AMME Inc. Applied Math Made Easy Teacher notes for Hi-Tech Brains Activity to teach linear equations by Slope-Intercept 14-Lab D High-Tech Brains 2-3 days This lab will reinforce the following three important concepts: what the slope of a line is, what the y-intercept of a line is, and the fact that a linear equation requires constant change. It also allows students to see that algebra and linear equations are present in everyday events. It is designed to be run without calculators but on optional page 7 students can use graphing calculators to better understand technology and to fine-tune their results. (TI-82 and 86 instructions are given.) In this lab, the first page is just a warm up on relations, constant change, and finding slope. Page two helps to teach dependent and independent variables and the students get to collect data about the WAVE. The main objective of this first mini lab is to teach students how to collect and graph data which is linear and then find the equation of the line of best fit. The WAVE works well. Wave: This will be done as a class. Students do the WAVE (like at a ball game) and you time it. We require each student to stand up from their desk and be seated before the next one starts. Do one person first and everyone records that time. Then maybe do three students, then maybe a row, two rows, three rows, etc. always starting with the same student. This will create a chart of data that will be difficult for students to recognize as linear or nonlinear until they graph it. After they graph it, they will calculate the equation of the line-of-best-fit. Of course some students may try to alter the data by doing the wave very slowly or by racing, yet it never seems to have much impact. The data has always been linear and the constant change (slope) will be the average time it takes for one person to do the wave. Independent: number of students Dependent: time to finish Linear relation Supplies needed: stop watch for the teacher. On the second day, before they begin the lab, you may wish to show them another example. I put a container on a scale, weigh it, and record the results. Then I put one pen in the container and record this new weight. Then put in 3, 5 or 6 similar pens and record the weights. Ask them if the equation will be linear. What will the constant change represent? (The weight of one pen.) What will the y-intercept represent? (The weight of the empty container.) Pairs of students will be assigned to start at one of eight different stations. Station #9 (Paper Fold) can be done when they are finished early at any station, they just stay where they are. At each station there will be a set of directions (only one copy needed) and the supplies. Since you probably have more than 16 students, we recommend that you make two sets of all the stations. We place the 8 stations in numerical order in each half of the room. Here is how we use slider lock bags to store all the supplies from each station. Each station is designed to be done relatively quickly (10-13 minutes) and we announce when it is time to move.
Students are asked to read the direction page at each station, collect the data, sketch a graph and if the data appears linear, find the equation of a best-fit line in slope intercept form. When students are getting towards the end at an assigned station, you should remind them that there is only a minute or two left for that station. Although if students are waiting to move to another station, they should do station # 9. We recommend that students not jump ahead to an empty station because it adds so much confusion and many of the students will find necessary stations are being used. At the end of the period, assign one partner to put away the station. Have them make note of the location and all the required supplies. At the start of the next day that student should also set up the station before the lab starts. Here is a list of the stations which can consist of any of your own mini-experiments; just make sure they are quick and mostly linear. AMME notes that not all these mini-experiments below are original ideas of AMME authors. Many are data collection ideas learned in workshops. We apologize for not knowing the origin of these ideas that we may properly credit their creators. #1 A Whole Lotta Washers: Students will measure the height of a stack of 3 washers. Then they will add more washers to the stack and continue to measure the new height. Independent: number of washers Dependent: height of stack Linear Supplies: not important 8-10 or so thick washers (or poker chips), metric ruler, it's nice if they are 2-3 mm thick, diameter is #2 Marble Weigh: Students weigh a plastic cup with five marbles in it and then continue to weigh it as congruent marbles are dropped one at a time into the cup. Independent: number of marbles Dependent: weight of cup with marbles Linear Supplies: metric scale, up to 20 marbles, two plastic containers #3 Block Count: Students lay wooden building blocks (cubes) side-by-side and count how many faces of the blocks are showing. Independent: number of blocks Dependent: number of faces Linear Supplies: blocks, perhaps wooden ones but we use plastic cubic centimeters stored in a plastic bag #4 Ping Pong Ball Drop: Students drop a ping pong ball from a designated height and time from the point of release till the impact time of the fourth bounce. Independent: height the ball is dropped from Dependent: time Probably Linear Supplies: one ping pong ball, meter stick or two, stop watch #5 Cylinder Fill: Students drop marbles into a graduated cylinder partially filled with water. Independent: number of marbles Dependent: change in water level Linear Supplies: 5-6 large marbles, 100 ml graduated cylinder, water, second container to drain after each experiment and paper towels #6 Losing Your Marbles: Students will weigh a container of marbles. Then they will take one marble out at a time and record the new weight. Independent: number of marbles taken out Dependent: weight Linear Supplies: 10-15 marbles of the same size, a container to hold them, a scale to weigh them. Summary of supplies for all stations:
