<p>In this lesson, students will plot data and determine the line of best fit. Students will:<br>- perform an experiment and generate a scatter plot.<br>- graph lines of best fit and construct equations for lines 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>- Correlation: A measure of the relationship between two variables.&nbsp;<br>- 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. Discrete representations are often associated with countable objects such as populations.&nbsp;<br>- Line of Best Fit: The line that most closely fits the bivariate data.<br>- Patterns: Regularities in situations such as those in nature, events, shapes, designs, and sets of numbers.&nbsp;<br>- Scatter plot: A graph of plotted points that show the relationship between two sets of data.</p>

<p>- Matching Stroop (rhymes with loop) Cards (M-A1-6-2_Matching Stroop Cards)&nbsp;<br>- Not Matching Stroop Cards (M-A1-6-2_Not Matching Stroop Cards)&nbsp;<br>- two Stopwatches (or other methods of keeping time) per group&nbsp;<br>- Stroop Lab Activity Sheet (M-A1-6-2_Stroop Lab Activity Sheet)&nbsp;<br>- Stroop Lab Instructions (M-A1-6-2_Stroop Lab Instructions)&nbsp;<br>- Stroop Lab Extension (M-A1-6-2_Stroop Lab Extension)&nbsp;<br>- Calculate the Line of Best Fit Worksheet (M-A1-6-2_Calculate LOBF Worksheet and KEY)&nbsp;<br>- Lesson 2 Exit Ticket (M-A1-6-2_Lesson 2 Exit Ticket and KEY)&nbsp;<br>- rulers&nbsp;<br>- graph paper</p>

<p>- The Stroop lab activity allows students to experience the difference in response times between matching and nonmatching opposites.&nbsp;<br>- Lesson 2 Exit Ticket assesses students' ability to use sequential data, associate it with appropriate values, generate a scatter plot, and provide a coherent interpretation.</p>

<p>Active Engagement&nbsp;&nbsp;<br>W: The attention-getter&nbsp;informs students about the lesson's focus on data and information gathering. They understand that they will be participating in an experiment and using their own data for this session.&nbsp;<br>H: This class begins with an introduction to the Stroop Lab, a psychological test. Students may initially question why they are participating in the lab, but after a few minutes, they will appreciate the challenge. They will wonder what they are going to do with the data, which will keep them engaged in what happens next.&nbsp;<br>E: Students will actively participate in this lesson since they are responsible for collecting their own data. Students are more attached to lessons that relate to their own lives. One advantage of this lab is that the experiment itself is simple, allowing students of all levels to participate. If advanced students require enrichment, there is an activity for them. If lower-level students require modeling or scaffolding, the teacher can supply it by starting with simpler examples that employ smaller quantities, developing larger quantities, and progressing to more complicated examples and larger quantities. Scaffolding may also include starting with positive integers and progressing to higher levels of abstraction, such as fractions and decimals.&nbsp;<br>R: Students will have adequate opportunity to think and review their cognitive processes. The teacher will watch and provide feedback during the lectures and exercises.&nbsp;<br>E: Students will use the Calculating the Line of Best Fit Worksheet to self-evaluate their understanding as they work in the Stroop Lab.&nbsp;<br>T: This lesson is designed for all learners. There is an enrichment worksheet for children who meet or exceed the benchmarks, and the activity is basic enough for students who require more learning opportunities.&nbsp;<br>O: This lesson starts with a fun lab, progresses to a worksheet for a think-pair-share activity, and ends with an autonomous exit ticket.</p>

