General Information
Subject(s): Mathematics
Grade Level(s): 6, 7
Suggested Technology:
Internet Connection
Instructional Time:
40 Minute(s)
Keywords: data, data collection, data analysis, graph, computer science, math, computer, statistics, quantitative, quantitative data, qualitative, qualitative data, list, programming, index, data types, if/then statements, variables, local variables, global variables, if/then else statements, xaxis, yaxis, range, app, programming
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Lesson Content

Lesson Plan Template:
General Lesson Plan

Learning Objectives: What will students know and be able to do as a result of this lesson?
 Students should be able to create a graph with different distributions from data collected.
 Students should be able to define a list and what object type it represents.
 Students should be able to code data and manipulate a computer program using if/then and if/then/else syntax structure.

Prior Knowledge: What prior knowledge should students have for this lesson?
 Students should be able to distinguish between different types of data (i.e., quantitative and qualitative).
 Students should be able to calculate the percentage of a given number.
 Students should be able to gather data and calculate percentage of a given total to get a desired value.
 Students should be able to differentiate the types of skewed distributed data (i.e., positive skew, negative skew, or no skew)

Guiding Questions: What are the guiding questions for this lesson?
 What kind of data can a person collect? What are the differences between quantitative, qualitative, discrete, continuous?
 How does a plotted graph relate to data used in a computer?
 How do computers initiate data input by a person?
 What programming structure does a user need to successfully input data into a computer?

Introduction: How will the teacher introduce the lesson to the students?
 Use part 1 in the attached Data Collecting document, open the class with a creative way for students to collect data. The only resources the students will need is a computer and Internet access. The U.S. Census website will provide students data they need to gather for this lesson opener. The purpose of this attention getter is to show different ways of gathering data and ways to evaluate data students observed based on their surroundings. With the data they collected from US Census website students should use their calculators to find the number of people in their age bracket for each city. Therefore, multiplying the "percentage in your age bracket" and the "total population" they should receive the total number in each city.
 The teacher should then have students discuss answers on their sheet with other students' to see how the data may differ. Use the question under the table in part 1 to bridge from this discussion into how computers can help us with computation and how they have their own unique way of writing variables.
 What is the difference from the city with the largest "18 years old and under" population to the city with the smallest "18 years old and under" population? Write an equation that could be used to solve this problem.
 Make sure students have solved the problem and walk them through transferring their equation to a formula with variables. For example, L  S = D where L = largest population, S = smallest population and D = difference. Use the attached Data Sets Represented in Computers presentation in the Resources and Material section to show the student how computers use variables, lists and data types along with conditions to perform mathematical operations and reasoning. Students will also us the attached Data Sets Vocabulary Worksheet to follow along with the PowerPoint.
 Have student complete parts 2 and 3 after viewing the presentation (PDF) and have a class discussion on the correct responses.

Investigate: What question(s) will students be investigating? What process will students follow to collect information that can be used to answer the question(s)?
Instructions for setting up and helping students collect data
 Use the material shown in the attached Skew or Not Investigate Activity Materials document. In part 4 of the attached Data Collecting document, students will create their own histogram based on the data they collected in when they visit the Census Reporter: Sex by Age website. Students will need to combine the intervals that the website shows to fit the intervals on the worksheet.
 Instruct students to tape a rubber band that has been cut open across their desk in a horizontal direction. The rubber band represents the xaxis (i.e., age ranges). Students will use the wipe off markers to draw an appropriate yaxis on their desk, representing number of people. Using the chenille stems have students place a chenille stem under the rubber band. Each chenille stem represents either the number of people in that particular age range on the yaxis, while the city and total population is represented on the xaxis.
 Students will then compare their graph to other graphs to see how distributions may be different in different cities.
How will you check for student understanding?
 There are Think Quick problems on the attached Data Sets Represented in Computers presentation to ask the students questions to see if they are following along with learning the computer science terminology. Ask the students questions throughout the lesson to make sure they understand the concept of graphing and describing their distributions as well. Parts 2 and 3 answers should be discussed before moving forward with the rest of the lesson as to help mitigate any misconceptions.
 Observe if students have x and y axis displayed correctly using the rubber band. Check if the chenille stems are placed underneath the rubber band.
 If the student has correctly set up the axes, check their understanding of the x and yaxis by asking which variable represents the xaxis and the yaxis. Answers:
 xaxis > age intervals
 yaxis > population
Common errors/misconceptions to anticipate and how to respond
 Rubber band is used to hold the chenille stems in place (prevent from sliding around). The students should also understand that it represents the xaxis for their graph. If the band is anything but horizontal (vertical or diagonal), explain what the xaxis is when referencing a graph and what position it must be in to correctly create a graph. Chenille stems below the xaxis would be ignored as the purpose of the stems is to allow the students to manipulate the graphs quickly and fix any errors without having to erase or start their graphs over again.
 Data collected by students should not all be the same since they are choosing their own cities to collect data from. Optional: choose the cities they will research and have them find the correct values.

