Playing with Probability, Percent, Ratios, and Circles Lesson 4

Children's Books

Using Children's Books to Understand Probability, Percent, Ratios, and Circles

The beginning of this unit plan can be found here.

Lesson 4

In today's lesson we are going to be using what we learned about percents and turning them into a visual display of data. Today's lesson is going to be fun because we are going to be creating charts so therefore the students are going to get to use markers and their artistic ability. Where in the other lessons in this book were used to introduce and give the students problems to solve, todays book in mostly going to be used for a background and reasoning for why we are going to calculate the central angle theorem. Today's lesson background information is a proof on the central angle. I do not expect my students to be able to comprehend the proof but do want to point out two things. The first being what a professional mathematical proof looks like because many have never seen one. Also the radius and diameter are used in the proof so therefore what they learned in previously math classes is not unimportant.

The students are going to take a probability and turn it into a percent. From there they are going to calculate the central angle of each of the percents. Finally they are going to draw a circle and then using the central angles they found create a circle graph or pie graph to model the date. Today's lesson is going to include everything that I want the students to be able to do except for taking and solving a probability problem out of a book. This step will be added in tomorrow's lesson. These problems are problems that should take a decent amount of time. So therefore I am not concerned with them working many problems like with the lesson on percents but just want them to understand the steps taken in this process. The finite mathematics book shows calculating the central angle and creating a circle graph but they do not show how these are related so hopefully in today's lesson my students will come to understand why we calculate the central angle and how that helps us create graphs.

Standards:

• Journalism
  • The student will understand and utilize oral, written, and visual communication.

• Write for an intended (prescribed) audience, recognizing the importance of ethics in information gathering and reporting. (This supports my lesson because we use the central angle theorem to determine the correct amount of the circle a certain percentage receives. In this lesson they will come to understand how visual displays of data can be misleading.)
• Exhibit a working knowledge for roles and procedures of management and production of various media. (They are going to be creating a pie/circle graph which is media. So therefore they need to understand the procedures of creating one.)
• Finite Mathematics
  • CLE 3182.1.4 Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to model mathematical ideas, and to communicate solution strategies. (Previously in the unit we have been working with verbal and written representations. In today's lesson they are going to be expected to move to pictorial and graphical displays of data.)
  • CLE 3182.5.4 Calculate and interpret statistical problems using measures of central tendencies and graphs. (The calculate part of this standard will be the students calculating the central angle theorem. The interpret part of this standard will be the understanding of how a greater part of the pie/circle graph means a person has a greater probability of getting that outcome.)

Objectives:

• TSWBAT calculate the central angle of a given percentage.
• TSWBAT create a circle/pie graph using the central angle

Assessment/Evaluation

• The informal assessment will occur when I am walking around while the students are observing. The formal assessment will be the homework I give them for this section along with the project which will be done tomorrow in class.

Materials

• Sir Cumference and the First Round Table
• Sir Cumference and the First Round Table PowerPoint
• SmartBoard
• Finite Mathematics Textbook
• Proof of the central angle theorem.

Activating Strategy

• We have been working with different ways to write data. Today we are going to learn how to create a visual display for our data. The first question I have to ask is do newspapers and TV programs ever create visual displays of data that are misleading.

Instructions

I am going to start today's lesson with the activating strategy. I am going to ask them if newspapers and TV programs ever mislead us. Hopefully they will come up with some instances where this is the case. If not I am going to ask them if they have ever seen the smaller print on an ad. This will hopefully prompt some discussion. I am going to mention that people can do this with the way they present graphs to us also. We can have this with bar graphs that are not proportional and with circle graphs also. We are going to make circle graphs today so we need to do everything in our power to make sure they are as informative and unbiased as possible. I am then going to start the book Sir Cumference and the First Round Table and read up until page 10. Then discuss with them why a square table would not allow us to be unbiased. Then I would read until page 13. We would then discuss why a parallelogram shape is not unbiased. I would ask the same question for a triangle table on page 16. I would ask and we would discuss the same question for an octagon on page 19. I would then read the rest of the book. I would ask the students for the reasons on why the circular table allows for equality. I would them those are some valid reason if they are valid and then mention one of the reasons is every person receives the same angle. This is due to the central angle theorem and I would show them the slide with it on it. I would show them how to calculate the central angle on problem 21 in section 1.7 of the finite textbook. I would then ask them to calculate the central angle of 45%. I would find a student who achieved the correct answer and have them model the problem on the board. I would then have them calculate the central angles of 20%, 30%, and 50%. I would walk around and observe. I would ask a student who calculated the correct answer to come to the board and do the problem for us. I would then tell them we are going to create circle graph with this data. I would draw a circle and using a protractor I would model for them the process to create a circle graph. I would then ask for questions. The next thing I would do would be to have them create 4 percents that add up to 100%. Then I would ask them to create a circle graph for their data. I would walk around and support them while they worked on this. Then we would wrap up and revisit our goals for this lesson. I would assign them problems 23 and 24 on page 52 in the Finite Mathematics textbook for homework.

Book

• The book I am going to use is called Sir Cumference and the First Round Table and it is going to support my lesson by helping answer the activating strategy question. In the book they are trying to create a table in which everyone's seat is fair. They go through several types of tables but cannot find one that is equal. Then they determine a circle would be fair. The book does not say why this is fair but it is because of the central angle theorem and that is not a difficult point to include while reading it. Also included in the book are the words radius and diameter which we do not talk about today but are good reminders of what is included when we talk about circles. Finally almost everyone knows that King Arthur had a round table and this book gives mathematical justification on the reasons. It is important in mathematics to have justification on steps and reasons.

Background

• Proof of the central angle theorem. (Handout for the students)

Reflection

• Today's lesson is the final learning lesson in the unit. Therefore today I would let the student's know that instead of a test at the end of this unit they are going to be expected to do a project with all of the concepts we have learned in this unit. I want to do this today and not the first day of the unit because if I would have stated this first they might have become overwhelmed. I know they know the information because they have been assessed on it so if they become nervous I can just ask a student a topic in the unit and they should be able to explain to me what they did. Therefore I can ease their fears.
• In today's lesson I need to remind them when things are mentioned what certain geometric concepts are. The book does a great job of talking about them but I need to make sure the students still understand because that will allow the lesson to proceed smoothly. I keep pulling problems from the Finite Mathematics textbook because I think it is important that the students understand that we are working on topics in it and not just making up my own class.
  
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