7.6.1Ma

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 * Grade: 7 Unit: 6 Week: 1 **
 * Content: Understanding Probability **
 * Dates: 4/8/2013 - 4/12/2013 **

How does the probability of an outcome affect the decision making process in real-life situations?
 * __ Theme Essential Question __**** : **


 * __ Essential Questions __**** : **
 * How does the study of probability influence the description of the likelihood of an event occurring?
 * How can you represent, describe, and use sample spaces for compound events in an organized way?


 * __ Standards __**** : **
 * ** 7. SP.5: ** Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.


 * __ Objectives __**** : **
 * The student will calculate simple probabilities
 * The student will utilize the values of probabilities to describe the likelihood of the event occurring.
 * The student will apply the concepts of independent and dependent events in determining probability.

Grade 7 is the introduction to the formal study of probability. Through multiple experiences, students begin to understand the probability of chance (simple and compound), develop and use sample spaces, compare experimental and theoretical probabilities, develop and use graphical organizers, and use information from simulations for predictions.
 * Background Information **
 * Taken from __Ohio Dept of Education Mathematics Model Curriculum 6-28-2011__ **

Help students understand the probability of chance is using the benchmarks of probability: 0, 1 and ½. Provide students with situations that have clearly defined probability of never happening as zero, always happening as 1 or equally likely to happen as to not happen as 1/2. Then advance to situations in which the probability is somewhere between any two of these benchmark values. This builds to the concept of expressing the probability as a number between 0 and 1. Use this understanding to build the understanding that the closer the probability is to 0, the more likely it will not happen, and the closer to 1, the more likely it will happen.

Additionally, students often struggle when converting forms of probability from fractions to percents and vice versa. To help students with the discussion of probability, don’t allow the symbol manipulation/conversions to detract from the conversations. By having students use technology such as a graphing calculator or computer software to simulate a situation and graph the results, the focus is on the interpretation of the data. Students then make predictions about the general population based on these probabilities.


 * Recommended: For a quick overview of the stands(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials at ** @http://www.azed.gov/educator-certification/**.**

Each student is to develop situations of their own that have a probability of 0, 1, and 1/2. Place students in pairs and allow the pairs to discuss their problems and solutions.
 * __ Assessment __**** : **
 * Product **


 * Key Questions **
 * What range of values can a probability of chance obtain?
 * What does it mean to have a probability of 0 indicate?
 * What does it mean to have a probability of 1 indicate?
 * What does it mean to have a probability of ½ indicate?

The student can find a probability of an event and discuss the likelihoods of the even.
 * Observable Student Behaviors (Performance ** )

1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||
 * ** Mathematical Practices **


 * __ Vocabulary __**** : **

Event probability Complement Independent dependent ||
 * ** Math ** ||
 * Experiment trial Outcome


 * __ Suggested Activities __** :
 * // Houghton Mifflin On Core Mathematics Middle School // Grade 7
 * Unit 7-1, Understanding Probability, p. 157-160
 * ABC //Mastering the Common Core in Mathematics//
 * Chapter 15.1, Probability, p. 189-190
 * Chapter 15.2, Independent and Dependent Events, p. 191-192
 * Chapter 15.3, More Probability, p. 193

v Gizmo Correlation v @http://sciencenetlinks.com/interactives/marble/marblemania.html Marble Mania: In this interactive, you'll explore randomness and probability. You'll be able to control how many and what color marbles to place in the online marble bag. You'll also be able to decide how many marbles to pull at a time and how many trials to run. An advantage to using this interactive is that you can run a large number of different trials in a short amount of time.
 * 7.SP.5
 * Geometric Probability-Activity A
 * Randomly throw darts at a target and see what percent are "hits." Vary the size of the target and repeat the experiment. Study the relationship between the area of the target and the percent of darts that strike it.
 * Probability Simulations
 * Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes
 * Compound Independent and Dependent Events
 * Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events.
 * High Recommended: None available at this time
 * JBHM 8th, GP 1, p.387-418
 * Glencoe 7th Algebra I, Chapter 14-3, p.769
 * // Teaching the Common Core Math Standards with Hands-On Activities, //
 * // 7.SP.5 – Activity p. 139 //


 * Diverse Learners **
 * Odyssey (teacher discretion)
 * Skills Tutor (teacher discretion)
 * Math’s Cool
 * Algebra’s Cool


 * __ Homework __**** : ** (Teacher Discretion)
 * @http://www.kutasoftware.com/free.html To print assignment on a variety of topics.
 * See appropriate Glencoe On Core, JBHM and ABC Materials under Suggested Activities
 * Exit Slip (Question or problem to answer before leaving class that will help guide instruction for the following day.)


 * __ Terminology for Teachers __**** : **

** E ** thnicity/**C**ulture | **I**mmigration/**M**igration | **I**ntercultural **C**ompetence | **S**ocialization | **R**acism/**D**iscrimination ** High Yield Strategies ** ** S ** imilarities/**D**ifferences | **S**ummarizing/**N**otetaking | **R**einforcing/**R**ecognition | **H**omework/**P**ractice | ** N ** on-**L**inguistic representation | **C**ooperative **L**earning | **O**bjectives/**F**eedback | ** G ** enerating-**T**esting **H**ypothesis | **C**ues, **Q**uestions, **O**rganizers  || Lesson Plan in Word Format (Click Cancel if asked to Log In)
 * ** Multicultural Concepts **


 * __ Resources __**** : **


 * __ Professional Texts: __**


 * __ Literary Texts __**


 * __ Informational Texts __**


 * __ Art, Music, and Media __**


 * __ Manipulatives __**
 * Marble Bag
 * Spinners
 * Number Cubes
 * Coins
 * Colored Chips
 * Graphing Calculator


 * __ Games __**


 * **Videos** **

This lesson activity allows students to explore probability through the use of spinners, dice, and a random image chooser. Students will discuss if a situation has a equal probability or unequal probability. Introduces probability, experimental and theoretical probability, complementary events. Introduces 6th graders to probability with some basic definitions and then an interactive dice roll to complete an experiment.
 * __ Smartboard Lesson, Promethean Lessons __**
 * 7S.P. 5 Exploring Probability
 * 7S.P. 5 Introduction to Probability
 * 7S.P. 5 Probability Introduction


 * __ Other Activities, etc. __**

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