**http://www.illustrativemathematics.org/illustrations/949
**

**http://www.illustrativemathematics.org/illustrations/950**

**http://www.illustrativemathematics.org/illustrations/951**

### COMMON CORE STANDARDS

**Content Standards**

**HS.S-CP.A.2 **Understand that two events *A* and *B* are independent if the probability of *A* and *B* occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

**HS.S-CP.A.3** Understand the conditional probability of *A* given *B* as *P*(*A* and*B*)/*P*(*B*), and interpret independence of *A* and *B* as saying that the conditional probability of *A* given*B* is the same as the probability of *A*, and the conditional probability of *B* given *A* is the same as the probability of *B*.

**HS.S-CP.A.4 **Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.

**HS.S-CP.A.5 **Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

**HS.S-CP.B.6 **Find the conditional probability of *A* given *B* as the fraction of *B*’s outcomes that also belong to *A*, and interpret the answer in terms of the model.

**Standards for Mathematical Practice**

MP 1: Make sense of problems and persevere in solving them.

MP: 3 Construct viable arguments and critique the reasoning of others.

MP 4: Model with mathematics.

MP 6: Attend to precision.

### DESCRIPTION OF LESSON

In this lesson titled “Statistics – Titanic” [part 1] [part 2] [part 3] from Illustrative Mathematics students are provided a contextual problem about a historic event that most students are familiar with: the Titanic. Students are provided with a table of data and were asked several questions regarding independence and conditional probability. Students need to make a claim and support their conclusion using appropriate evidence and reasoning. The lesson is intended for group work. There are three tiers for this lesson. However, there are not recommendations for ELL students.

### CAUTIONS

Some of the cautions of this lesson include a lack of support for English language learners. There is also a lack of procedural skill development. There are sample solutions but there is no rubric for providing unbiased assessments. There is also a lack of technology support. There is a lack of additional practice to provide opportunities for transfer. Teachers should provide more assessment for the task. There should also be an addition of some way to adjust this for more multicultural students.

### RATIONALE FOR SELECTION

The lesson provides a contextual approach to understanding independent events and conditional probability. There are multiple tiers to meet the needs of diverse learners and extend the task for advanced learners. There is a balanced approach to teaching, including conceptual understanding and computation. The lesson also provides a seemingly simple question and allows students to make predictions and engage in mathematical inquiry. Each tier provides a different amount of questions and provides different scaffolds to support all students.