Items for all stations can be stored in slider lock bags titled with station s number. #1 8-10 or so thick washers, it's nice if they are 2-3 mm thick, diameter is not important #2 metric scale, up to 20 marbles and a container to hold them #3 blocks, perhaps wooden ones but we use plastic cubic centimeters stored in a plastic bag or even dice #4 one ping pong ball, meter stick, stop watch #5 5-6 marbles, 100 ml graduated cylinder, water, second container to drain after each experiment and paper towels. #6 10-15 marbles of the same size, a container to hold them, a scale to weigh them. After the lab is done, you can incorporate technology if you wish. If you have access to graphing calculators then follow these steps to enter that data. Students are told not to go ahead before you tell them to. However, if this is the first time they have used the calculators, they usually are pretty good about it. We have found that it gets very confusing when some students try to jump ahead and then they run into a problem. You will also want to ask them to raise their hand as soon as they get stuck, not after you have moved several steps further on. Using the TI-83 or -86 Graphing Calculators TI-82s are very similar to TI-83s and can use that page. TI-85's directions are not included. Students can just follow the directions on page 7 as you work together. They will be entering the class data regarding the wave. It really helps if you have an overhead projector display at the same time. At the end students will try to write an equation of the Wave line. Of course, calculators can do a linear regression, but we usually don t tell them that at the start. Have them choose y= and type an the equation they think will match their data points and press graph again to see how close it is. If the slope or the y-intercept is off quite a bit they should press y= again and adjust their equation over and over again until it hits as many of the data points as possible. Thus they find the equation of the line-of-best-fit. Here is an example you could show at the start before they enter the Wave data: Enter these ordered pairs in the calculator: (1, 5.5), (2, 8.5), (3,10.5), (4,12.5) and (5, 15.5) Enter the data and graph a scatter plot. Then have them enter these equations and graph them: y = 2x + 4 Now adjust the y-intercept and regraph y = 2x + 3. They can see what happens. y = 3x + 3 will show what happens when there is a change in slope and then graph y = 2.5x + 3. Some students may get an error message of Invalid Dim or Dim Mismatch when trying to graph a y= equation. To correct it, have them first go to the y= screen. They will notice that one of the Plots at the top of the screen is dark, meaning it is turned on. Just have them move the cursor up to the darkened plot and then press enter to turn it off. Teacher directions to quickly find the line of best fit: Your students will write the equation by hand, but you may wish to tell them about this after the lab is done. To have the calculator determine the linear regression, choose: Stats, right arrow and Calc. Choose #5, linear regression. It also shows the r-factor. The closer r is to one, the better. N5182 County D Fond du Lac, WI 54937-9175 877-658-8939 email: aim@ammeinc.com Fax 920-922-7250 www.ammeinc.com
Student directions for each station. We print this sheet on card stock and then cut the stations apart. Place the correct set of directions at each station. #1 A Whole Lotta Washers: Carefully read EVERYTHING before you begin. Overview: You will be stacking up washers and measuring their overall height in millimeters. 1. Decide which variable (number of washers, height) is independent and which is dependent. 2. Stack up 3 washers near the edge of the desk so you can accurately measure their overall height in millimeters. Be careful when you measure. If you don t get eye-level with the desktop, your reading will probably be off due to a thing called parallax. (It s similar to sitting in the passenger seat in a car and reading the speedometer. It appears to have a different reading than what the driver sees.) Record the height. 3. Then stack another washer on top and measure the overall height. Continue to do so until you have enough data to make an accurate graph. (Note: If the data is not linear, you can't find the equation representing the data. Write "Not Linear" in the blank for the equation. Also, do not use "breaks" in any of the axes in this lab.) --------------------------------------------------------cut--------------------------------------------------------- #2 Marble Weigh: Carefully read EVERYTHING before you begin. In order to learn what this lab has to offer, you and your partner will need to be mature math students. Discuss ideas and share thoughts as you look for the constant change (slope) and the y-intercept. Your goal should be to recognize almost immediately whether or not the data will be linear and what part of the data is going to tell you the slope. Overview: Weigh an plastic cup containing five marbles and then continue to weigh it as more congruent (same size and shape) marbles are added to the cup. 1. Decide which variable (weight of cup with marbles, # of marbles) is independent and which is dependent. 