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Playing with Probability, Percent, Ratios, and Circles

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

This unit plan is going to encompass four main topics and then relating them back together. The first day we are going to go over probability with word problems presented in the book Probably Pistachio . This will be a great opportunity for the students to be introduced to basic probability and the pulling out of information from word problems. The second day we are going to talk about Percent using the book Twizzlers Percentages Book and an activity using Twizzlers. This will allow them to be comfortable to taking multiple items and turning them into proportions of the whole. The third day we are going to talk about ratios using the book Pythagoras and the Ratios: A Math Adventure. This will allow them to become comfortable doing two things. They are pulling information out and turning it into ratios and turning a percent into a ratio. The fourth day we are going to use the 
book Sir Cumference and the First Round Table to introduce the ideas of ethics in reporting and measurement of the central angle. This will allow them to create graphs using data and show how people can create graphs of data which could possibly be misleading. The final lesson will allow for us to wrap up all of the information we have learned in this section. It hopefully will be almost like a work day. I am going to read the book A Very Improbably Story and stop at each point where the author creates a problem using probability that we can solve. When I reach one of these points I am going to ask my students to create 4 items. They are the probability written in math terms, percents that represent the problem, ratios that represent the problem, and a circle graph that represents the problem. This will show the students how all of the math is tied together.

Lesson 1

The first lesson is going to involve the students taking word problems from the book, Probably Pistachio , and turning them into mathematical terms. I idea in the first lesson is to establish what mathematics looks like when written down in words and then taking those words and turning them in this case into probability. The first thing I am going to do is do a warm-up so the students can see probability before they start to have to identify it out of a book. I picked this book in particular because it makes the identifying the probabilities easier because they are always in the thought bubbles of the characters. Also I picked this book because in it it introduces the ideas of a certain event, a n uncertain event, and an impossible event. So when we come to these items in the book it will be very easy to identify why probability is important.
I plan on using several instances of informal assessment with a formal assessment occurring after this lesson and after the entire unit. The informal assessment will mostly consist of me walking around and checking the student's thoughts and answers. This is possible because my class size is 20 students which is relatively small. This lesson will hopefully be very similar to the final lesson in this unit with the last lesson including more questions for the students to ponder. There is no way I can get this book for each student in the class so I plan on reading it to them and stopping each time we get to a probability to break up the instruction. Besides the reading and mathematics objectives in the lesson my hope is the students will understand how these concepts apply in real life and in their lives particularly. This lesson is the first lesson in this unit because it answers the why question and the lessons in the middle of the unit do not answer that question as easily.

Standards:

    • The student will understand and utilize oral, written, and visual communication.
      • Apply terms and expressions common to the industry to speaking, listening, and writing activities. (This will support my lesson because the student will need to understand oral (me talking), written (the book's works), and visual (the books pictures) communication to create the math from it. Mathematics and probability have symbols which are unique to it which the students need to understand.)
    • CFU 3005.3.15 Generate notes while collecting information. (It is important for the student to take notes will collecting the information in this lesson because the notes created will allow the student to answer the probability questions. Also in the final lesson they will be expected to do this on their own so we are introducing it now.)
  • Finite Mathematics
    • CLE 3182.1.6 Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between mathematics and the real world. (This is the whole goal of this lesson. The student must take reading and turn it into mathematics. Hopefully they will see the connection to the real world by reading the book.)
    • CLE 3182.5.1 Develop concepts in probability, including sample spaces and event probabilities. (This is the key idea in this lesson the concepts of probability. The major concepts will be a certain, uncertain, and impossible event in a certain sample space.

Objectives:

  • TSWBAT take probability written in language and turn it into mathematical terms.
  • TSWBAT solve probability problems.

Assessment/Evaluation

  • The students will be assessed in two ways. Informal will be walking around while the students try and take probabilities and solve them. Formally will be an exit ticket, homework, and a project after the last lesson.

Materials

  • Probably Pistachio
  • Probably Pistachio PowerPoint
  • SmartBoard

Activating Strategy

I will start the lesson in the PowerPoint by asking the question. If I was to randomly pick a student to answer a question in this class what would be the probability that the student will be a female?
Instructions
I would start today by going over their homework. I would start today's lesson by asking the activating strategy question. Then I would tell the students we need to identify two items to solve this problem to determine the probability. I would say the probability is just the chance we have of getting what we desire. I would say the sample space which is just all of the possibilities. The next thing is the event which is the possibilities which give us the result we want. I would inform the students today's objectives so the understood the goals for this lesson. I would then start reading Probably Pistachio . I would read the first 8 pages stopping after page 8. I would ask the question what does Jack desire for his lunch. I would then say the sample space is the total number of days. I would then ask out of 5 days how many were pastrami? I would point out that 4 pastrami days out of 5 days gives us the probability of 4/5. I would then continue reading until page 14. I would introduce the term a certain event. I would ask if we are certain of something then what the probability of it occurring is. I would now read to page 16. I would introduce the term an impossible event. I would ask if we were sure something is not going to occur what is its probability? I would read to page 18. I would ask them the question looking at the bubble what is the total number of possibilities? Out of these possibilities which are the result we want? Then I would ask the students what is the probability of getting popcorn and to solve it in their notes. I would then walk around and assess the students on how they were doing. (If a student is struggling then there are more than welcome to look at a partner's work and ask them for help. I want them and they do an unbelievable job of collaborating together.) When they were done I would ask a student who reached the correct solution to explain it to the rest of the class. I would then read to page 22. I would then ask them to identify what event is on page 21 and to write the probability of it on their notes. I would again walk around and ask a student to explain when they were done. I would read up until page 26. Again on the piece on their notes I would ask the students to identify the probability of Jack getting the ice cream he wants. This would be the final informal assessment and therefore they did not receive as much guidance on it as in the other problems. I would then read the remainder of the book. At the end I would ask the students for their thoughts on the book. Then as an exit ticket the students would be asked to solve the activating strategy and to give me the sample space and events for this problem. For homework they will be expected to complete problems 1-20 in the Finite Mathematics textbook on page 424.

Book

  • The book I am going to use is called Probably Pistachio and it is about a boy who has the worst day ever because the probabilities do not play out in his favor. It supports the lesson because the students will have to determine what a probability is in the book and then how to solve it. As pointed out previously the book hits on the topics of impossible, certain, and uncertain events. Also it gives a wide range of probability problems which leave the ability for me to discuss if that is good or bad odds for us. With this probabilities are not guarantee which the book shows. Also I believe the book is very engaging so therefore my students will enjoy it. Finally the book is not extremely long so therefore the seniors I have will not have time to decide the book is "lame."

Background Information

  • Blaise Pascal and Pierre de Fermat were the mathematicians who invented probability. They invented probability because they were arguing with each other while they were gambling.

Reflection

  • I believe this is going to be a great lesson. It really ties in to my overarching objectives as a teacher which are for the students to be responsible critical thinkers. The responsible will be hit on later in the unit but probability as a whole requires critical thinking and then adding the fact that they are going to have to pull the information out of a book adds a whole new element. Also they do not have to get this lesson today even though that is my goal to get the rest of the unit which I believe will be beneficial.
  • In this section I really need to stress how the students will be able to take what they learn today and apply it in their lives. I also need to be very enthusiastic about the reading because this is out of their normal classroom instruction. I need to make the point that even though this book is considered a children's book that does not mean it does not have beneficial stuff for us to learn.
The rest of the lessons can be found here:

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