CCGPS Mathematics Unit-by-Unit Grade Level Webinar Analytic Geometry Unit 7: Applications of Probability November 12, 2013 Session will be begin at 8:00 am While you are waiting, please do the following: Configure your microphone and speakers by going to: Tools – Audio – Audio setup wizard Document downloads: When you are prompted to download a document, please choose or create the folder to which the document should be saved, so that you may retrieve it later.

CCGPS Mathematics Unit-by-Unit Grade Level Webinar Analytic Geometry Unit 7: Applications of Probability November 12, 2013 James Pratt – Brooke Kline – Secondary Mathematics Specialists These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

The big idea of Unit 7 Incorporating SMPs into applications of probability Resources Welcome!

 Question: In the Middle School and Coordinate Algebra Unit Frameworks, I noticed they have included both Formative Assessment Lessons (FAL) and Short Cycle Tasks (SCT) from the Mathematics Assessment Project. Why do the Analytic Geometry Unit Frameworks only contain FALs? Wiki/ Questions

Wiki/ Questions  Formative Assessment Lesson (FAL)/Classroom Challenges

Wiki/ Questions  Short Cycle Task (SCT)/Assessment Tasks (Novice, Apprentice, Expert)

Analytic Geometry Short Cycle Tasks  Unit 1 – Hopewell Geometry, Floor Pattern  Unit 2 – Pythagorean Triplets, Triangular Frameworks  Unit 3 – Circles in Triangles, A Golden Crown, Bestsize Cans, Funsize Cans, Propane Tanks  Unit 4 – The Real Number System, Cross Totals, Arithmetic with Polynomial and Rational Expressions  Unit 5 – Sidewalk Stones, Patchwork, Table Tiles, Building Functions, Functions, Reasoning with Equations & Inequalities, Seeing Structure in Expressions  Unit 6 – no short cycle tasks included in the unit  Unit 7 – no short cycle tasks included in the unit

Teacher Edition – page 98 All four functions are neither odd nor even. Unit 5: Parent Graphs Revisited Task

Using the Venn diagram, determine the following sets. S.CP.1

What’s the big idea? Understand independence and conditional probability and use them to interpret data Use the rules of probability to compute probabilities of compound events in a uniform probability model

What’s the big idea? Standards for Mathematical Practice

What’s the big idea? Dan Meyer Robert Kaplinsky Teaching Channel Illustrative Mathematics Expeditionary Learning MAP Standards for Mathematical Practice

Coherence and Focus K-9 th  Basic probability (no formulas)  Probability models  Two way tables 11th-12th  Multiplication Rule for Probability  Making decisions based on probability

Suppose that today there is a 60% chance of rain, a 15% chance of lightning, and a 20% chance of lightning if it’s raining. What is the chance of both rain and lightning today? Adapted from Illustrative Mathematics S-CP Rain and Lightning Examples & Explanations

Suppose that today there is a 60% chance of rain, a 15% chance of lightning, and a 20% chance of lightning if it’s raining. What is the chance of both rain and lightning today? P (rain) =.6 P (lightning) =.15 P (lightning | rain) =.2 Adapted from Illustrative Mathematics S-CP Rain and Lightning Examples & Explanations

Suppose that today there is a 60% chance of rain, a 15% chance of lightning, and a 20% chance of lightning if it’s raining. What is the chance of both rain and lightning today? P (rain) =.6 P (lightning) =.15 P (lightning | rain) =.2 Adapted from Illustrative Mathematics S-CP Rain and Lightning Examples & Explanations Need to determine P (lightning and rain)

Suppose that today there is a 60% chance of rain, a 15% chance of lightning, and a 20% chance of lightning if it’s raining. What is the chance of both rain and lightning today? P (rain) =.6 P (lightning) =.15 P (lightning | rain) =.2 Adapted from Illustrative Mathematics S-CP Rain and Lightning Examples & Explanations P (lightning and rain)/ P (rain) = P (lightning | rain)

Suppose that today there is a 60% chance of rain, a 15% chance of lightning, and a 20% chance of lightning if it’s raining. What is the chance of both rain and lightning today? P (rain) =.6 P (lightning) =.15 P (lightning | rain) =.2 Adapted from Illustrative Mathematics S-CP Rain and Lightning Examples & Explanations P (lightning and rain)/.6 =.2 P (lightning and rain) =.12 There is a 12% chance of both rain and lightning today.

