lesson+plan


 * MATH LESSON OVERVIEW**


 * INTERN NAME: ** Phuong Ho, Sue McMonigal, Vanessa Walter
 * Date **** : ** March 1, 2012


 * Grade Level/Course Name: ** 7th Grade math


 * Lesson Title: Introduction to probability **

Introduce probability through real life examples of impossible, possible or certain. Relate this concept to the numerical values for probability (0 – 1). Students will use a number line to place various events in the realm from impossible to certain and assign numerical values. This is the first lesson in a unit on probability and the ties to real life will be explicit.
 * Purpose of Lesson: **// Summarize the big idea or central focus (e.g. Introduce a new concept/skill/representation; Deepen a concept/reasoning skill; Strengthen computational fluency/procedural skill with understanding; foster persistent problem-solving) How does this lesson fit within the larger concept or unit? This should be linked to your objectives/learning targets. //

7.4.B Determine the theoretical probability of a particular event and use theoretical probability to predict experimental outcomes.
 * STANDARDS ** (state and common core):

Students will be able to give real life examples of things that are certain, impossible and possible. Students will be able to assign numerical values that correspond to the probability of a real life event, and place them on a number line.
 * LEARNING TARGETS/OBJECTIVES: ** Clearly state what math concepts/skills you expect the students to know and be able to do as a result of this lesson. Include at least 1 objective that supports student engagement/participation (e.g. elicit, listen to, or share math ideas) and addresses academic language development.


 * MATH ASSESSMENT PLAN: **

On target: Students can give examples from their life of certain, impossible and possible events, but cannot yet relate to a numerical probability. Not there yet: Students cannot give real life examples of certain, impossible and possible events, || Small groups will make a poster of the certain, possible and impossible events they came up with.
 * **Evidence:** What is evidence of strong/emerging understanding of the learning target (e.g. above & beyond, on target, not there yet)? || **Tools:** Describe or attach formative & summative assessment tools used to gather evidence of learning and monitor student progress and engagement/participation. ||
 * Above and beyond: Students can give examples from their life of certain, impossible and possible outcomes and give a numerical value that corresponds to their examples.

Pairs of students will make a number line and place events from 0 to 1 as they move from impossible to possible to certain. ||

• __Learning Issues__: (cognitive demand; key understandings/confusions/errors associated with this topic; prior mathematics knowledge, specific strategies students might use) Students use prior knowledge of the real world to come up with impossible, possible and certain events. Numerical values of probability, from 0 – 1, can cause some students trouble as they are expressed as fractions, decimals and percentages interchangeably. Prior knowledge of fractions, decimals and percentages is very useful, and this unit can support that knowledge. Students can also represent probabilities with pictures or models.
 * LEARNING CONTEXT: **

• __Student Engagement__: How will this lesson support equitable student engagement and participation (e.g. student mathematical/intellectual contributions are valued and respected; strategies that address status issues)? Students work in small groups to come up with real life examples of possible, impossible or certain, and draw from their own life experiences. Students work with a partner to place possible event on a number line between 0 and 1.

• __Relevance/Cultural Funds of Knowledge__: How does the lesson connect to citizenship, responsibility, application, family/community/cultural assets and/or social/cultural relevance? Students draw from their own life experiences to come up with examples for the first activity, and use these examples to generate numerical probabilities in the closing activity

Students will write, speak, listen and represent in this lesson. Terms include: Certain, impossible and possible which will be linked to their numerical representations of 1, 0 and between 0 and 1, respectively.
 * ACADEMIC LANGUAGE DEMANDS: ** Briefly summarize the language demands of this lesson. (e.g. reading, writing, speaking, listening, representing, specialized vocabulary, discourse practices) Note: give examples of specific vocabulary/terms emphasized in the lesson.


 * INSTRUCTIONAL SUPPORTS ** : //How will the lesson support access to and development of __math understanding and academic language__ related to the learning targets for specific subgroups or individuals?//


 * ** English language learners ** || Students work in small supportive groups. Students can speak in either language and can represent pictorially if needed. Not all students need to write for the group project. ||
 * ** Students with various math confidence levels ** || All students have life experiences and can relate to the possible, impossible or certain section of the lesson. ||
 * ** Students with special needs/learning disabilities (IEP, 504) ** || Students work in small supportive groups. Not all students need to write for the group project, but can interact with group in their preferred method. All students have life experiences and can relate to the possible, impossible and certain section of the lesson. ||

White board or smart board for initial examples and modeling. Poster paper for each small group. Markers for each small group. One basic number line from 0 to 1 for every two students, for numerical probability placement in summary activity.
 * MATERIALS/TECHNOLOGY/MEDIA: Attach handouts/activity sheets; list special materials or technology resources associated with lesson. **

