How will students learn? 

There will be several ways to interact with me in an online class: through synchronous interaction and asynchronous interactions.

Here are some examples of ways I will engage in synchronous interactions:

Live course orientation. 

Synchronous online meeting. 

How will the students learn?

*The students will be able to discuss what makes word problems challenging. Explain that one strategy for solving
word problems effectively is to identify “key words” which indicate a mathematical operation. 

How will they interact with myself and each other?

I will use the gradual release method of teaching: " I do, we do, you do" 
- First, I demonstrate how to do it (using several examples).  
- Next, the students do some problems along with me.
- Finally, they complete some problems on their own that I will check for accuracy and give more guidance if needed. 

How is class time structured?

The material taught in an online course follows a structure. Just like a traditional course, students start at the beginning of the education objectives and progress through the coursework. They move from the most introductory topics the class covers to the most advanced.

What topics will be covered?

Students will be able to master the following in this lesson: 

Listed below are some of the questions that you may ask during this lesson and what they need to master. The questions I will ask will depend on the students' responses. My focus in this part of the lesson is to have students try and picture the problem in their head and creating a graphic organizer template to make sense of what is happening in any given Math problem. Students will come up with a variety of answers. Some example questions I could ask include:

1) What do you notice about this word problem? (answers may vary: there are 8 zebras and 5 monkeys, it has animals, it has numbers, etc.)
2) What is different in the problem? (answers may vary: there are different animals, numbers are different, there's more zebras, there are less monkeys, etc.)
3) What are we trying to find out? (how many less monkeys there are than zebras)
4) How can we represent this part of the story? (draw, write a number, use manipulatives)
5) What would help us organize our thinking and our work? (answers may vary: draw it out, act it out, write an equation, etc.)
6) What strategies can we use to solve this problem? (we can match up 5 zebras and 5 monkeys then see how many zebras are left, that will tell us how many fewer monkeys we have than zebras.)

Class break down per day of instruction. Note *(instructional minutes may vary depending of skill set of students/groups)

Introduction and Rationale
Throughout these lessons I will be building the students skills and knowledge of multiplying and dividing fractions. 



 Day #1 (50 minutes)*
Introductory Probability Problems

The opening activity gets students talking about and defining the concept of probability and student’s definitions will likely revolve around the “fairness” of the game.  As you can see in my Introduction to Probability PowerPoint, we take this introductory understanding and build on it throughout the lesson. 

Guiding the lesson, I make sure to include student involvement.  Periodically, I ask students to turn and talk with their thinking groups or people sitting nearest to them. Some strategies and questioning I use to help promote student dialogue include:

    For example #1, I have students collaborate to devise a third option that would be a fair way of assigning food. Students are very creative with this!  It is fun to critique the ideas that are brought to the table for discussion (MP3)! 
    For example #2, I ask the students if they ever “pulled a fast one” on a brother or sister that is similar to the situation in the example.  The students like to share these stories, and many of them will bring a lot of laughs!
    Many of the students will have suggested the idea of a random number generator in conversation from the first examples, #1 and #2, prior to seeing example #3! 
    For examples #5 and #6, I introduce the students to the mathematical notation used when determining probabilities.   

If I have additional time, I like to ask the students what principals from our statistics unit can apply as we study probability.  



Day #2 (60 minutes)*

It's all about chance

Objective
SWBAT use the language of probability to describe different events
Big Idea
The students will be learning about probability language and how it pertains to their lives.

Do NOW
(10 minutes)*

For this experiment, I will have 20 blue marbles and 15 green marbles in a paper bag.

We are going to do an experiment! Let’s try and find out, without looking in the bag and counting, whether there are more blue or more green marbles in the bag. Randomly choose four students to record the numbers and colors of marbles for each of the four draws.

Think – Pair-share (using the following questions)

Based on the first 4 draws, can we determine how many marbles of each color are in the bag?

Next, allow I am going to choose 5 marbles from the bag (be sure to return the marbles to the bag) record the results and ask the following questions.

What are the totals for each color of marbles?

Do you think there were more marbles of one color than the other?

If so, what do you think the ratio of one color to the other might be?

Finally, open the bag and count the number of marbles of each color.

Ask the students to determine the ratio of one color to the other color?

Ask students to draw a conclusion about the ratio of blue marbles to green marbles? (The probability of drawing a blue marble is four times greater than drawing a green one.) Allow students to come up with other statements like it is more likely to draw a blue marble than a green marble.  Or it is unlikely to draw a green marble out of the bag.  

Learning about probability
30 minutes

In this part of the lesson, I’m going to be introducing/reinforcing the language of probability.  In the do now activity, students may have already been using words like likely, unlikely, certain or impossible.  Ask them if they have ever heard these words in real life? (weather, lottery, events)  Use the PowerPoint to facilitate the discussion on probability

Slide 3 shows the probability of even occurring using percents.  Ask the students what they are looking at when determining probability.  (I want them to see that probability is placed on a number line and that the closer to zero or 1 will determine whether an event will or will not occur).  I also want them to see that probabilities can be written as fractions, decimals, or percents because of the use of a number line.

Slide 4:  Using the questions from this slide have students articulate to show their answers.  This is a good way to formally assess whether or not they are getting the language of probability.

Slide 5 is a review of changing from Fractions to decimals to percents.  Before showing slide 5, I will review this orally with the students to see if they can recall this information on their own.  I may even use a think-pair-share to hold them accountable for the reasoning.  Once you have gone through all of the conversions, show them slide 5 and have them make notes of this in their notes.

Slide 6 has them using the conversions. 

