful manner. Board is creative.Board relates well to the theme and rules of the game.Board is done in an artful and thoughtful manner. Board is somewhat creative.Board somewhat relates to the theme and rules of the game.Board is done in a somewhat artful and thoughtful manner. Board is not very creative.Board does not relate to the theme and rules of the game.Board is not done in an artful or thoughtful manner.
Instructions/ Rules Rules are completely clear and well thought out.No grammar or spelling errors have been made.Good copy is extremely neat and tidy with a clear readable font. Rules are clear and well thought out.Few grammar and spelling errors have been made.Good copy is neat and tidy with a clear readable font. Rules are unclear, with little thought included.Many grammar and spelling errors have been made.Good copy is messy. Font is difficult to read. No rules included or rules are very unclear, with no thought included.A lot of grammar and spelling errors have been made.Good copy is very messy. Font is difficult to read.
Probability Question A strong probability question is posed.Tree Diagram is complete and accurate with no errors.Experiment was conducted and was done at least 20 times.Questions were answered in full and were completely accurate. A somewhat strong probability question is posed.Tree Diagram is complete and accurate with few errors.Experiment was conducted and was done at least 10 times.Questions were answered in full and were almost completely accurate. A weaker probability question is posed.Tree Diagram is incomplete with errors.Experiment was conducted and was done less than 10 times.Questions were not answered in full and were somewhat accurate. A week probability question is posed, or no probability question was posed.Tree Diagram is not included or is incomplete with many errors.Experiment was not conducted or was conducted less than 10 times and results were not recorded well.Questions were not answered in full and were very inaccurate.
Board Game Task Sheet Work sheet was filled out completely.Specific plans were laid out clearly as well as an accurate account of how they contributed to the group. Work sheet was filled out completely.Specific plans were laid out as well as an accurate account of how they contributed to the group. Work sheet was not filled out completely.Vague plans were laid out. A somewhat accurate account of how they contributed to the group was included. Work sheet was not filled out or done very poorly.No plans were laid out. An account of how they contributed to the group was not included or inaccurate.
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