2. Make sure the beam is balanced. Place the smallest cup on the scale and add 5 marbles. Record the weight along with 5 for the number of marbles. 3. Drop in more marbles and weigh again. 4. Repeat three or four more times with varying amounts of marbles. (Note: If the data is not linear, you can't find the equation representing the data. Write "Not Linear" in the blank for the equation. Also, do not use "breaks" in any of the axes in this lab.) --------------------------------------------------------cut--------------------------------------------------------- #3 Block Count: Carefully read EVERYTHING before you begin. In order to learn what this lab has to offer, you and your partner will need to be mature math students. Talk, share, and discuss as you look for the constant change (slope) and the y-intercept. Your goal should be to recognize almost immediately whether or not the data will be linear and what part of the data is going to tell you the slope. Overview: Lay blocks side-by-side and count how many faces of the blocks are showing. 1. Decide which variable (number of blocks, number of faces) is independent and which is dependent. 2. Lay one block in front of you on the desktop. Without lifting it, as you survey all the sides of the block, count how many individual faces you could see. Record your data. 3. Lay a second block alongside the first block and touching it on one face. Again count the number of faces (of individual blocks) which would be visible without lifting the blocks. 4. Repeat with many other blocks.
#4 Ping Pong Ball Drop: Carefully read EVERYTHING before you begin. Overview: Drop a ping pong ball from different heights and find the time from the point of release until the impact of the fourth bounce in hundredths of seconds. 1. Decide which variable (time, height) is independent and which is the dependent variable. 2. One person holds the meter stick vertically with the zero on the desk top and decides if the height will be measured from the bottom or the top of the ball. First drop the ball from 1 m while your partner times how long it takes for the ball to bounce a fourth time. 3. Repeat the experiment by dropping it from one meter again to double check your data. If the time is close, then you may take the average. Reject bad data and repeat. 4. Then continue the experiment by using three or four other heights measured in meters. (Double check each one.) (Note: If the data is not linear, you can't find the equation representing the data. Write "Not Linear" in the blank for the equation. Also, do not use "breaks" in any of the axes in this lab.) --------------------------------------------------------cut--------------------------------------------------------- #5 Cylinder Fill: Carefully read EVERYTHING before you begin. In order to learn what this lab has to offer, you and your partner will need to be mature math students. Talk, share, anddiscuss as you look for the constant change (slope) and the y-intercept. Your goal should be to recognize almost immediately whether or not the data will be linear and what part of the data is going to tell you the slope. Overview: Drop large marbles into a partially filled graduated cylinder of water. 1. Decide which variable (change in water level or volume, number of marbles) is independent and which is dependent. 2. Measure the water level in the graduated cylinder. Record this on your T-bracket with zero for the number of marbles. 3. Now you will drop one marble into the cylinder, but be careful, water drops splashed up on the sides may change the reading of the amount of water. So ease each marble into the water. 4. Measure the volume of the liquid again and record the data. Repeat the lab with different amounts of marbles as many times as you can. (Note: If the data is not linear, you can't find the equation representing the data. Write "Not Linear" in the blank for the equation. Also, do not use "breaks" in any of the axes in this lab.) --------------------------------------------------------cut--------------------------------------------------------- #6 Losing Your Marbles: Carefully read EVERYTHING before you begin. Overview: You will record the weight of a container holding 10-15 marbles and as you take marbles out, you will again weigh the container. 1. Decide which variable (weight, number of marbles taken out) is independent and which is dependent. 2. Weigh container containing 10-15 marbles (don t count exaclty how many - it is not important) and record it along with zero as the number of marbles taken out. 3. Take one marble out and record the new weight. Continue to take out more marbles and record the new weight at that time. When you have enough data, make an excellent graph. (Note: If the data is not linear, you can't find the equation representing the data. Write "Not Linear" in the blank for the equation. Also, do not use "breaks" in any of the axes in this lab.)