Group conversation time
(20 minutes)

Once the direct instruction has been completed

Questions 1 – 6 ask the students to determine if the probability is certain, likely, as likely as not, unlikely, or impossible.  Students may come up with different responses so I’m going to be encouraging and listening to them reason out their thoughts.  Before I call they will have to show me their answer, I will ask them to justify their answer (SMP 3)

Questions 7 – 11 ask the students to write their probabilities as fractions, decimals, or percents.  The students will need to show their work when solving these problems.  

Closure
(5 minutes)

Students will be working on coming up with a scenario that represents the following situations:  certain, likely, as likely as not, unlikely, and impossible.  I want them to come up with an event to represent each.  Have students work alone before sharing with the group. Some scenarios can be used for whole group discussion. (SMP 3)

For example:

    Think of an event  that is certain will happen(60 minutes in an hour, 24 hours in a day, 7 days in a week)
    Think of an event that is impossible to happen (61 minutes in an hour, 8 days in a week)
    Think of an event that is as likely as not to happen (flipping a coin, you are either a boy or a girl)

Next, the students will be writing an equivalent to .8 as a fraction and a percent.  Have them show their work to support their answer and then share their answers with the class.


Day #3
Compound Events - Visual Displays of Sample Spaces

Objective
Students will be able to represent the sample space of compound events and calculate the probability of events using their sample space.

Big Idea
Ever wonder how many outfits you can make out of what is in your closet? After this lesson, students will be able to.

Explore
Compound Events Explore Narrative: In this lesson, students will model (MP 4) probability through the creation of a sample space (MP 5) using a tree diagram.  Drawing tree diagrams can be difficult and cumbersome for some students, so it will be important they pay close attention to precision (MP 6).  Students will be asked to persevere with problems without my assistance (MP 1).

Summarize

Summary Poster: To summarize the lesson, I am going to give each table one scenario to create a visual display for.  The student will correctly identify all combinations in the sample space, and then answer any questions that were included in the scenario. 


Day #3 (60 minutes)*
Experimental and Theoretical Probability
Objective
SWBAT explore the similarities and differences between theoretical and experimental probabilities.
Big Idea
Students will be able to see the relationship between theoretical probability and experimental probability by computing both at the same time.

Vocabulary
20 minutes

Vocabulary

To start the lesson, I’m going to go over some common vocabulary of probability.  I chose 2 words that they may hear throughout this lesson.  Once we have the vocabulary down, I want them to look at Theoretical Probability.  I’m going to tell them what it means, but I want them to think about what it will look like.  So, I will ask them.  By looking at how theoretical probability is written(words), tell me how that will look on paper (numbers).  I’m hoping to hear them tell me it will be a fraction or a ratio (SMP 
2) I will also ask them if they recognize any base word in Theoretical?  We have all heard the word “theory” before, what does that mean?  After students have responded to this, I will show them the slide on Experimental Probability.  Again, I will ask them if they recognize a base word? (experiment) and then ask them what does it mean to do an experiment?  I will show them how to write experimental probability (words) and ask them what it will look like in numbers?

Questioning of vocabulary

Before moving on, I will have students do a think-pair-share using the following question:

How are theoretical probabilities alike and how are they different?


Theoretical vs Experimental Probability
20 minutes

Next, I’ve constructed the power point so that each slide has an event that starts out by finding the theoretical probability and then finding the experimental probability.  I have the students doing the experiment 50 times, but I may start off by asking them to roll it once and record it.  Make their comparisons. Students may have a difficult time making a comparison especially since the probabilities will be written as fractions.  To help with this, I would encourage students to write their probabilities as decimals and percents too.  Decimals and percents make for much easier comparisons.  Then have them roll it 10 times and make a comparison.  Then roll it 20 times and make a comparison.  I would do this just a couple of times to get students to realize that the more times the experiment is done, the better our chances of getting our experimental and theoretical probability to match.  (when doing the experiment, remind students that they will each get a turn doing the experiment.  Dice, spinners and coins should be passed around the table so all students are engaged in the activity and all students should be recording the results)

Finding the Complement
(15 minutes)*

After the students have completed their comparisons, I want them to look at the complement of an event.  They have already been given the definition, so I’m going to try and get them to apply the definition of each scenario given.   So, I will say… Knowing the definition of complement,  Make a statement using the complement of “there is a 10% chance of rain today”.  I’m looking for kids to say that there is a 90% chance it won’t rain today so it is likely it will not rain.

If there is a 45% chance of you passing this test, make a statement using the complement.  I’m looking for students to say, “there is a 55% chance that I will not pass the test so it is as likely as not that I will pass”.

Each of these scenarios can be completed independently at first, then shared with partners so the students can hear different ways of expressing the probabilities.


Closure
(15 minutes)

Allow students time to write down their thoughts on the following 3 questions.  Reflecting in writing is a good way for students to solidify their learning.  As a whole group, have the students share their thoughts.

Explain whether you and a friend will get the same experimental probability for an event if you perform the same experiment. (I’m expecting to hear that you will not get the same probability because the experiment is based on chance.  It is possible, but unlikely.)

Explain whether you and friend will get the same theoretical probability for an event if you are using the same experiment (this is certain because this is what should happen and they are looking at the same event)

Tell why it is important to repeat an experiment many times. (the more times the experiment is performed the better your chances of matching the theoretical probability)

Common Misconceptions:

Often times, students will write the theoretical probability based on the numerical value.  For example, when asked to find the P(5) on a die.  Students will say 5/6.  When I see this happening, I simply say “ how many 5’s are on the die”, they respond “1”.  I explain that this is the chance of getting a 5, 1/6.