**MATH LESSON FLOW**

===I. INTRODUCTION/LAUNCH What will hook students into this lesson? How will the launch connect to or activate prior math knowledge? The introduction might also include rationale for learning this topic, interesting problem, connection to background knowledge, review and/or assessment of pre-skills). Include specific language demands and participation Structure(s) used: Whole class, Pair, small groups, individual/independent work. ===

Events will be listed on board when students come in and will be things like the next President of the United States will be male, the sun will rise in the East tomorrow, Glee is on TV tonight, the Stahl golf team will win the city tournament, you will get an A in math this quarter, you will go to sleep by 9 tonight. . . These our our events that students just classify. || Listening, speaking, reading || Whole class discussion ||
 * ** LAUNCH TASK(S) DESCRIPTION: ** || ** LANGUAGE **
 * DEMANDS ** || ** PARTICIPANT STRUCTURES ** ||
 * First introduce learning target: Today you will be able to use real life examples and classify events as impossible, possible or certain. You will be able to assign a number to express these probabilities from 0 to 1, inclusively. We start with a whole class discussion of impossible and certain as 0 and 1 probability, followed by discussion of things that are possible and where they fall in between 0 and 1.
 * ** Student Voice: **// How will you focus students’ attention on the learning targets of the lesson? //// Describe how students will //// express their understanding of the learning target and resources to support their learning progress. // || ** LANGUAGE **
 * DEMANDS ** || ** PARTICIPANT STRUCTURES ** ||
 * Students will write learning target in their math journal (journal writing in L1 is encouraged) and will discuss with their partner before we move into activity 2. || Listening, speaking and writing || Individuals and partners. ||


 * II. EXPLORE:**// Describe //// the core activities of your lesson that facilitate mathematical exploration, inquiry, and discourse about the main concept/skill //** . **


 * ** TASK(S) DESCRIPTION ** What rich mathematical task(s) will students be doing or thinking about? || ** LANGUAGE **
 * DEMANDS ** || ** PARTICIPANT STRUCTURES ** || ** ASSESSMENT **
 * TOOL(S) ** ||
 * Students will be working in small groups to identify life events that are certain, impossible and possible, and will represent them on a poster for the class to see before the period is over. Within these three categories students will assign a numerical value to estimate the probability of the events. || Listening, speaking, writing and representing || Small group work. || Groups will receive peer and teacher feedback on their posters**.** ||


 * ** MATH EXTENSIONS: Early finishers ** || ** MATH EXTENSIONS: Struggling Students ** ||
 * Come up with events that are very probable and also those that are very unlikely but possible. Explain in writing why they are either highly likely or highly unlikely. || Concentrate on the impossible and certain, the extremes of the spectrum and how the probability ranges from 0 for impossible to 1 for certain. Model flipping a coin for example of possible outcomes (heads or tails both possible). ||

Students should be able to come up with some events from their life experiences. Sorting into the three catagories should go fairly smoothly, though some might disagree over the probability of an event. The closure activity may cause more issues, when students use their own judgement to asign a probability. || TEACHER FOCUS QUESTIONS (teacher actions): Questions/prompts to address a productive or problematic math strategy, question, error, student confusion; or extend math understanding. What are some things that happen everyday? What are some things that almost never happen? What are somethings that are actually impossible? Once they have come up with ideas, is this possible? Is it likely or unlikely? Where would you place that probability mathematically? ||
 * POSSIBLE STUDENT QUESTIONS, STRATEGIES, CONFUSIONS, ERRORS… (student actions): What are some MATHEMATICS QUESTIONS/STRATEGIES (both productive and problematic) you expect students to pose/try/use? This includes math knowledge and community/family resources they might draw upon.


 * III. SUMMARIZE/CLOSURE:**


 * ** DEBRIEF ACTIVITY DESCRIPTION: **// How will you debrief the lesson with students, specifically pulling out important mathematical ideas of the lesson? Be specific. //

After all groups have presented their posters, have student pairs develop numerical probability for the events their group came up with. Explain, with one partner assign a number value for the impossible, possible or certain events from your group project || ** LANGUAGE ** With your partner, put these events on a number line that goes just from 0 to 1. Explain to each other why the numerical probability fits with the events you have chosen. Put your names on it and hand it to me on your way out the door. || ** Speaking, listening, representing ** || ** Pairs ** || On the bottom of your number line, as a pair, reflect on what you are certain you understand from todays lesson, what you possibly understand but would like to spend more time on and if anything from this lesson currently seems impossible. I will collect these before you leave. || ** Writing ** || ** Partner reflection ** ||
 * DEMANDS ** || ** PARTICIPANT STRUCTURES ** ||
 * ** ASSESSMENT/EXIT TASK: **// What can you ask students to do that will inform your next instructional step (e.g. follow up problem, reflection question)? //
 * ** STUDENT VOICE: **// Describe and attach documents (if applicable) that demonstrate //// how students will self-assess and communicate their own progress towards the math learning targets (i.e. what they are doing well and what they need to work on to meet or exceed the learning targets). //
 * ** Homework (if Applicable): ** ||  ||   ||