14-Lab D High-Tech Brains Name Your brain has been pumped quite full of algebra. In fact, we could say that you have a high-tech brain by now. I have noticed it runs like the Energizer bunny; it keeps going and going and going. 1) Today we will review your study of patterns and you will get to apply your knowledge to actual events. You know that slope is constant change. What's the slope in this chart? a) x 1 2 3 4 5 m = b) x 1 2 3 4 5 m = y 2 5 8 11 14 y 3-1 -5-9 -13 As you study the charts below, you'll notice the x-values are not a simple 1, 2, 3, 4, and 5. 2) Fill in the missing numbers. a) x 2 5 8 11 14 b) x 6 8 10 12 14 y 5 7 9 13 y 3 5 9 11 c) x 12 13 14 15 16 d) x 4 2 0-2 -4 y 1 5 13 17 y 1 2 4 7 e) x 2-1 -4-7 -10 f) x 2 3 4 5 6 y 1-9 -14-19 y 1 1 1 1 3 a) Linear graphs come only from a relationship that have a change. b) In which problems were the changes always constant? Those groups of data are linear and therefore their graphs have slope. 4) Find the slope of the following, but be careful, not all x's increased by 1 each time. a) Slope of linear relation a = b) Slope of linear relation b = rise, or change in y run, or change in x =? 3 = 3 rise, or change in y run, or change in x = c) Slope of linear relation c = d) Slope of linear relation e = 5 a) Graph relation f, which is also linear. c) Tell me why you won't get a line for d. b) Slope of linear relation f = d) Graph relation d.
Real life data does not come in nice charts. It may even be hard to see if there is a constant change. It's time to take you out to the ball game and see how to analyze real data. Let's pretend we re all going to see Albert Pujols play. He just smacked a line drive for a hit and the crowd cheers. In the bleachers the Wave starts. People are getting up and down, waving their hands and cheering. The scoreboard lights up says: "ATTENTION EVERYONE: We have data! Yes, even the wave is data. 6) You can collect data which can be put on a coordinate plane as long as there are two variables to make the ordered pairs. The wave has two variables. One variable is the number of people and the other variable is time. Here is an important concept to learn: Independent and dependent variables Since the time it takes to complete the wave depends on the amount of people that join in, we say that time is the dependent variable. If there is a dependent variable, then there must be an variable. 7 a) The number of people is the independent variable. The independent variable is graphed on the x-axis and the variable is graphed on the. b) Here's another way to remember it: To find the independent variable just decide which one comes first while doing the wave. Do you start with the number of people or the amount of time? We started with the so it must be the independent variable. As Nike would say, Just do it. Let's do the wave. Stop here and wait for your teacher to help. 8) Work Space: First label the axes with their proper names. Then record the data. people (x) time (y) Wave Data Check your data out. Does it look linear? When we are not sure, we plot the data. Do that now, but watch the scale. Of course, it will be somewhat hard to be accurate, since time was measured to hundredths. a) Draw a line of best fit. Remember, it must go through at least two of your points and try to have the same number of points above the line as below it. b) Next find the slope. Label any two points on your line with their coordinates. (If you can find the coordinates of an "easy" point that the line goes though, you may use it.) c) Use the coordinates to help you find the rise, run, and slope. Watch the scale as you count. d) What's the y-intercept? (Just look at your graph.) e) Write the equation in slope intercept form, and then replace the x and y with T's and P's. y = T =
