<p>Students will learn to make predictions in this lesson by utilizing the line of best fit. Students are going to:<br>- make a scatter plot that shows distance versus time.<br>- draw the line of best fit and write it down.<br>- enter numbers for <i>x</i> and <i>y</i> to calculate predictions using the line of best fit.</p>

<p>- How are relationships expressed mathematically?<br>- How may data be arranged and portrayed to reveal the connection between quantities?<br>- How are expressions, equations, and inequalities utilized to quantify, solve, model, and/or analyze mathematical problems?<br>- How can mathematics help us communicate more effectively?<br>- How may patterns be used to describe mathematical relationships?<br>- How can we utilize probability and data analysis to make predictions?<br>- How may detecting repetition or regularity help you solve problems more efficiently?<br>- How does the type of data affect the display method?<br>- How can mathematics help to measure, compare, depict, and model numbers?<br>- How precise should measurements and calculations be?<br>- How are the mathematical properties of things or processes measured, calculated, and/or interpreted?<br>- How can we identify if two variables correlate linearly?&nbsp;<br>- How can data be used to anticipate future outcomes?</p>

<p>- Continuous: The representation of data for which no individual values other than a range between intervals can be established. Continuous data is usually associated with physical measurements such as growth.&nbsp;<br>- Discrete: The representation of data for which one-to-one correspondence is established between individual points of data and the medium of representation.<br>- Correlation: A measure of the mutual relationship between two variables.<br>- Line of Best Fit: One line that most closely approximates the trend of bivariate data.<br>- Patterns: Regularities in situations such as those in nature, events, shapes, designs, and sets of numbers, and that suggest predictability.<br>- Scatter plot: A graph of plotted points that show the relationship between two sets of data.&nbsp;<br>- Slope: The rate of change of the ordinate with respect to the abscissa; the ratio of the change in the vertical dimension to the corresponding change in the horizontal dimension.</p>

<p>- Walking Lab (M-A1-6-3_Walking Lab)&nbsp;<br>- masking tape&nbsp;<br>- stopwatches (two per group of three students) or other timing devices&nbsp;<br>- Lesson 3 Exit Ticket (M-A1-6-3_Lesson 3 Exit Ticket and KEY)</p>

<p>- Teacher observations of student performance during the two activities should include an evaluation of questions asked of one another and the teacher. Do the questions demonstrate a comprehension of what they are designed to do? Do any of the questions reflect what they learned during the activity?&nbsp;<br>- Lesson 3 Exit&nbsp;Ticket asks high school students to consider the qualitative aspects of the reasoning behind how much it costs to maintain an automobile and how well it is maintained. The topic is one that the students find interesting in general. Plotting the points to create the line of best fit and making interpretations are required of the students using the matching pairs of sample data.&nbsp;<br>&nbsp;</p>

<p>Active Engagement&nbsp;&nbsp;<br>W: Students will collect data from their own experiences to generate predictions.&nbsp;<br>H: All students prefer to be involved in their own learning. When students learn that they will be collecting data on their personal walking speed, they want to know why. They want to know how they can anticipate their own futures, and this experiment demonstrates how.&nbsp;<br>E: Students will actively participate in a walking activity. Students value encounters in which they play an active role in their learning. It provides intrinsic incentive, increasing their odds of mastering the material.&nbsp;<br>R: During the walking lab, the teacher will go around to ensure students are on track. If they are not, they will be given time to consider why they did what they did and what they need to do to improve their thinking patterns.&nbsp;<br>E: Students will have adequate time throughout the lesson to show their knowledge, particularly during the exit ticket.&nbsp;<br>T: This lesson is designed for kinesthetic learners, but all students benefit from active learning.&nbsp;<br>O: This class opens with an attention-grabbing activity that engages students in active learning. This exercise should allow students to complete the exit slip independently and receive fast feedback before any exams.</p>

<p>Before class starts, mark off a hallway or sidewalk, starting at 10 feet and moving up to 100 feet in increments of 10.<br><br><strong>"There is data all around us, which is utilized to make predictions about future events. Equations of the lines of best fit are used to forecast the values of the variables&nbsp;and scatter plots are used to visualize the correlation between the variables. We're going to measure your walking speed today, create an equation of the line of best fit, and use it to estimate how long it would take you to walk farther."</strong><br><br><strong>Part 1</strong><br><br><strong>The purpose of this lesson is to make predictions using the line of best fit."</strong><br><br><strong>"Assume that the equation </strong><i><strong>y</strong></i><strong> = 2.5</strong><i><strong>x</strong></i><strong> + 50 describes the relationship between mathematical interest and end-of-year average. Mathematics interest is scaled from 0 to 20."</strong><br><br><strong>"Is this a positive or negative relationship? How do you know?" </strong>Students should claim that the relationship is positive because the slope is positive. As a result, as the <i>x</i>-value increases, so does the <i>y</i>-value.<br><br><strong>"Given that interest is the </strong><i><strong>x</strong></i><strong>-variable and the end-of-year average is the </strong><i><strong>y</strong></i><strong>-variable, what does the slope of 2.5 tell us about the relationship between interest and average?" </strong>Students should note that the slope suggests that for every 1-point increase in mathematics interest, the end-of-year average rises by 2.5 points.<br><br><strong>"What does the </strong><i><strong>y</strong></i><strong>-intercept of 50 show?"</strong> Students should notice that the <i>y</i>-intercept shows that at a level of 0 mathematics interest, the end-of-year average is 50.<br><br><strong>"If a student has a mathematics interest level of 15, what is his or her expected end-of-year average? If we substitute 15 for </strong><i><strong>x</strong></i><strong>, we will have the answer."</strong><br><br><i><strong>y</strong></i><strong> = 2.5 × 15 + 50</strong><br><br><i><strong>y</strong></i><strong> ≈ 87.5</strong><br><br><strong>"The average at the end of the year is approximately 88."</strong><br><br><strong>"What is the student's approximate mathematics level if the year-end average is 72?"</strong><br><br><strong>"We may solve by replacing 72 for </strong><i><strong>y</strong></i><strong>."</strong><br><br><strong>72 = 2.5</strong><i><strong>x</strong></i><strong>+50</strong><br><br><strong>72-50 = 2.5</strong><i><strong>x</strong></i><br><br><strong>22 = 2.5</strong><i><strong>x</strong></i><br><br><i><strong>x</strong></i><strong> ≈ 8.8</strong><br><br><strong>"The student has an approximate interest level of 9 in mathematics."</strong><br><br>Distribute the Walking Labe (M-A1-6-3_Walking Lab) and divide the students into groups of three. One student will be the walker, while the other two will be the timers, and they will then swap. Students will time each other's walking distance in 10-foot increments. Each distance will be repeated twice, and the students will average the results. They will make a scatter plot of distance against time, draw and write a line of best fit, and answer the questions on the walking lab worksheet.<br><br><strong>Part 2</strong><br><br>Give out the Lesson 3 Exit Ticket (M-A1-6-3_Lesson 3 Exit Ticket and KEY) to assess students' knowledge.</p>