
Lesson Plan Template:
Guided or Open Inquiry

Learning Objectives: What will students know and be able to do as a result of this lesson?
Students will be able to identify the independent and dependent variable and describe the relationship between bivariate data.
Students will be able to interpret the scatter plots as having positive, negative, or no correlations.
Students will be able to explain that the correlation coefficient must be between 1 and 1, and explain the strength of what these values represent to include no correlation with a value of zero.
Student will be able to create scatter plots and add a regression line using GeoGebra.
Students will be able to use GeoGebra to demonstrate how to display the computed statistical information and collected, and identify the correlation coefficient for a given data set.
Students will be able to make conjectures about wingspan and distance traveled based on data.

Prior Knowledge: What prior knowledge should students have for this lesson?
Students are able to discriminate between dependent and independent variables of correlated data.
Students are able to graph points and create scatter plots by hand and using GeoGebra.
Students can visually interpret scatter plots as positive, negative, or no correlation.
Students can visually interpret positive and negative scatter plot correlations as strong or weak.

Guiding Questions: What are the guiding questions for this lesson?
Is there a correlation between the wing span of a glider and the distance it will travel? If so, how strong or weak is the correlation?

Introduction: How will the teacher inform students of the intent of the lesson? How will students understand or develop an investigable question?
Launch: Use the attached PowerPoint.
Divide students into pairs or small groups of 3. Display examples of scatter plots with varying correlation strengths (Slide 2). Students will ThinkPairShare for 1 minute of the characteristics of strong, moderate, weak, or no correlation of bivariate data. Students will then be shown various graphs that show a variety of correlations from strong to none, both positive and negative (Slide 3). Students determine the strength and direction of each scatter plot in terms of strong, moderate, weak or no correlation and positive or negative correlation. Conduct formative assessment using slide 4 as an answer guide by circulating the room and viewing student work. Display answers for students to check their work (Slide 4). Clarify any misunderstandings before moving to next slide.
Next, display examples of correlations coefficients ranging from 1 to 1 (Slide 5). Students will ThinkPairShare for 1 minute on the characteristics for correlation coefficients ranging from 1 to 1, recognizing that 1 represents a strong negative correlation, 1 represents a strong positive correlation, and 0 represents no correlation. Students will then be shown various scatter plots with different correlations and a list of correlation coefficients (Slide 6). Students will match the correct correlation coefficient to the appropriate graph. Conduct formative assessment using slide 7 as an answer guide by circulating the room and viewing student work. Display answers for students to check their work (Slide 7). Clarify any misunderstanding before moving to next slide.
The teacher will provide each group of students with a bivariate data set (study time vs test score), so each group has the same data set (Slide 8). The teacher can either print this page and hand it out to student groups or have students write down the data. The teacher will demonstrate how to launch GeoGebra (Slide 9). The teacher will demonstrate how to insert data into GeoGebra's spreadsheet (Slide 10 and 11). The teacher will pause and allow the students to duplicate the same process on their own computers as the teacher walks around room providing assistance as needed. The teacher will demonstrate how to create a two variable regression analysis scatter plot using GeoGebra (Slide 12, 13, and 14). The teacher will pause while students repeat the process on their own computer as teacher circulates the room providing assistance as needed. The teacher will then think out loud and interpret the scatter plot, describing the various characteristics while asking students to indicate the estimated direction, strength and correlation coefficient. The teacher will demonstrate how to add a line of best fit to the scatter plot (Slide 15). The teacher will pause and allow the students to duplicate the same process on their own computers as the teacher walks around room providing assistance as needed and conducting formative assessment. The teacher will then demonstrate how to display the computed correlation coefficient and data next to the graph (Slide 16). The teacher will pause, while students duplicate the process as teacher circulates to assist students and conduct formative assessment 5. The teacher and students will reflect on estimate correlation coefficient and computed rvalue misconceptions of estimated characteristics to actual values.
The teacher will pass out the GeoGebra assessment packet which should include the following attachments: glider instructions, finished glider pictures with notes, and a summative assessment document with a blank data table and essay questions.

