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In this activity, students investigate a set of bivariate data to determine if there is a relationship between concession sales in the park and temperature. Students will construct a scatter plot, model the relationship with a linear function, write the equation of the function, and use it to make predictions about values of variables.
Learning Objectives: What should students know and be able to do as a result of this lesson?
Create scatter plots of real-world bivariate data.
Informally fit a line to data.
Write the equation of a line fitted to data.
Use the equation to make predictions about values of the variables.
Prior Knowledge: What prior knowledge should students have for this lesson?
Graphing in the coordinate plane
Writing linear functions given two points on its graph
An understanding of the meaning of the correlation coefficient
Guiding Questions: What are the guiding questions for this lesson?
What is a scatter plot?
How can functions be used to model real-world bivariate data?
How can models of real-world bivariate data be used to make predictions about values of variables?
Teaching Phase: How will the teacher present the concept or skill to students?
Bell-Ringer The bell ringer attached to this lesson is intended to check students' knowledge of linear functions. You can use "Plickers" to complete this activity. See Plicker instructions in the "Further Recommendations" section.
Lesson Introduction Prior to the lesson, copy the key terms and their definitions and display them on the board. Have your students work with a partner to match key terms to their definitions. When your students are finished, review the definitions of the terms and ask students to self-assess. Correct answers are:
Scatter plot - A graph of bivariate data (i.e., data that consists of two values graphed as ordered pairs in the coordinate plane)
Bivariate data - Paired data collected on each of two variables
Trend Line - A line graphed on a scatter plot that models the relationship between two variables
Positive correlation - A linear relationship between two variables in which the value of one variable increases as the value of the other variable increases
Negative correlation - A linear relationship between two variables in which the value of one variable increases as the value of the other variable decreases
Problem Introduction Introduce the following problem: To manage ordering supplies at the park concessions more efficiently, data on the daily temperature and sales of ice cream was collected. The high temperature (in degrees Fahrenheit) for 10 days (one day every two weeks over the course of 20 weeks) and the number of units of ice cream sold on each of these 10 days was recorded (see Guided/Independent Practice attachment for data, graph, and additional information).
Guide your students create a scatter plot of the data. Ask them to describe the trend in the data and to estimate the correlation coefficient. Model describing the trend as a strong linear relationship (i.e., the greater the temperature, the greater the number of units of ice cream sold). Display a scatter plot created with technology (e.g., Excel or GeoGebra) with a line of best fit drawn. Explain that the equation of the line models the relationship between the two variables, temperature and ice cream sales. Model identifying two points on the line of best fit and writing its equation. Use the equation to predict the sales when the temperature is 72 degrees and when the temperature is 50 degrees.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
The lesson begins with the teacher guiding the students through the process of creating a scatter plot, writing the equation of the line of best fit, and using the equation to make predictions. Provide students with the temperature-hot drinks data (see Guided/Independent Practice attachment).
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Provide students with the temperature-hot drinks data (see Guided/Independent Practice attachment). Explain that data on the sales of hot drinks was also collected. The high temperature (in degrees Fahrenheit) for the same 10 days and the number of hot drinks sold on each of these 10 days was recorded. Ask your students to:
Create a scatter plot of the data.
Describe the association between the variables.
Estimate the correlation coefficient.
Use a ruler to draw a line of fit.
Write the equation of their line of fit.
Use the equation to make a prediction about the number of sales when the temperature is 72 degrees and 50 degrees.
At this time, circulate through the room to provide assistance and feedback. When the students are finished, ask a student to share his or her work. Then discuss:
Interpolation versus extrapolation and confidence in predictions made using models.
The relationship between the slope of the line of fit and the sign of the correlation coefficient.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The teacher will review the following points with students and assign the attached summative assessment:
Linear functions can be used to model the relationship between two variables by fitting a line to a scatter plot of real-world data.
Once a function is fitted to data, it can be used to make predictions about values of variables.
See the attached Summative Assessment. Note that an answer key is included beginning on the second page of the document.
The eacher will:
Assess student responses to the Bell-Ringer during a whole-class discussion.
Ask probing questions during Guided Practice in order to check for understanding of the concepts.
Circulate throughout the classroom as students are working independently to provide feedback.
Feedback to Students
The teacher will discuss the bell ringer providing immediate verbal feedback.
Feedback will be given throughout the class period as the teacher circulates through the classroom and monitors student work.
A grade and written comments can be given on the summative assessment and returned to students the following day.
Accommodations & Recommendations
Allow students extra time to complete the activity.
Provide graphs with axes already scaled and labeled.
Allow students to use calculators.
Provide sets of data that can be modeled by exponential functions.
Introduce the concept of a least squares regression line.
Have your students use graphing technology or software to calculate the equation of the least squares regression line.
Suggested Technology: Computer for Presenter, Computers for Students, Internet Connection, LCD Projector, Microsoft Office
Special Materials Needed:
Plickers (the basics):A Plicker is an image similar to a QR code on a piece of paper that can be scanned by a tablet or smart phone. How the student holds the Plicker image determines the response to a question you create within the app or Plickers website. What follows is a step-by-step guide to the website (https://www.plickers.com/) and app.
Steps for Integrating Plickers:
Go to the Plickers website and create a teacher account.
Choose the tab labeled classes at the top of the page and type in your class roster. It will assign to each student an individual Plicker. You can add additional classes and students later if you want.
Choose the tab on the website labeled cards to print out the students' Plickers.
Choose the library tab to create questions. Responses can be either in multiple choice or true/false format. Select the correct response(s) for each question and click the tab labeled "add to plan" below each question to attach it to the appropriate class you have already created.
If you have a computer connected to a smart board, projector, or apple tv in your classroom and are connected to your Plickers account, select the live view tab on the website to display the question and answer choices for the students. A full screen tab and another small button with an arrow that allows you to hide the response panel will appear beside each question.
When students are holding up their Plickers to answer a question, you will need to use your smart device to choose the Plickers app, and select the question you wish to use. Scan the room by selecting the camera button which will appear at the bottom of the screen. You will see the name of the student and their individual response for each question selected located at the top of your screen on the smart device. Also, a bar graph will appear so you can view whole group data as well. The number of participates scanned is also provided to make certain that all students have responded.