1ACE Exercise 1 Investigation 1 1. A group of students conducts the bridge-thickness experiment with construction paper. Their results are shown in this table. Bridge-Thickness Experiment Thickness (layers) 1 2 3 4 5 6 Breaking Weight (pennies) 12 20 29 42 52 61 a. Make a graph of the (thickness, breaking weight) data. Describe the relationship between bridge thickness and breaking weight. 134
1ACE Exercise 1 (continued) Investigation 1 b. Suppose it is possible to use half-layers of construction paper to build the bridges. What breaking weight would you predict for a bridge 3.5 layers thick? Explain how you made your prediction. c. Use the group s data to predict the breaking weight for a construction paper bridge 8 layers thick. Explain how you made your prediction. 135
2ACE Exercise 4 Investigation 2 4. This table gives the average weights of purebred Chihuahuas from birth to 16 weeks. Average Weights for Chihuahuas Age (weeks) 0 2 4 6 8 10 12 14 16 Weight (oz) 4 9 13 17.5 21.5 25 30 34 39 a. Graph the (age, weight) data. Draw a line that models the data pattern. 136
2ACE Exercise 4 (continued) Investigation 2 b. Write an equation of the form y = mx + b for your line. What do the values of m and b tell you about age in this situation? What do the values of m and b tell you about weight in this situation? c. Use your equation to predict the average weights of Chihuahuas for odd-numbered ages from 1 to 15 weeks. Average Weights of Chihuahuas Age (wk) 1 Weight (oz) 3 5 7 9 11 13 15 d. What average weight does your linear model predict for a Chihuahua that is 144 weeks old? Explain why the prediction is unlikely to be accurate. 137
3ACE Exercise 11 Investigation 3 11. Testers drive 8 vehicles 200 miles on a test track at the same speed. The table shows the amount of fuel each vehicle used. Vehicle Type Large Truck Large SUV Limousine Large Sedan Small Truck Sports Car Compact Car Sub-Compact Car Fuel Used (gal) 20 18 16 12 10 12 7 5 Miles per Gallon 10 a. Find the fuel efficiency in miles per gallon for each vehicle. HINT Complete the table. Remember, each vehicle was driven for 200 miles. b. Make a graph of the (fuel used, miles per gallon) data. Describe the pattern of change shown in the graph. 138
3ACE Exercise 11 (continued) Investigation 3 c. Write a formula for calculating the fuel efficiency based on miles per gallon (y) from fuel used (x) on a 200-mile test drive. d. Using your formula, tell how fuel efficiency (i.e. miles per gallon) changes as the amount of fuel used increases from 5 to 10 gallons. From 10 to 15 gallons. From 15 to 20 gallons. 5 gallons to 10 gallons: HINT What is the miles per gallon when 5 gallons of fuel are used? What is the miles per gallon when 10 gallons of fuel are used? 10 gallons to 15 gallons: What is the difference between the miles per gallon when 5 gallons of fuel are used and when 10 gallons of fuel are used? 15 gallons to 20 gallons: e. How do the answers for part (d) show that the relationship between fuel used and miles per gallon is not linear? HINT Are the changes in part (d) above all the same? If the relationship was linear, would the changes all be the same? 139
Check-Up 1. The party room at the miniature golf course is decorated with golf ball patterns like this: Step 1 Step 2 Step 3 a. Complete this table showing the number of golf balls in the next 5 steps of the pattern. HINT You may want to draw Steps 4 and 5 to help you find the pattern. Golf Ball Patterns Pattern Step Number 1 2 3 4 5 6 7 8 Number of Balls Used 1 3 6 What number of balls would be needed for the 20th step in the pattern? Explain your reasoning. 140
Check-Up (continued) Investigation 1 b. For each graph, explain why the graph does or does not match the pattern relating number of balls to design step number. Explain the reasons for your choice. 1. 2. Number of Balls Number of Balls Design Step Number Design Step Number 3. 4. Number of Balls Design Step Number Number of Balls Design Step Number 141