14-Lab D page 3 Shortened High-Tech Brains Name Station #1 A Whole Lotta Washers Read the directions carefully. Guess: Will the data be linear? Title the T-bracket and both axes with the proper labels. Perform experiment, record data Label the scale and graph the data. a) If linear, label 2 coordinates on the line. Use them to find slope = (Write slope as a decimal.) b) If linear, what's the y-intercept? c) Write the equation of the line of best fit with proper variables: H = d) Now answer # s 10 and11 on the last page of the lab. Station #2 Marble Weigh This lab will be of no value to you unless you think this: What does the constant change and the y-intercept represent? Read the directions carefully. Guess: Will the data be linear? Title the T-bracket and both axes with the proper labels. Perform experiment, record data Label the scale and graph the data. a) If linear, label 2 coordinates on the line. Use them to find slope = (Write slope as a decimal.) b) If linear, what's the y-intercept? c) Write the equation of the line of best fit with proper variables: W = At this time, answer questions #10 and #13 on the last sheet of this lab. Station #3 Block Count This lab will be of no value to you unless you think: Is there a constant change and what s it and the y-intercept represent? Read the directions carefully. Guess: Will the data be linear? Title the T-bracket and both axes with the proper labels. Perform experiment, record data Label the scale and graph the data. a) If linear, label 2 coordinates on the line. Use them to find slope = (Write slope as a decimal.) b) If linear, what's the y-intercept? c) Write the equation of the line of best fit with proper variables: F = d) Now answer question #9 on the last page.
Station #4 Ping Pong Ball Drop Read the directions carefully. Guess: Will the data be linear? Title the T-bracket and both axes with the proper labels. Perform experiment, record data Label the scale and graph the data. a) If linear, label 2 coordinates on the line. Use them to find slope = (Write slope as a decimal.) b) If linear, what's the y-intercept? c) Write the equation of the line of best fit with proper variables: T = d) After each station, answer question #10 on the back page. Also answer #15 now. Station #5 Cylinder Fill This lab will be of no value to you unless you think. Think: what will the constant change and the y-intercept represent? Read the directions carefully. Guess: Will the data be linear? Title the T-bracket and both axes with the proper labels. Perform experiment, record data Label the scale and graph the data. a) If linear, label 2 coordinates on the line. Use them to find slope = (Write slope as a decimal.) b) If linear, what's the y-intercept? c) Write the equation of the line of best fit with proper variables: V = d) At this time, answer question s 10 and 12 on the last sheet of this lab. Station #6 Losing Your Marbles Read the directions carefully. Guess: Will the data be linear? Title the T-bracket and both axes with the proper labels. Perform experiment, record data Label the scale and graph the data. a) If linear, label 2 coordinates on the line. Use them to find slope = (Write slope as a decimal.) b) If linear, what's the y-intercept? c) Write the equation of the line of best fit with proper variables: W = d) Answer question #10 on the back page.
