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Lesson Content

Lesson Plan Template:
General Lesson Plan

Learning Objectives: What should students know and be able to do as a result of this lesson?
 Students will be able to calculate and analyze variance and standard deviation.
 Students will be able to analyze data sets by comparing the variance and standard deviation of real world data given two data sets.

Prior Knowledge: What prior knowledge should students have for this lesson?
Prior to the lesson, students should be able to:
 Collect data
 Read and interpret a data set
 Identify and calculate measures of central tendency
 Understand how measures of central tendency are used in the real world
 Identify variability

Guiding Questions: What are the guiding questions for this lesson?
 How do specific values of data affect measures of spread such as mean absolute deviation, standard deviation, and variance?
 What information does standard deviation and variance provide us with?

Teaching Phase: How will the teacher present the concept or skill to students?
 The teacher will distribute a WarmUp Activity (or display it on the Promethean board) that will require students to practice their prior knowledge of finding measures of central tendencies.
 The teacher will review the warmup and connect prior knowledge of finding the measures of central tendency and the importance of the measures of central tendency while emphasizing the difference of the individual values from the mean. Make the connection to variance and standard deviation.
 The teacher will present students with the concept of measures of variability. Explain the meaning of standard deviation and how to calculate it. (Use the PowerPoint presentation.)
 The teacher will explain how variability can consist of range, variance, interquartile range, and standard deviation. The term variability is utilized interchangeably with variation. The two are different as variability is regarded as the element of the entity that is apparent and variation involves assessing that element.
 The teacher can explain how deviation from the mean and frequency of each value help estimate the standard deviation without calculating it. The teacher can also explain how the shape of the data (graph) is related to the value of standard deviation.
 Explain that without standard deviation, you can't get a handle on whether the data is close to the average (as are the diameters of car parts that come off of a conveyor belt when everything is operating correctly), or whether the data are spread out over a wide range (as are car prices).
 Ask students their ages and find the variance and standard deviation to show how small the spread is. Create a dot plot and identify the mean on the dot plot; discussing what attributes of the dot plot show that the standard deviation will be relatively small.

Guided Practice: What activities or exercises will the students complete with teacher guidance?
 Students will pick a partner for the activity, or the teacher may choose to pair up the students.
 Each student and their partner find an area where they will kick the ball.
 Students will kick a rolling ball into a marked goal.
 The teacher will walk around and guide students through their activity. He/she will set up a data table on the board for students' data.
 Have students walk up to board to write down how many goals they scored (girls in one color and boys in another).
 As a whole class, the standard deviation and variance will be calculated for the boys.

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Students will calculate the girls' data on their own and complete the data analysis (crossbar) worksheet.
Students will find the following data in the class lab:
 Mean
 Deviation from the mean
 Squared deviation from the mean
 Standard deviation

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
 Students will complete an Exit Slip answering the essential questions:
 What are the proper steps to calculate the standard deviation of a data set?
 What can the variance and standard deviation determine?
 Ask the students to use half a sheet of paper to answer questions.
 Give students five minutes to answer the questions.
 As students are dismissed, they will turn in their exit slips to be evaluated by the teacher.

Summative Assessment
 Students will complete a lab report/worksheet analyzing the class data on accuracy. They are to find the variance and standard deviation in the report.
 Students will complete an essential question exit slip.

Formative Assessment
A WarmUp Activity will be conducted during the first ten minutes of class. The teacher will receive feedback on students' prior knowledge of analyzing a graph and measures of central tendency.
 Give each student in the groups a copy of the WarmUp Activity.
 Give them seven minutes to answer the following questions on the handout.
 At the end of the seven minutes go over the answers of the handout.
Class discussion feedback and teacher observation will be used as a formative assessment throughout the lesson. The teacher can make a connection to the last Warm Up question: "Is there a definition/terminology for the difference (deviation) of each value from the mean?" These discussions and observations will allow the teacher to guide students and to better understand their knowledge of the standards being assessed. The teacher can also lead students to make a connection between variability and variance. The class will be assessed through their lab report.

Feedback to Students
During the class activity, the teacher can provide the answers to the class for checking, or have students compare their answers and discuss discrepancies in small groups or as a whole class discussion. If students misunderstand something, the teacher will moderate a discussion with the class, asking questions to help students clarify the main concepts. The teacher can lead students to think about what would happen to the standard deviation if the mean increases.
Accommodations & Recommendations
Accommodations:
 Students with special needs can be given additional help in constructing the proper graph.
 The formulas will be written on the board for the students.
 Provide a printed set of instructions for students.
Extensions:
Students will research data on what percent of shots 20 different professional soccer players make successfully and change the percentage to how many out of 10 shots would be made. The students will find the standard deviation for the professional soccer players and compare it to the class data, discussing the variability within each set of data.

Suggested Technology: Basic Calculators
Special Materials Needed:
Materials for Students:
 Ruler
 Notebook
 Class set of worksheet
 Paper
 Calculator
Materials for the Teacher:
 Answer keys
 Measuring tape
 Duct tape
 Rolling ball (mini soccer size)
 Board (display data set)
Further Recommendations:
 The teacher can use a Promethean board to display the warmup.
 The teacher should have an area allocated for students to kick the ball.
 The teacher should have a station (of the goal marked and proper distance) to model expectations.
 The teacher should already have supplies divided into the number of groups.
Additional Information/Instructions
By Author/Submitter
This lesson incorporates the following math practice standards:
1. Make sense of problems and persevere in solving them.
4. Model with mathematics.
6. Attend to precision.
Source and Access Information
Contributed by:
David Galarce
Name of Author/Source: David Galarce
District/Organization of Contributor(s): MiamiDade
Access Privileges: Public
* Please note that examples of resources are not intended as complete curriculum.