BALANCING MONEY AND EXCELLING AT IT TOO! MODELING THE LAW OF THE LEVER NAME:

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1 BALANCING MONEY AND EXCELLING AT IT TOO! MODELING THE LAW OF THE LEVER NAME: Resource Key DATE: PERIOD: Today you ill collect and analyze data using a modified seesa. Your goal ill be to find the relationship beteen the distance of a coin from the fulcrum (pivot point of the seesa) and its eight. To do this, you ill be balancing different coins ith a quarter that is secured to your seesa. Your group ill need: 1 standard ruler 1 round pencil or pen 1 bag of coins (3 quarters, 2 dimes, 2 nickels, and 2 pennies) scotch tape (about 3 pieces) Activity Setup: 1. Lay and secure a round pen or pencil to the middle on your desk using 2 pieces of scotch tape. The middle of the pencil ill act as your pivot point (fulcrum). 2. Place the center of the ruler (hich is located at 15 cm) on the center of the pencil, perpendicular to the pencil. This is your seesa. 3. Place a quarter on one side of the seesa, preferably ithin 5 cm of the fulcrum. Secure the quarter to the ruler using a piece of scotch tape. When beginning data collection, you ill calculate the distances from the center of the coins (in millimeters) that you place on the seesa to the fulcrum. Coin Masses: Quarter = 5.6 g Nickel = 4.9 g Dime = 2.2 g Penny = 2.5 g Data Collection: 1. Record the position of the secured quarter relative to the fulcrum. Vary. Ex: 40 mm 2. Taking 1 quarter from your bag, place the quarter on the seesa in such a ay that it balances the secured quarter. Record the position of this quarter relative to the fulcrum. 40 mm Continue balancing the secured quarter using the masses in the problems to follo. Remember to record the distance from the coin(s) to the fulcrum (in millimeters). 3. Find the balance point using 2 stacked quarters. Record it here. 20 mm 4. Find the balance point using 1 dime. Record it here. 100 mm

2 5. Find the balance point using 2 stacked dimes. Record it here. 50 mm 6. Find the balance point using 1 nickel. Record it here. 45 mm 7. Find the balance point using 2 stacked nickels. Record it here mm 8. Find the balance point using 1 penny. Record it here. 90 mm 9. Find the balance point using 2 stacked pennies. Record it here. 45 mm Extension Problems: 10. Find the least expensive ay to balance your money (stacked if more than one coin is used). Record the coins used here. 1 penny Ansers ill vary based on placement of initial Record the distance here. 90 mm quarter. 11. Find the most expensive ay to balance your money (stacked if more than one coin is used). Record the coins used here. 2 quarters Record the distance here. 20 mm 12. Find the least expensive ay to balance your money ith to coins that have 20 mm beteen them. Record the coins used here. 2 pennies Record the distances here. 55 mm, 35 mm 13. Find the most expensive ay to balance your money ith to coins that have 20 mm beteen them. Record the coins used here. 1 quarter and 1 dime Record the distances here. Quarter: 20 mm, Dime: 45 mm

3 Data Analysis using a graphing calculator: No you ill analyze the distances from the fulcrum vs. corresponding eights of the coins data by inputting the data into lists 1 and 2 of your graphing calculator, generating a scatter plot to determine the trend of the data, and generating a regression model. 1. Complete the table belo. Type and Number of Coins Total Weight of Coin(s) Distance from the Fulcrum 1 Quarter 5.6 g 40 mm 2 Stacked Quarters 11.2 g 20 mm 1 Dime 2.2 g 100 mm 2 Stacked Dimes 4.4 g 50 mm 1 Nickel 4.9 g 45 mm 2 Stacked Nickels 9.8 g 22.5 mm 1 Penny 2.5 g 90 mm 2 Stacked Pennies 5.0 g 45 mm 2. Enter the Total Weight of Coin(s) data into list 1 of your graphing calculator and the corresponding Distance from the Fulcrum into list 2. To do this, press STAT Highlight 1:Edit and press ENTER Enter the values into the lists using the arro and ENTER keys to move. When finished, press 2 nd MODE to Quit. 3. Create a scatter plot of the data by pressing 2nd Y= 1:Plot1 Off ENTER Highlight ON Type: Scatter (1 st graph type) Xlist:L1 Ylist:L2 Mark: Highlight + 4. To see the scatter plot, press ZOOM 9:ZoomStat. This ill result in the calculator setting an appropriate indo to vie the data. Sketch the plot belo, labeling your axes and setting the scale appropriately. Distance from Fulcrum (mm) eight of coin(s) (grams)

4 5. What type of trend do you see in the data? The graph looks like the positive half of a hyperbola or inverse square. This means that the distance of the coin(s) from the fulcrum is inversely proportional to the eight of the coin(s). Heavier coins result in less distance relative to the fulcrum. k 6. Using the inverse variation model d =, find the k value by substituting one of your data points for distance and corresponding eight. Write your equation here. d 224 =. Found by substituting 40 for d and 5.6 for. 7. Enter your equation into Y= in your graphing calculator and press GRAPH. Does your model appear to fit the data ell? Please explain. The model fits the data very ell, going through all of the points (see graph above). 8. Try different k values in your equation to see if you can get a better fit. Once you are 224 satisfied ith the k value, enter the ne equation here. d = 9. To have the calculator find a regression model for the data: Press STAT highlight CALC scroll don to A:PrReg press ENTER Press 2 nd 1, 2 to direct the calculator to the data in lists 1 and 2. Press ENTER. Enter the calculator s Poer Regression model here. y = x Compare and contrast your model to that of the calculator s. Summarize your findings. The models are almost identical. The calculator s k-value as about 222 vs. our 224, and the exponent as Very close to 1, meaning the x in the denominator is to the first poer.

5 Data Analysis using Excel: 1. Run Microsoft Excel. 2. Double-click on LaofLever document. 3. Enter the Total Weight of Coin(s) and Distance from Fulcrum Data in the appropriate columns of the table. 4. Click on the Chart Wizard Icon on the Toolbar (the Bar Graph Icon). 5. Under Chart Type (ithin Standard Type Card) select XY Scatter. 6. Click NEXT. 7. Click the SERIES card. Delete hat information might be in the NAME area by highlighting it and pressing del. X Values should read =sheet1$c$10:$c$17 (coin eight data) Y Values should read =sheet1$d$10:$d$17 (balance point data) 8. Click NEXT. 9. On the TITLE card, Enter La of Lever in Chart Title. Enter Coin Weight in Value (X) axis. Enter Balance Point in Value (Y) axis. 10. Click NEXT. 11. Click FINISH. 12. Under the CHART menu on the toolbar, click on Add Trendline 13. Click on Poer under the TYPE Card, then click on the OPTIONS Card. Check the box Display equation on chart. 14. Click OK. 15. Click on the equation and move it to the loer right-hand corner of the box. 16. Click on the box and move it to the right of the data (if it isn t already there). 17. Click the PRINT icon to print out your graph. SUMMARY: Please rite a short summary comparing the 3 methods you used in this activity for finding the relationship beteen distance from the fulcrum and eight. Which method did you prefer and hy? Did the methods help you in understanding inverse variation? Ansers ill vary.