<p><strong>"One of the main applications of data analysis is to create predictions about real-world events. The first step is to gather data. We plan to conduct a cognitive psychology experiment. The experiment was named after J.R. Stroop, the person who first perform it."</strong><br><br><strong>Part 1</strong><br><br>Distribute the Stroop Lab Instructions and the Stroop Lab Activity Sheet (M-A1-6-2_Stroop Lab Instructions and M-A1-6-2_Stroop Lab Activity Sheet). Also, distribute the Matching Stroop Cards and the Not Matching Stroop Cards (M-A1-6-2_Matching Stroop Cards and M-A1-6-2_Not Matching Stroop Cards). These should be divided into the shape of a deck of cards in advance. One student at a time will name the ink colors in the matching list. This signifies that both the word and its color match. The other two students will act as timers. Repeat the process with the non-matching list. Remember, the student names the color of the ink, not the word itself. (For example, if the printed word is <i>Blue</i> but the ink is red, the student will say "red.")<br><br>Students will complete the activity sheet, answer the questions,&nbsp;and create the scatter plot. They might require some assistance in drawing the line of best fit or determining the equation.<br><br><strong>"A line of best fit is one that goes through a scatter plot and fits the majority of the data. It attempts to pass through as many spots as possible, with half of them above the line and half below it. How do we develop an equation for the line that we've drawn?" </strong>Hopefully, students will contribute ideas. <strong>"We find the slope of the line using two points on our drawn line, as well as the y-intercept using one of our drawn lines. The slope-intercept equation is known as the </strong><i><strong>line of best fit</strong></i><strong>. We utilize this equation to make predictions."</strong><br><br><strong>“The </strong><i><strong>line of best fit </strong></i><strong>is the one that most closely approximates the bivariate (two-variable) data. Consider the following example.”</strong></p><figure class="image"><img style="aspect-ratio:863/181;" src="https://storage.googleapis.com/worksheetzone/images/Screenshot_33.png" width="863" height="181"></figure><p><br><strong>"Let's create a scatter plot, draw our projected line of best fit, and write the equation of the line of best fit."</strong><br><br><strong>"Let's first find two points on the line we drew, or two points extremely near to that line, to determine our slope.”</strong><br><br><strong>“We can use the points (45000, 150000) and (60000, 185000).”</strong><br><br><i><strong>m</strong></i><strong> = </strong><i><strong>y</strong></i><strong>2 - </strong><i><strong>y</strong></i><strong>1x2 - </strong><i><strong>x</strong></i><strong>1</strong><br><br><i><strong>m</strong></i><strong> = 185000 - 15000060000 - 45000</strong><br><br><i><strong>m</strong></i><strong> = 3500015000</strong><br><br><i><strong><u>m</u></strong></i><strong><u> ≈ 2.3</u></strong><br><br><strong>"Now, we can determine the </strong><i><strong>y</strong></i><strong>-intercept using one of those points."</strong><br><br><strong>"We should utilize the point (45000, 150000)."</strong><br><br><strong>"A line's slope-intercept form is expressed as </strong><i><strong>y = mx + b</strong></i><strong>, where </strong><i><strong>m</strong></i><strong> represents the slope and </strong><i><strong>b</strong></i><strong> represents the </strong><i><strong>y</strong></i><strong>-intercept."</strong><br><br><strong>"Substituting our slope, we have </strong><i><strong>y = 2.3x + b</strong></i><strong>."</strong><br><br><strong>"Our point's </strong><i><strong>x</strong></i><strong>- and </strong><i><strong>y</strong></i><strong>-values can be substituted to get:</strong><br><br><strong>150000 = 2.345000+ </strong><i><strong>b</strong></i><br><br><strong>150000 = 103500 + </strong><i><strong>b</strong></i><br><br><i><strong>b</strong></i><strong> = 46500.”</strong><br><br><strong>"Therefore, </strong><i><strong>y</strong></i><strong> = 2.3</strong><i><strong>x</strong></i><strong> + 46500 is the equation of the line of best fit."</strong><br><br><strong>"We can use the graphing calculator to find the line of best fit as well."</strong><br><br><strong>The </strong><i><strong>x</strong></i><strong>- and </strong><i><strong>y</strong></i><strong>- values can be entered into the L1 and L2 lists. Next, go to Stat, Calculate and Choose LinReg (a+bx). By doing this, you will get the </strong><i><strong>y</strong></i><strong>-intercept, </strong><i><strong>b</strong></i><strong>, and the slope, </strong><i><strong>a</strong></i><strong>."</strong><br><br><strong>"The graphing calculator provides the following slope and </strong><i><strong>y</strong></i><strong>-intercept with our data."</strong><br><br><i><strong>a</strong></i><strong> ≈ 38859</strong><br><br><i><strong>b</strong></i><strong> ≈ 2.5</strong><br><br><strong>"Therefore, </strong><i><strong>y = 2.5x + 38859</strong></i><strong> is the exact line of the best fit equation."</strong><br><br><strong>"We selected points on the line to determine the slope and </strong><i><strong>y</strong></i><strong>-intercept, which is why this equation differs slightly from the equation we found. We should regard the equation we discovered as a close approximation, and it is entirely appropriate for our intended level of understanding at this time."</strong><br><br><strong>"What more does we infer from our scatter plot?"</strong><br><br><strong>"We find a positive correlation."</strong><br><br><strong>"According to the slope, the price of a home rises by $2.50 for every dollar an annual earnings increase."</strong><br><br><strong>"The </strong><i><strong>y</strong></i><strong>-intercept shows that the house would cost $38,859 if one were to earn $0 per year."</strong><br><br><strong>Part 2</strong><br><br>Distribute the Calculate the Line of Best Fit Worksheet (M-A1-6-2_Calculate LOBF Worksheet with KEY). First, assign it to the students to do independent, and then in pairs. Once the pairs have completed their work, ask them to collaborate with another pair and present their findings.<br><br><strong>Part 3</strong><br><br>To determine whether students have a grasp of the material, distribute the Lesson 2 Exit Ticket (M-A1-6-2_Lesson 2 Exit Ticket and KEY).<br><br><strong>Extension:</strong><br><br>Students who have access to computers can input their data and have the computer determine the line of best fit by using the website <a href="http://illuminations.nctm.org/ActivityDetail.aspx?ID=146"><span style="color:#1155cc;"><u>http://illuminations.nctm.org/ActivityDetail.aspx?ID=146</u></span></a>. The line of best fit that the students wrote and the one that the computer provided can be compared and contrasted.<br><br>Give students the Stroop Lab Extension (M-A1-6-2_Stroop Lab Extension) if they finish the Stroop lab early.</p>