Examples & Explanations Adapted from Illustrative Mathematics – S-CP The Titanic 1 On April 15, 1912, the Titanic struck an iceberg and rapidly sank with only 710 of her 2,204 passengers and crew surviving. Some believe that the rescue procedures favored the wealthier first class passengers. Data on survival of passengers are summarized in the table below. We will use this data to investigate the validity of such claims. (Data source: SurvivedDid not surviveTotal First class passengers Second class passengers Third class passengers Total

Examples & Explanations Adapted from Illustrative Mathematics – S-CP The Titanic 1 If one of the passengers is randomly selected, what is the probability that this passenger was in first class and survived? If one of the passengers is randomly selected from the first class passengers, what is the probability that this passenger survived? SurvivedDid not surviveTotal First class passengers Second class passengers Third class passengers Total

Examples & Explanations Adapted from Illustrative Mathematics – S-CP The Titanic 1 If one of the passengers is randomly selected, what is the probability that this passenger was in first class and survived? SurvivedDid not surviveTotal First class passengers Second class passengers Third class passengers Total

Examples & Explanations Adapted from Illustrative Mathematics – S-CP The Titanic 1 SurvivedDid not surviveTotal First class passengers Second class passengers Third class passengers Total

Examples & Explanations Adapted from Illustrative Mathematics – S-CP The Titanic 1 If one of the passengers is randomly selected from the first class passengers, what is the probability that this passenger survived? SurvivedDid not surviveTotal First class passengers Second class passengers Third class passengers Total

Examples & Explanations Adapted from Illustrative Mathematics – S-CP The Titanic 1 If one of the passengers is randomly selected from the first class passengers, what is the probability that this passenger survived? SurvivedDid not surviveTotal First class passengers Second class passengers Third class passengers Total

Examples & Explanations Adapted from Illustrative Mathematics – S-CP The Titanic 2 Are the events “passenger survived” and “passenger was in first class” independent events? Support your answer using appropriate probability calculations. SurvivedDid not surviveTotal First class passengers Second class passengers Third class passengers Total

Examples & Explanations Adapted from Illustrative Mathematics – S-CP The Titanic 2 Are the events “passenger survived” and “passenger was in first class” independent events? Support your answer using appropriate probability calculations. Two events A and B are independent if P (A|B) = P (A) SurvivedDid not surviveTotal First class passengers Second class passengers Third class passengers Total

Examples & Explanations Adapted from Illustrative Mathematics – S-CP The Titanic 2 SurvivedDid not surviveTotal First class passengers Second class passengers Third class passengers Total

Examples & Explanations Adapted from Illustrative Mathematics – S-CP The Titanic 2 SurvivedDid not surviveTotal First class passengers Second class passengers Third class passengers Total

Analytic Geometry EOCT Released Items Released Items: Housed in the Assessment Division of GADOE Assessment/Assessment/Documents/Analytic%20Geometry% 20Released%20Items%20Booklet%20Revised% pdf Assessment/Assessment/Documents/Analytic%20Geometry% 20Released%20Items%20Booklet%20Revised% pdf Released Items Commentary: Housed in the Assessment Division of GADOE Assessment/Assessment/Documents/Analytic%20Geometry%2 0Released%20Items%20-%20Commentary%20Revised% pdf There are 18 released items and commentary about each item available for Analytic Geometry

Analytic Geometry EOCT Released Items

Analytic Geometry Released Item #18

Data on AG Released Item #18

Unit 7 Frameworks The following tasks in Unit 7 are related to this released item: The Conditions are Right The Land of Independence False Positives Are You Positive

EOCT Study Guide Assessment/Assessment/Documents/EOCT%20Anal ytic%20Geometry%20Study%20Guide%20FINAL% pdf

EOCT Study Guide Assessment/Assessment/Documents/EOCT%20Anal ytic%20Geometry%20Study%20Guide%20FINAL% pdf

Resource List The following list is provided as a sample of available resources and is for informational purposes only. It is your responsibility to investigate them to determine their value and appropriateness for your district. GaDOE does not endorse or recommend the purchase of or use of any particular resource.

CCGPS Resources  Georgia Virtual Learning -  SEDL videos - or  Illustrative Mathematics -  Mathematics Vision Project -  Dana Center's CCSS Toolbox -  Tools for the Common Core Standards -  LearnZillion - Assessment Resources  MAP -  Illustrative Mathematics -  CCSS Toolbox: PARCC Prototyping Project -  Smarter Balanced -  PARCC -  Online Assessment System - Resources

LearnZillion Revised A more “user friendly” version of the Learnzillion lessons support learning new strategies, sharing with parents, helping absent students.

LearnZillion Revised

LearnZillion Revised

LearnZillion Revised

LearnZillion Revised

LearnZillion Revised

LearnZillion Revised

LearnZillion Revised

Resources Professional Learning Resources  Inside Mathematics-  Annenberg Learner -  Edutopia –  Teaching Channel -  Ontario Ministry of Education -  Achieve -  Expeditionary Learning: Center for Student Work - Blogs  Dan Meyer –  Robert Kaplinsky - Books  Van De Walle & Lovin, Teaching Student-Centered Mathematics, Grades 5-8

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Thank You! Please visit to share your feedback, ask questions, and share your ideas and resources! Please visit to join the 9-12 Mathematics listserve. Follow us on Brooke Kline Program Specialist (6 ‐ 12) James Pratt Program Specialist (6-12) These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.