1. Licensing information Users should treat this material as a working draft. This material can be used in its current form, customized, redistributed and/or printed or displayed by the user. The author(s) request feedback on all materials so that they can be continually improved and updated. This material is licensed under the Creative Commons Attribution license: ( http://creativecommons.org/licenses/by/2.5/ ). http://creativecommons.org/licenses/by/2.5/ Author: Kevin Hall Wording for the legal statement above is adapted from the legal statement for Trigonometry, published in 2009 by The CK-12 Foundation: http://about.ck12.org/http://about.ck12.org/

2. Today’s topic is rates. What are some examples of rates?

3. Warmup: 5 pencils cost $.60. How much would 13 pencils cost?

4. A cheeseburger with 10 fries has a total of 622.5 calories. The same cheeseburger with 20 fries has a total of 855 calories. How many calories are there per fry? Try on your own:

5. A bus with 4 people on it weighs a total of 29,440 lbs. The same bus with 11 people on it weighs a total 30,735 lbs. On average, how much does each person weigh?

6. A bus with 4 people on it weighs a total of 29,440 lbs. 29,440 4 = 7360 Does each person weigh 7360 lbs? Why does this method give us the wrong answer? When you divide up the picture into 4 pieces, what does each piece represent?

7. The bus with 11 people on it weighs a total of 30,735 lbs. 30,735 11 = 2,794.1 Does each person weigh 2,794.1 lbs? Again, why does this method give us the wrong answer? Why is this answer different from our last answer?

8. The correct solution: What’s the difference between the 2 pictures?

9. A bus with 4 people on it weighs a total of 29,440 lbs. The same bus with 11 people on it weighs a total 30,735 lbs. On average, how much does each person weigh? The correct solution:

10. How does this relate to the formula for slope?:

11. A cheeseburger with 10 fries has a total of 622.5 calories. The same cheeseburger with 20 fries has a total of 855 calories. How many calories are there per fry? The correct answer on the cheeseburger problem:

12. The next goal for today is to use slope in real- life scenarios. At 8:51, plane starts descending. At 8:56, plane is at 28,130 ft. At 9:05, plane is at 24,258 ft. If the plane is descending at a constant rate, when will it land?

13. First we’ll do an example problem.

14. Based on the data below, when will you have only $200 left? Days $ 01,500 1,4942 1,4884 1,4826 - 6

15. Based on the data below, when will you have only $200 left? Days $ 01,500 1,4942 1,4884 1,4826 Actually, the rate is NOT -6. The rate is ____. Why? -3

16. Based on the data below, when will you have only $200 left? Days $ 01,500 1,4942 1,4884 1,4826 - 3 11,497 31,491 51,495 y = mx + b y = -3x + b 1,500

17. Based on the data below, when will you have only $200 left? Days $ 01,500 1,4942 1,4884 1,4826 - 3 11,497 31,491 51,495 y = mx + b y = -3x + 1500 1,500 200 Does the $200 represent x or y? Now just solve the equation.

18. Today we’re leaning how to find the rate when the x-values are not increasing by 1. xy 01,500 1,4942 11,497 31,491 1,500 We already know this xy 01,500 1,49424 121,497 361,491 1,500 We need to know this

19. At 8:51, plane starts descending. At 8:56, plane is at 28,130 ft. At 9:05, plane is at 24,258 ft. If the plane is descending at a constant rate, when will it land?

20. At 8:51, plane starts descending. At 8:56, plane is at 28,130 ft. At 9:05, plane is at 24,258 ft. If the plane is descending at a constant rate, when will it land?

21. Image credit of bus (from Wikimedia Commons): “This image has been released into the public domain by its author, Radagast. This applies worldwide.public domainRadagast http://commons.wikimedia.org/wiki/File:Grt_nova_bus.png