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09/15/09 AB

Variables and Patterns
Big Idea:   Observation and description of changes in the world around us are the first steps in finding and learning about patterns. Essential Question: How can I use graphs, tables and symbols to solve problems? Notes: The radius is half of the diameter. I = 350n- equation Do not use multiplication in an equation. A- ** (miles) ||
 * A. Copy and complete the table and graph on the previous page to show the relationship between distance and time if the students traveled at the rate of 55 miles per hour.
 * Time (hours) || Distance
 * 0 || 0 ||
 * 1 || 55 ||
 * 2 || 110 ||
 * 3 || 165 ||
 * 4 || 220 ||
 * 5 || 275 ||
 * 6 || 330 ||
 * 7 || 385 ||
 * 8 || 440 ||

1. 3 Hours 2. 4 1/2 Hours 3. 5 1/2 Hours B. 1- 275 miles 2- 192.5 miles 3- 151.25 miles
 * B. Use your table and graph to estimate the total distance traveled after

****C. If the students continued driving at a steady 55 miles per hour, how far would they go in 1. 10 Hours 2. 12 1/3 Hours 3. 15 Hours** C- 1. 10 Hours= 550 Miles 2. 12 1/3 Hours= 247.5 Miles 3. 15 Hours= 825 Miles

D. The pattern to find out how many miles you are traveling at any given time is to multiply the number of hours you have been traveling for, with fifty-five. The reason you multiply by fifty-five is the number of miles you are traveling every hour. **
 * D. Look for patterns in the table and graph that help you calculate the distance traveled at any given time. Write a rule, using words, that explains how to calculate the distance traveled for any given time.

E- 55 miles x the number of hours you have been traveling for. Example: 55 miles x 4 hours= 220 miles.
 * E- Use symbols to write your rule from part D as an equation.**

//**Problem 4.1 Follow Up**//

1. Using the table, graph and the equation, I can find the distance of 3 hours which is 165 miles, then I would add 165 by 13.75. So the answer is 178.75 miles.
 * 1. How could you find the distance traveled after 3 1/4 hours by using the table? The graph? The equation?

a. Richmond, Virginia-about 55 miles from Williamsburg b. Baltimore, Maryland-about 3/4 of the way from Williamsburg to Philadhelpia c. Philadelphia, Pennsylvania-about 310 miles from Williamsburg 2. a. For them to reach there destination it will take them exactly 1 hour. b. For them to reach there destination it will take them 4 1/4 hours. c. For them to reach there destination it will take them 5 3/4 hours. ** **
 * 2. Estimate how much time it took the students to reach each of the following cities on their route: