Licensing information Users should treat this material as a working draft. This material can be used in its current form, customized, 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-Share Alike license: (http://creativecommons.org/licenses/by-sa/3.0/). 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/

Teaching notes For questions listed as “worked examples” on the 2.3 student handout, the teacher shows the solutions step-by-step, and students answer the reflection questions on the handout. For questions listed as “practice” on the student handout, do NOT show the complete solution until students have had a chance to work through it on their own. You can show it gradually while they work, timing it so each step comes up after most students have done that step. While they work, you can walk around the room praising their success and prompting them where necessary. Print out the solutions before class, so you’re not trying to solve the problems when you’re supposed to be walking around checking their understanding.

EXAMPLE: If you earn $9 every 2 hours, how much will you earn in 18 hours? Studying this example problem will help you solve the next question on your own.

2). EXAMPLE: If you earn $9 every 2 hours, how much will you earn in 17 hours? $ 4.50 a). Can you explain this part? $ 4.50 $ 4.50 $ 4.50 $ 4.50 How much? $ 4.50 $ 4.50 $9 = $4.50 per hour $ 4.50 $ 4.50 2 hours $ hour = 4.50 $ 4.50 $ 4.50 $ 4.50 $ 4.50 $4.50 $ 4.50 $ 4.50 $ 9 $4.50 $4.50 $4.50 $ 4.50 2 hours 1 hour 17 hours First, how much is each hour worth? Then, how much are 17 hours worth? b). Why do we multiply here? $ hour 4.50 • 17 hours = $76.50

3). If 6 lbs of noodles can serve 8 people, how many pounds would be needed for 14 people? = 0.75 lb 0.75 lb per person 0.75 lb 0.75 lb 8 people 0.75 lb lb person 0.75 lb 0.75 lb = 0.75 0.75 lb 0.75 lb 0.75 lb 0.75 lb 0.75 lb 0.75 lb 0.75 lb 8 people 1 person 14 people First, how much for each person? Then, how much for 14 people? lb person 0.75 • 14 people = 10.5 lb

4). How many gallons of gas would a U. S 4). How many gallons of gas would a U.S. Army tank use in driving 14 miles, since it uses 120 gallons to go 40 miles? What we need to know first. What we want to find out. for each mile Gallons for 14 miles a). Can you explain this? 120 gallons 40 miles gallons gallons 3 3 • 14 miles = 42 gallons mile mile b). What does this represent? c). Can you explain this?

5). How far could a U.S. Army tank go on 14 gallons of gas, since it uses 120 gallons to go 40 miles? What we need to know first. What we want to find out. for each gallon Miles for 14 gallons 40 miles 120 gallons divide miles 0.33 • 14 gallons = 4.67 miles gallon miles 0.33 gallon rounded

Discussion How were #4 and #5 related? What was the same about them? What did you have to do differently in them?

3 laps in 4 minutes 6). You ran . At that rate, far will you run in 11 minutes ? When she started this problem, Alisha made a mistake. for each minute Laps for 11 minutes This does not represent each minute. What’s not correct? 4 minutes 3 laps min. 1.33 lap