Analyze: How will students organize and interpret the data collected during the investigation?
Instructions to help students organize, analyze, and interpret their data
Students will look at each other's graphs and discuss how data distributions can appear the same or differently depending on the cities. This should allow for a rich discussion on what the students discovered about the cities across the United States. Students are to make histograms which have age intervals/ranges and distributions that can be described as; skewed, clustered, outliers, symmetric, bell shaped, etc.
How will you check for student understanding?
When a student has correctly distributed the population across each age bracket, the teacher can walk around the class room asking students specific question about their data. Question relevant to the activity: What type of skew is the distribution, positive, negative, or no skew; create a positive, negative, or no skew, etc.
Common errors/misconceptions to anticipate and how to respond
 If the student's data has a large number greater than the range of the graph or the desk. Students then must change the range of the numbers on the yaxis. Either smaller multiples, (i.e., instead of by ten change to 20), or whatever multiple is needed to fit the range of their data.
 For part 5 in the Data Collecting document students are to collect data about themselves. The data represented there is just an example.

Closure: What will the teacher do to bring the lesson to a close? How will the students make sense of the investigation?
Instructions for leading the closing discussion
 Students should discuss or journal write using if/then statements a procedure as to how to graph data in a histogram. For example: if the data falls in the 04 range then graph the data as the first bar, if the data falls in the 59 range then graph the data as the second bar, etc.
 Advanced students could use the code they learned to write this procedure in a more advanced way using code language (i.e., if/then, if/then... else).

Summative Assessment
How will the students show that they met the learning objectives?
 Parts 56 on the Data Collecting documents serves as a summative assessment. It reviews the types of data collected, how data is used in the computers, structure of If/Else statements, and initializing variables and list. Students will need to access the Internet for part 5 of this document.
 When students are completing Part 5, the teacher should make sure that the students have subtracted the percentage correctly for this question: What is the difference between the percentage of people in the population at your age and the percentage of people in the populations of the other person's age?
 This question, and the way in which students subtract, (which percentage is the subtrahend and the minuend) is important as shown in the coding part in Part 5. The code programs the computer to determine which way the subtraction sentence should be set up, based on which percentage is larger. Students, at this level, should know they use the larger percentage as the minuend when they want to know the difference between the values. The code exercise makes them aware of this learned thought process and makes that a computer may need to be told this when its programmed.

Formative Assessment
Standardized language: Specific suggestions for conducting Formative Assessment can be found in the Investigate and Analyze phases of the lesson where it says, "How will you check for student understanding?"

Feedback to Students
Standardized language: Specific suggestions for providing Feedback to Students can be found in the Investigate and Analyze phases of the lesson where it says, "Common errors/misconceptions to anticipate and how to respond."
Accommodations & Recommendations
Accommodations:
 Students that struggle could be given specific data to graph so that they are concentrating on making a histogram instead of gathering the actual data.
 Other materials instead of chenille stems could be used like strips of paper, newspaper, or string.
Extensions:
 For a final check, instructors could ask students to turn in a screen shot of their graph to use later in other lessons or as a review.
 Posters could be created using the screen shots to display similarities and differences between cities and states based on age intervals of the population. Furthermore, students can go global and research locations outside of the United States.

Suggested Technology: Internet Connection
Special Materials Needed:
 Rubber bands
 Chenille Strips (pipe cleaner)
 Tape
 Expo erasable marker
 Internet for data
 Attached files
Additional Information/Instructions
By Author/Submitter
This is lesson 1 of 3 in the Data Set and Deviation Statistics Unit. Lessons 2 and 3 will have students create a pedometer app to gather walking data for analysis in lesson 3.
Source and Access Information
Contributed by:
Name of Author/Source: Amanda Wright
Access Privileges: Public
* Please note that examples of resources are not intended as complete curriculum.