Investigate: What will the teacher do to give students an opportunity to develop, try, revise, and implement their own methods to gather data?
The teacher will pass out GeoGebra assessment packet which should included the following attachments: glider instructions, finished glider pictures with notes, and a summative assessment document with blank data table and essay questions.
Students will be given or will make a soda straw glider prior to investigation, depending on skill level, based on given specifications of attached glider instructions. Students will toss the glider 10 times in a controlled indoor environment. Students will record the distance the glider traveled. Distance will be determined by the point of release from the students hand to the point where the glider first touches the ground. (Option 2  Students time, to a hundredth of a second, with a stop watch, for time the glider traveled in the air. Time will be determined by the moment the glider is leaves the students hand to the time it touches the floor.) The glider may need some adjustments to ensure it flies straight. (See build instructions for instructions to change flight surfaces. Students may need to practice and adjust to optimize flight.) Students will then cut off 1/2 inch of the main wing, decreasing the total wing span by 1 inch. Students will repeat the process of tossing and recording the distance for another 10 trials. Students will repeat this process of cutting, tossing, and recording until the main wing has been decreased to a total 4 inches, depending on time constraints. This should be four 1/2 inch cuts off both ends of the wing, such that the final length of the main wing is 4 inches.

Analyze: How will the teacher help students determine a way to represent, analyze, and interpret the data they collect?
Students will independently enter their collected data into a new GeoGebra spreadsheet, create a scatter plot with a line of best fit, and determine the correlation coefficient of the regression line. Students will print their results, with the statistics, data and graph displayed on the same page and circle the correlation coefficient for their regression line. Students will indicate whether the the strength and directions of the regression line based on the correlation coefficient by writing it on the printed copy. Results will vary greatly.

Closure: What will the teacher do to bring the lesson to a close? How will the students make sense of the investigation?
Students should be able to explain the correlation between wing span and distance travel based on the data collected. There should be a strong correlation between wing span and distance traveled. If students analyzed wing span and time, they should see a moderate correlation between wing span and time. Reason for this: as the wing span decreases the glider becomes less balanced and has a tendency to fly up and then stall. This leads to a short distance traveled but a longer than expected fight time.

Summative Assessment
Students will create a scatter plot for the data set collected comparing decreasing wing spans to the distance traveled (and/or flight time) of a soda straw glider using GeoGebra and determine the correlation coefficient, interpret the strength of the regression line, and describe the correlation between wing span and distance traveled (or wing span and flight time).

Formative Assessment
The teacher will be monitoring and observing the students throughout the lesson to check their understanding of the listed leaning objectives below.
Sample questions:
 How do we visually determine the strength of correlation of a scatter plot, as strong, moderate, or none?
Answer: The strength of correlation can be visually determined by how close the data points appear to be linear. (See PowerPoint slides 3 and 4)
 How can we determine the strength of a line of best fit for a scatter plot?
Answer: The strength of line of best fit can be determined by how close the data points are to the line drawn. (See PowerPoint slide 2) A more formal approach would include analyzing the correlation coefficient that technology can calculate.
 If given a scatter plot how do we approximate the value of the correlation coefficient?
Answer: To approximate the value of the correlation coefficient we visual see how close the data points appear to be linear. The more linear the points appear, the correlation coefficient will be closer to 1 or 1. The more scattered with no apparent trend the data points appear the correlation coefficient will be closer to zero.
 How can you decide whether a correlation exists between paired numerical data based on context of data?
Answer: The stronger the correlation coefficient of the regression line, it will be reasonable to suggest there is a correlation, provided the data is can be reasonably related to each other.

Feedback to Students
The teacher will circulate around the room and answer student questions or generate probing questions to extend students' thinking or correct misconceptions.
The teacher will provide suggestions to optimize student success and time as needed so students can correct any misconceptions.