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September 16th 2008 JO 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?


 * 4.1**
 * 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 a rate of 55 miles per hour.**
 * Time || Distance ||
 * 0 || 0 ||
 * 1 || 55 ||
 * 2 || 110 ||
 * 3 || 165 ||
 * 4 || 220 ||
 * 5 || 275 ||
 * 6 || 330 ||
 * 7 || 385 ||
 * 8 || 440 ||

At 3 hours the distance is 165 miles. At 4 1/2 hours the distance is about 247.5 miles. And at 5 1/4 hours the distance is about 289 miles.
 * B. Use your table and graph to estimate the total distance traveled after**
 * 1. 3 hours 2. 4 1/2 hours 3. 5 1/4 hours**

1. 10 hours 2. 12 1/3 hours 3. 15 hours** At 10 hours the distance would be 550 miles. At 12 1/3 the distance would be 678.4 miles. And at 15 miles the distance would be 825 miles
 * C. If the students continued driving at a steady 55 miles per hour, how far would they go in

The pattern is that it increases by 55 miles every hour. So now that I know the pattern I could just simply add for example 440 miles which is 8 hours by 55 which would equal 495 miles.
 * D. Look for patterns in the table and graph that help you calculate the distance traveled for any given time. Write a rule, using words, that explains how to calculate the distance traveled for any given time.**


 * E. Use symbols to write your rule from part D as an equation.**

Distance= 55 x time (hour)

1. How could you find the distance traveled after 3 1/4 hours by using the table? The graph? The equation?**
 * 4.1 F.U

Using the table, I can find the distance of 3 hours which is 165 miles, then I would add 165 by 13.75. I found 13.75 by dividing 55 by 4. so the answer is 178.75 miles

2**. Estimate how much time it took the students to reach each of the following cities on their route:**

b. Baltimore, Maryland-about 3/4 of the way from Williamsburg to Philadelphia c. Philadelphia, Pennsylvania-about 310 miles from Williamsburg**
 * a. Richmond, Virginia-about 55 miles from Williamsburg

a. it will take them about 1 hour b. it will take them about 4 1/4 hours c. it will take them about 5 3/4 hours