Quiz + The Language of Probability

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Objective

Quiz + SWBAT use the language of chance to describe probability.

Big Idea

Students take a quiz and then complete notes and classwork to introduce probability

Quiz

30 minutes

Students enter silently. Quizzes are on their desks and they are to begin as soon as possible. They are allowed to spread out and sit at empty tables and are given the option to use cardboard dividers and noise canceling head phones. Instructions on the SmartBoard notify students that they will only have 30 minutes to complete this quiz (a timer will be displayed). All students must enter their answers into clickers. This makes the grading process much faster, allowing me to have the time to analyze the data. At the end of the quiz, all students will be asked to turn in their quizzes, and the Class Notes and Class Work will be distributed.

This quiz will assess knowledge of vocabulary (quartile, box-and-whisker), calculating measures of variation (IQR and MAD), and other statistical topics including mean, median, mode and range. After analyzing the data I determined that I need to continue reviewing:

  • Calculating and interpreting mean absolute deviation
  • Second tier vocabulary, to ease the discomfort in patients” means to help them feel better, not feel pain.
    • Strategies for breaking down terms and phrases to decode their meaning

More than 50% of my students scored below a 70% on this quiz. This meant the grade would not go into the grade book and we will need to continue reviewing these topics throughout next week.

The main topic that most students seemed to struggle with is mean absolute deviation, calculating and understanding what it represents. I also think students struggled with decoding the differences between each multiple choice answer choice at the end of the quiz so that they could select the correct one. Again, I need to continue teaching second tier and third tier vocabulary directly so that students can understand the differences. More so, I need to find strategies that are applicable to different word problem solving, including multiple choice questions. 

Class Notes

10 minutes

After students turn in their quizzes they are handed Class Notes. They must work on pre-reading the handout if they finish early, trying to understand the materials and fill in the blanks on their own.

The first two terms are basic and given to students. It is important not to make the assumption that because these are basic building blocks for probability, students will automatically understand their meaning after reading the term and definition for the first time. We review these terms with the following questions:

  • Give an example of probability; ask students to do the same
  • In a given example, what is the “event”?

Example: a coin is flipped 10 times. What is the probability that it will land on heads?

  • What is another way to say “what is the probability…? How likely is it…?
  • What is an event in this question? Landing on heads

 

We continue by reviewing the concepts of population and sample. Personally, I have always struggled with the concept of probability itself. When I have trouble with a concept, I make sure to create a cheat sheet for myself of the most important ideas I need to communicate during a class. This resource is attached as the “Teacher cheat sheet”.

 

Reviewing the basic vocabulary, terms and linguistic details belonging to this concept is equally as important as reviewing the probability continuum pictured at the bottom of the notes. This number line is included in our standards as a must know. Because I know my students have struggled with fractions in the past, I proactively think of questions to push these specific students in understanding how they are related to each other:

  • What fraction represents a 50/50 chance of something happening? 50%?
  • If something is 25% likely to happen, is that more or less than half?
  • Where would you place this probability on the continuum (number line)/ give various examples
  • Give a fraction example of an event that could be “unlikely”
  • Draw the pie visual that shows an even that is            likely to happen

Class Work + Closing

20 minutes

After reviewing the important topics in the class notes, students are given their Classwork, which is due at the end of class. I will be using the results to determine how much review and revisiting of these topics I need to cover the following day. I review the first couple of problems with students. Some students may already know how to answer these problems, but some may need the important refresher that answers are to be given in fraction or percent form when asked for the probability. Some students will also need guidance in looking out for the type of question being asked: is it asking for the probability? Or for the number of outcomes possible?

This last 10-15 minutes after an assessment is a great time to work with small groups of students. I target students who usually do not perform well on quizzes because I know their self-esteem may be low at this time and I do not want to risk them not trying on a new topic.  Most of the work time is spent cheerleading and allowing student to talk about their frustration while attempting to show them that it is possible to keep going and working hard.

Once there are 5 minutes left in class I review at least one other question in Part A section and one question in the part B section. Checking in about the continuum is very important as our future conversations about probability will be built around the concept of this number line and the fractions associated with the likelihood of an event occurring.

Classwork sheets are collected and homework is distributed.