14-Lab page 5 High-Tech Brains Name 9 a) Line 4-5 blocks up again and explain very clearly what the slope of 3 represents in Station #3, Block Count. You should be able to see the "3 faces." b) On that line of blocks, where do you see the y-intercept of 2? 10) It is possible that different groups have different equations. Rate each station with: a) This station was non-linear. b) Every group's equation should be almost exactly the same. c) Every group's equation should be similar. (The slope will be the same, but "b" will probably vary.) d) Every group's equation will vary considerably. #1 Whole Lotta Washers (washers vs ht) #2 Marble Weigh (weight of marble and container) #3 Block count (no. of faces) #4 Ping Pong Ball Drop (time for 4 bounces) #5 Cylinder fill (drop marbles in) #6 Losing Your Marbles 11) On the Whole Lotta Washers station, what specific thing does the slope tell you about washers? 12) On the Cylinder Fill station, you dropped marbles into a partially filled cylinder of water. The y-intercept represents the While the slope is the water displacement of 13) On the Marble Weigh station, you weighed a container and then added marbles and found the total weight. The y-intercept is the weight of while the slope represents the 14 a) Elrod and Mitzi had a 5.2 cm tall box. Then they stacked sheets of cardboard of the same thickness on top of it. They measured the height after 5 sheets were placed on top and found the total height to be 6.7 cm. As they added more sheets, they measured the total height and found it was linear. What is the independent variable? Explain why you choose that one. b) Find the slope of their linear equation. Of course, I must see your work. (Use your noggin to find the constant change, this will tell me if you understood the lab, or just went through the motions. Hint: It is not 5.2, 6.7 or 1.5.) c) Write the equation with appropriate variables. 15) Extra credit: Can you explain what the y-intercept on station # 4, Ping Pong Ball Drop represents? It seems as though if you drop the ball from 0 cm, it should take 0 seconds, but that's probably not what you found.
14-Lab D page 6 High-Tech Brains Name 9 a) Line 4-5 blocks up again and explain very clearly where the slope of 3 is found on Station #8, Block Count. You should be able to see the "3 faces." b) On that line of blocks, where do you see the y-intercept of 2? 10) It is possible that different groups have different equations. Rate each station with: a) This station was non-linear. b) Every group's equation should be almost exactly the same. c) Every group's equation should be similar. (The slope will be the same, but "b" will probably vary.) d) Every group's equation will vary considerably. #1 Whole Lotta Washers (washers vs ht) #2 Marble Weigh (weight of marble and container) #3 Balloon Blow (time vs. breaths) #4 Ping Pong Drop (time for 4 bounces) #5 Cylinder fill (drop marbles in) #6 Bottle Drain (time to empty) #7 Losing Your Marbles #8 Block count (no. of faces) (weight vs marbles out) #9 Paper fold (folds vs. layers) 11) On the Whole Lotta Washers station, what specific thing does the slope tell you about washers? 12) On the Cylinder Fill station, you dropped marbles into a partially filled cylinder of water. The y-intercept represents the While the slope is the water displacement of 13) On the Marble Weigh station, you weighed a container and then added marbles and found the total weight. The y-intercept is the weight of while the slope represents the 14 a) Elrod and Mitzi had a 5.2 cm tall box. Then they stacked sheets of cardboard of the same thickness on top of it. They measured the height after 5 sheets were placed on top and found the total height to be 6.7 cm. As they added more sheets, they measured the total height and found it was linear. What is the independent variable? Explain why you choose that one. b) Find the slope of their linear equation. Of course, I must see your work. (Use your noggin to find the constant change, this will tell me if you understood the lab, or just went through the motions. Hint: It is not 5.2, 6.7 or 1.5.) c) Write the equation with appropriate variables. 15) Extra credit: Can you explain what the y-intercept on station # 4, Ping Pong Ball Drop represents? It seems as though if you drop the ball from 0 cm, it should take 0 seconds, but that's probably not what you found.
