Instructor: Ms. Marithza Rendon / Grade & Subject: 9th/ 10th Accelerated Analytic Geometry (Math)
Lesson Title: Exploring the Bell Curve and Applying the Empirical Rule / Date: February 12, 2015
  1. LESSON PLAN LEARNING OUTCOMES AND PROCEDURES

Essential Question(s) / Central Focus / How does a bell curve relate to data? What is the Empirical Rule? What is the total area or proportion underneath the curve?
Learning Objective(s) /
  • Students will be able to learn how the bell curve can be used to represent normal distributions and how the empirical rule can be used to make conclusions based on normal bell curve. Students will be able to relate this information and understand how their standardized test scores are evaluated and interpreted using this information.
  • Students previously learned how to calculate standard deviation and other measures of central tendencies. For this lesson, students will be able to visualize how standard deviations affect the spread of data and apply previous knowledge learned.
  • This lesson is a brief introduction to the AP Statistics course students can choose to take in the near future. Students will be able to understand how statistics is used in many careers and gain a basic understanding over these major concepts.

CCGPS or GPS Standard(s) / MCC9-12.S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
MCC9-12.S.ID.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
MCC9-12.S.IC.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
Instructional Strategies & Learning Tasks that Support Diverse Student Needs / Introduction to Lesson / As a warm-up to the class, students will be asked to calculate the mean and standard deviation of a data set. Two students will be asked to calculate both measures of central tendencies on the main board and explain their throughout process to the class. Before beginning the notes, I will then ask students who plan to take the SAT or ACT. I will explain to students how SAT/ACT scores are collected and normally distributed. With the interest of students on how standardized scores are collected and interpreted, I will then begin the notes on the power point introducing the bell curve.
The introduction should take approximately 10 minutes.
Body of Lesson /
  1. A PowerPoint presentation will be shown to students to teach students the information needed to comprehend the lesson. The presentation will demonstrate students what a bell curve looks like (visualization) and written properties of the curve. One student will be asked to read one slide during the presentation (auditory presentation) while students are writing their notes. The instructor will then give a detailed explanation of the information and include solid examples to clarify any definitions. The presentation will include a brief explanation of the standard normal distribution. To further understand the bell curve, the presentation will demonstrate students what the empirical rule states and include visualizations for students. As a class, the students and the instructor will answer a few questions that apply the empirical rule. The instructor will explain how important it is to draw the bell curve and model how to create a bell curve. The instructor will model how to interpret the bell curve to answer questions. This part of the lesson should take approximately 15 minutes.
  2. After answering any questions from the students, the instructor will then explain the next activity. The activity involves students working in pairs to complete their own unique problem using the empirical rule. Students will be asked to create their own bell curve using the information provided to students and answer a series of questions by interpreting data. Students will be asked to complete their task on a piece of construction paper. This part of the lesson should take approximately 15 minutes. If students complete their task, they will be asked to assist other classmates.
  3. Once students complete their task, students will be asked to present their work to their classmates. Presentations should take approximately 5 minutes to complete.

Closure / Students will then be asked to come together as a class. To assess student comprehension over this lesson, a brief discussion will take place. Students will be asked to share what they learned or how they think they could use this information in the future. The responses of students will determine if students understood the empirical rule, bell curves, and important vocabulary words and symbols of this lesson. A handout will be given to students and students will be asked to complete the assignment at home. This closure should take approximately 5 minutes.
Learning Supports: Differentiation, Modification(s), and Accommodation(s) /
  • To differentiate the instruction, I will provide my students with a variety of means of instruction. Visual and auditory statements will be used to support my struggling readers in the classroom. Students who enjoy reading will be given formal definitions to support the main ideas.
  • To support my students who have ADHD, I will keep the instructional part of the lesson brief and provide my students different opportunities to practice this mathematical concept. By providing my students with different tasks, students will not be as distracted and remain focused throughout the class.
  • For students who preform above grade level, I will group these students who normally need extra assistance. Students who perform below grade level will receive peer tutoring from their classmates and receive extra assistance from the instructor.
  • Extra time may need to be given to students to complete the tasks to ensure student learning in the classroom.

Formal and Informal Assessment / During the group activity, I will assess student comprehension over major concepts of the lesson and mathematical vocabulary. The results of the assignment with assess student comprehension formally. The assignment will determine if students understand bell curves and the empirical rule. By listening to student conversations and questions, I am able to determine student understanding informally. I will be able to provide students with individual feedback during the activity as well. At a later date, I will use a quiz and summative test to formally assess student learning. The discussion at the end of the lesson will determine if students understood the standards listed above.
  1. RESOURCES

Academic Language / Language Functions / The key learning task for this lesson is to gather information of a normal distribution curve to interpret and analyze results. Students will be able to use their academic language while interpreting their data.
The purpose of this lesson is: Interpreting
Students will be able to interpret data and information on normal curves using the empirical rule. During the learning task, students will be able to practice interpreting data.
Vocabulary / By interpreting data, students will need to know what key vocabulary words mean while being asked to complete the task. Students would also need to use mathematical vocabulary words while writing their results and verbally explaining their results to their peers.
Syntax or Discourse / Students will be able to write how to use formulas and notations throughout the lesson. Notations (Greek symbols) include , which stand for mean and standard deviation respectively. Students will also be able to explain their interpretations of data to the class.
Materials /
  • Projector with a computer with the PowerPoint presentation titled “The Bell Curve and the Empirical Rule” (attached).
  • Expo Markers and a white board to write the agenda and warm-up. Also, the marker and white board will be used to model practice problems on the board
  • 14 pre-cut problems. One problem will be given to each group
  • 14 pieces of construction paper
  • Glue and markers for students to complete their assignments
  • Approximately 30 copies of the Empirical Rule handout (attached)

Technology / A PowerPoint presentation will be provided to demonstrate students the key ideas over the lesson. This PowerPoint lesson will be posted on the class website for further support student learning. Calculators will also be used to calculate formulas and make calculations. Calculators will be used to support students while calculating and interpreting data.

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