: Identifying Proportional and Non-Proportional Relationships in Tables Classwork Example: Which Team Will Win the Race? You have decided to walk in a long distance race. There are two teams that you can join. Team A walks at a constant rate of. miles per hour. Team B walks miles the first hour and then miles per hour after that. Task: Create a table for each team showing the distances that would be walked for times of,,,,, and hours. Using your tables, answer the questions that follow. Team A Distance Time (h) (miles). 7. 0. Team B Distance Time (h) (miles) a. For which team is distance proportional to time? Explain your reasoning. Team A, because the miles divided by the hours always gives a constant rate (. mph). b. Explain how you know distance for the other team is not proportional to time. The first hour the rate is miles per hour. The second hour the average rate is mph. y/x does not have the same answer for each pair. : Identifying Proportional and Non-Proportional Relationships in Tables Date: //7 S. 0 7 Creative Commons Attribution-NonCommercial-ShareAlike.0 Unported License.
c. At what distance in the race would it be better to be on Team B than Team A? Explain. Team B is faster than team A when the distance is less than 0 miles. Both teams take hours to go 0 miles, but team B walks more miles in, and hours. d. If the members on each team ran for 0 hours, how far would each member run on each team? Team A:.x0= miles Team B: miles in the first hour + each of the next 9 hours= += miles e. Will there always be a winning team, no matter what the length of the course? Why or why not? No, at hours, both teams have walked 0 miles. 7 f. If the race is miles long, which team should you choose to be on if you wish to win? Why would you choose this team? Team A. /.=. hours. Team B: - (walked in first hour)= miles left. At miles per hour it would take more hours for a total of hours. I would choose team A. g. How much sooner would you finish on that team compared to the other team?. hours= minutes. Exercises. Bella types at a constant rate of words per minute. Is the number of words she can type proportional to the number of minutes she types? Create a table to determine the relationship. Minutes 0 Number of Words 0 The relationship is proportional, because the rate is words per minute (y/x=) for each pair. : Identifying Proportional and Non-Proportional Relationships in Tables Date: //7 S. Creative Commons Attribution-NonCommercial-ShareAlike.0 Unported License.
7. Mark recently moved to a new state. During the first month he visited five state parks. Each month after he visited two more. Complete the table below and use the results to determine if the number of parks visited is proportional to the number of months. To get the number of months: - (in the first month)= / (per month)=9 First year plus 9 more months=0 months. Number of Months 0 Number of State Parks 7 9 It is not proportional because the number of state parks per month is not constant.. The table below shows the relationship between the side length of a square and the area. Complete the table. Then determine if the length of the sides is proportional to the area. Side Length (inches) Area (square inches) y/x Area of square=side length squared (times itself) 9 It is not proportional, because y/x is not constant. : Identifying Proportional and Non-Proportional Relationships in Tables Date: //7 S. Creative Commons Attribution-NonCommercial-ShareAlike.0 Unported License.
7 Problem Set. Joseph earns $ for every lawn he mows. Is the amount of money he earns proportional to the number of lawns he mows? Make a table to help you identify the type of relationship. Number of Lawns Mowed Earnings ($) 0 0 It is proportional because the rate ($ per lawn) is for each pair.. At the end of the summer, Caitlin had saved $0 from her summer job. This was her initial deposit into a new savings account at the bank. As the school year starts, Caitlin is going to deposit another $ each week from her allowance. Is her account balance proportional to the number of weeks of deposits? Use the table below. Explain your reasoning. Time (in weeks) Account Balance ($) 0 0 0 No, it is not proportional. The balance divided by the time does not give the same rate for each pair. : Identifying Proportional and Non-Proportional Relationships in Tables Date: //7 S. Creative Commons Attribution-NonCommercial-ShareAlike.0 Unported License.
7. Lucas and Brianna read three books each last month. The table shows the number of pages in each book and the length of time it took to read the entire book. Pages Lucas Read 0 Time (hours) 9 Pages Brianna Read 0 Time (hours) y/x.0.0.0 y/x.0.0..0 a. Which of the tables, if any, shows a proportional relationship? Lucas' table is proportional because it took him a constant rate of.0 hours to read each page. b. Both Lucas and Brianna had specific reading goals they needed to accomplish. What different strategies did each person employ in reaching those goals? Lucas read at a constant pace. Brianna adjusted her pace for the different books, but she still met her goal. : Identifying Proportional and Non-Proportional Relationships in Tables Date: //7 S.7 Creative Commons Attribution-NonCommercial-ShareAlike.0 Unported License.