14-Lab D page 7 Review of graphing calculators Name Here's how to use a graphing calculator to find the equations from your data. I need you to follow these directions carefully. Do not go on to the next step until I tell you to do so. If you are having problems, let me know right away. Steps for using a TI-83 graphing calculator. In the margin, notice the small blanks. When you have a step done, check it off. We will be entering the data from the wave t-bracket (page 2) into the calculator. Make sure your chart is complete. Next you must clear any old lists in the calculator. Push the 2nd button (in the top left corner) and then the MEM button (above the + in lower right corner.) Either type in 4 or move down to 4) clear lists and push enter. (Screen should read ClrList.) Push Enter and the screen should read Done. Check to see if there are any old equations left. Push the "y=" button in the top left corner. If there is "stuff" on the right side of the equal signs, push the "del" (delete) button and then the "enter" button to get rid of it or use the Clear button. Then you can start to enter data. Then push stat again and choose edit by pushing enter. You will enter your data in the first two lists, L1 and L2. It should be easier to enter all the L1 data (the x-values). Then use the right arrow to start to enter the corresponding y-values in the L2 (the times). You will want to set the Window (top row) for your range and domain. Set the L1-values. Choose the minimum to be -1 (beware - choose the (-) key for the negative 1, not the subtract key) and the maximum to be a little more than the total amount of the independent variable (people in the wave.) Leave the x-scale set at 1. Now set the L2-values, the time. Choose -1 for the minimum and set the maximum at about 2 seconds more than our final time. Leave the y-scale set at 1. You're getting close to be being able to graph it. Choose 2nd and then y=, which is Stat Plot. This stands for plotting statistics. Choose 1, turn on (move the cursor to on and push enter). For type choose the one on the left, scatter plot which looks like a bunch of points. Choose Graph and the calculator will graph your data points. Now that you can see your data, your challenge will be to find the line of best fit. You will guess and check. Start by pushing the "y =" button. You can type in the equation that we found. (The calculator won't be able to use any variables except x and y. The x and y s are located on a key in the upper left, labeled X,T,øN.) Push graph again to see your points and this new line. Finally you probably can fine-tune the equation to fit the data even better. Is the slope steep enough? Does the y-intercept match up? Discuss it with a peer for a moment and decide if you want to choose a different slope or y-intercept to start. Keep guessing until you get an equation that is the very best match you can make. What is your final equation which you feel matches best?
14-Lab D page 7 Review of graphing calculators Name Steps for using a TI-86 graphing calculator In the margin, notice the small blanks. When you have a step done, check it off. We will be putting in the data from the wave t-bracket (page 2) into the calculator. Make sure your chart is complete. Next you must clear any old lists in the calculator. Push the 2nd button and then the Stat button (above the +) Then push the F2 key at the top to choose Edit from the window menu. If there is data in there, you will need to delete each piece. Move the cursor on top of each number and then push the DEL button. Use the arrow keys to help and continue until they are gone. You will now enter your data in the first two lists, L1 and L2. It should be easier to enter all the L1 data (the x-values). Put a number in and push enter. Then use the right arrow to start to enter the corresponding y-values in the L2 (the times). Push 2nd and Stat again. Push the F3 key at the top to choose plot. You will turn plot 1 on by pushing F1. Turn it on by moving the cursor to on and push enter. You will need to set the Window for your range and domain before you graph. Push GRAPH, (below the 2nd key). Then push the F2 key to select WIND. Set the x-values. Choose the minimum to be -1 (beware - choose the (-) key for the negative 1, not the subtract key) and the maximum to be a little more than the total amount of the independent variable (people in the wave.) Leave the x-scale set at 1. Now set the y-values, the time. Choose -1 for the minimum and set the maximum at about 2 seconds more than our final time. Leave the y-scale set at 1. Push the F1 key to see if there are any old equations left in the calculator. If there are push CLEAR to get rid of them. (It s below the four arrow keys.) You can graph it. Choose 2nd and then F5 to get the word graph in top row of your window's menu. Now that you can see your data, your challenge will be to find the linear equation of best fit. You will guess and check. Start by pushing the F1 button to choose y(x) =. You can type in the equation that we found. (The x is found on the x-var key. The calculator won't be able to use any variables except x and y.) Push 2nd and F5 to again graph your points and this new line. Finally you need to fine-tune the equation to fit the data even better. Is the slope steep enough? Does the y- intercept match up? Discuss it with a peer for a moment and decide if you want to choose a different slope or y-intercept to start. Keep guessing until you get an equation that is the very best match you can make. Push F1, type in a new equation over the top of the old one and graph it again. (2nd and F5) What is you final equation which you feel matches best?