## 1. I. Introduction

### 1.1. Geometry: Probability Basics

1.1.1. Grade Level: 9th-11th

1.1.1.1. California Common Core Mathematics Standards

1.1.1.1.1. S-CP-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.

1.1.1.1.2. S-MD-6 Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

1.1.1.1.3. S-MD-7 Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

### 1.2. Why Differentiation?

1.2.1. In classrooms today, not only are they filled with a diverse cultural population, all students are at different academic levels, and have different social/emotional and support needs. "In a differentiated classroom, commonalities are acknowledged and built upon, and student differences also become important elements in teaching and learning" (Tomlinson, 2017, pg.8). Since there are various needs per student in a classroom, the concept of differentiation has great value when planning and implementing a lesson. Students who need additional academic support will value from scaffolding or even learning experiences in the classroom. Advanced learners will benefit from being challenged beyond their level to promote academic growth.

1.2.2. Students will be learning the foundations of probability through a discovery based lesson called "Trash Can Probability".

### 1.3. Instructional Strategies

1.3.1. A) Compacting

1.3.1.1. Through this three step process defined in the text (Defining goals based on assessment, planning for instruction for students to achieve mastery, and providing alternative assignments), I am able to provide opportunities for success for advanced learners (Thomlinson 2017, pg. 23). For this particular lesson all students will be pre-assessed based on a computer based homework assignment done the night before using an edulastic.com quiz. In this quiz they were to work with fractions, converting fractions to decimals, and ranking fractions and decimals in order from least to greatest. This will help me be aware of students who have the appropriate readiness to identify the value behind fractions before we start associating it with proportions for probability. For the discovery based activity in class I will also group the more advanced learners together and provide them with an additional worksheet for if they complete before others where they will examine a word problem to see if they can use their prior knowledge to discover the probability of a specific scenario happening.

1.3.2. B) Differentiated Homework with Homework Checkers

1.3.2.1. In my classroom students have two homework options when completing textbook assignments. There is Homework A and B. These assignment letters are given based on the seating chart I give to my students, and students with A are advanced and B is the average students. I also give appropriate accommodations for those with Individualized Education Plans (IEPs). Differentiated homework is when "the teacher assigns students homework based on readiness so that students' work is appropriate for their current points of development with the content" (Tomlinson 2017, pg.24). I typically walk around to check for homework completion, but students will work with peers in small groups of A or B assignments to discuss their work and strategies they took to complete problems.

1.3.3. C) Flexible Grouping

1.3.3.1. "The teacher forms groups based on the match of the task to student readiness, interest or approach to learning" is an aspect of flexible grouping in the classroom (Tomlinson 2017, pg. 24). The classroom seating chart is set up in rows where each student sits next to an elbow partner. Each pair is a more advanced student paired with an average student so they can discuss key concepts through opportunities during direct instruction. Students also can easily form groups with the peers around them. Since I can easily identify advanced students I am able to form groups of students for the discovery based activity. In this activity, Trashcan Probability, Students will be in groups of three based on their level of readiness. Within these groups students will be attempting to make baskets from differing distances and analyzing data on results, students will begin to understand the concept of chance and quantify the likelihood of an event using a value from 0 to 1.

1.3.4. D) Interest Centers or Interest Groups

1.3.4.1. This activity is an opportunity for students to collaborate with their peers in a fun and interesting way. Students will be shooting hoops to discover probability through how often they are making baskets from various distances. I have a classroom that loves sports so it sparked their interest when it was presented to them. after this activity and some direct instruction notes on the Common Core Standards, students will split back into their groups from earlier and create their own probability game or word problem for the class to try based on the interests in the group. It could be another sport, a question based on food, or any other interest the group may have. This provides students with the opportunity to "think more broadly or more deeply about a topic than the text or standards suggest" (Thomlinson 2017, pg.24).

1.3.5. E) Learning Centers/Learning Stations

1.3.5.1. Students will work in breakout groups to complete the discovery based activity and will revisit those groups later to create their own game or question that can be used to determine the answer to a probability question. At the start of the next class day, posters of the question or game from each group will be displayed about the classroom. Students will rotate with their group members to find probability for each scenario presented by their peers. These stations provide students with the opportunity to build on their skills and knowledge from the content.

1.3.6. F) Tiering

1.3.6.1. The discovery based portion of the lesson is not dependent on student readiness, but the notes and homework is. In order for students to be able to understand what is presented to them at varying levels I utilize scaffolding through the modeling of content. Like the text mentions, I "provide varied levels of scaffolding to enable most students to access high-quality learning experiences" (Thomlinson 2017, pg.24). After the activity of testing probability through making trash can baskets, students will sit through a direct instruction portion. They will be presented with step by step guides on how to find probability given various events. There will also be an introduction of key academic vocabulary.

1.3.7. G) Varying Questions

1.3.7.1. Throughout instruction I utilize open ended questions to be able to get students to explain what they know or are discovering. With the Trashcan Probability activity, students will be asked the following... -What do the terms certain, likely, equally likely, and unlikely mean to you? -What do you predict the likelihood will be of making baskets at each distance? -Describe scenarios where the probability of success would be 1/certain and 0/impossible. -What is probability in your own words? One key component I use when asking various questions is to "use wait time before taking answers" (Thomlinson 2017, pg.24). Students need time to think and not feel rushed or that someone else will dive in and answer for them. When choosing individual questions I will also be aware of readiness level and use questions as a way to help gear students toward a deeper understanding of material.