Algebra 3.5 day 1.notebook. September 10, Bellwork

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1 Bellwork 1

2 Go over Quiz 2

3 Partners 3

4 Before we have our HW quiz, check your work and answers with last night's HW with your partner. If there is something your partner is not sure about, help them. If there is something you're not sure about, ask your partner. If there are problems you both aren't sure about, ask me. 4

5 9/ Word Problems and Solving Proportions Mastery Objective: You will be able to: Write and solve a 2 step linear equation given a verbal model Solve proportions Language Objective: Translate a verbal model into an algebraic equation. 5

6 Solving Proportions A proportion is one fraction or ratio set equal to another. There are lots of ways to solve these. The most popular is to Cross Multiply. When I cross multiply here I get 3(12) = 18(x)...or 36 = 18x I still need to solve the equation. Cross multiplying is only the first step. So from 36 = 18x, I divide both sides by 18 to get x=2 or use the multiplicative inverse property and multiply by the reciprocal to get x=2 6

7 Solving Proportions Even with more complicated proportions I still cross multiply first. 7

8 With a Partner: Ms. Gadget's car broke down on the turnpike. Acme Towing charged $30 plus $3 per mile to tow the car. If Ms. Gadget paid $162, how far was the car towed? 8

9 With a Partner 2 Working as a waiter, Michael earns $7.00 per hour plus tips. Last night he received $36.50 in tips and earned a total of $ How many hours did he work? 9

10 What does this problem have in common with the last one? How can we use that commonness to help up do word problems like these? Working as a waiter, Michael earns $7.00 per hour plus tips. Last night he received $36.50 in tips and earned a total of $ How many hours did he work? Ms. Gadget's car broke down on the turnpike. Acme Toing charged $30 plus $3 per mile to tow the car. If Ms. Gadget paid $162, how far was the car towed? 10

11 Linear models In the examples we looked at each problem had a starting amount, a rate of change and an ending amount. You can turn this into an equation with this model: rate of change * variable + starting amount = ending amount very important! 11

12 With a Partner: Create a problem Based on the two problems we looked at come up with a situation where there is a starting amount, a rate of change and an ending amount. Describe the situation in sentences, then write the equation for that situation. 12

13 On Your Own: Create a problem Based on the two problems we looked at come up with a situation where there is a starting amount, a rate of change and an ending amount. Describe the situation in sentences, then write the equation for that situation. 13

14 Closure: Explain how you write the equation in the situation when the original amount is given as well as the final amount and the rate of change. 14

15 Example 3: A banana has 80 calories. This is 5 calories less than one seventh of the calories in a banana split. How many calories are in a banana split? 15

16 Example 4: The pressure on a scuba diver at sea level is 14.7 lbs per square inch (psi). The pressure increases psi for each foot of depth. Suppose the pressure on a diver is 41.4 psi. How deep is she? 16

17 With a Partner 3: Mr. Kork sold his car for $8,400. This was $200 more than two fifths of what he had paid for the car originally. How much had Mr. Kork paid for the car? 17

18 With a Partner 4: A spring is 2 in. long with no weight suspended from it. For each ounce of weight, the spring stretches 0.3 in. until it reaches its maximum length of 8 in. How much weight must be added for the spring to reach its maximum length? 18

19 On Your Own Jennifer lit a 12 inch candle and let it burn. She found that after each hour, the candle was 3/4 inch shorter. If she let the candle burn until it was only 1 inch tall, how many hours did it burn? 19

20 On Your Own Snorkel and two friends rented 3 life jackets and a sailboat. The life jackets were $3 each and the boat was $12 an hour. The total cost was $81. For how many hours did they rent the sailboat? 20

21 Homework 3.5 day 1 Worksheet 21

22 22

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