PRE-ALGEBRA

PRE-ALGEBRA

Reasoning Strategy: Working Backwards (5-6)

You should work backwards if you know the end result and are looking for something that happened earlier.

Example #1: You are planning to go to a baseball game that starts at 1:00 p.m. You want to arrive 30 minutes early. The train ride from your town to the city will take ¾ of an hour. The walk to the train station from your home is 15 minutes and from the train station to the stadium is 10 minutes. When should you plan to leave?

Game starts at 1:00 p.m.

Want to arrive at stadium 30 min. before 1:00 p.m. = 12:30 p.m.

Train arrives in city at 12:30 – 10 (amount of time to walk to stadium) = 12:20 p.m.

Train departs town at 12:20 – 45 (amount of time on train) =12:20 – 20 = 12:00 – 25 = 11:35 a.m.

Must leave home at 11:35 – 10 (amount of time to walk to train station) = 11:25 a.m.

You must leave home at 11:25 a.m.

When and how should you work backwards?

PRE-ALGEBRA

Reasoning Strategy: Working Backwards (5-6)

Example #2: On Monday, the temperature at the South Pole dropped 9oF from Sunday’s low. On Tuesday, it fell another 7oF, then rose 13oF on Wednesday, and 17oF more on Thursday. On Friday, it dropped 8oF to -50 F. What was Sunday’s low temperature?

Thursday’s temp. = -50 + 8 (drop of 8 backward = +8) = -42 Wednesday’s temp. = -42 -17 (rise of 17 backwards = -17) = -59Tuesday’s temp. = -59 -13 (rise of 13 backwards = -13) = -72Monday’s temp. = -72 +7 (drop of 7 backwards = +7) = -65Sunday’s temp. = -65 +9 (drop of 9 backwards = +9) = -56 oF

Sunday’s low temperature was -56oF.

Example #3: You spent ½ of your money at the movie theater and ¼ of it at the arcade. You have $17.50 left. How much money did you have originally?

Since ½ + ¼ = 3/4, then you must have ¼ of the original amount left = $17.50 Since ¼ + ¼ + ¼ + ¼ or ¼ x 4 = 1, then $17.50 x 4 = original amount = $70

You originally had $70.

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Your flight leaves the airport at 10:00 A.M. You must

arrive 2 hours early to check your luggage. The drive to the

airport takes about 90 minutes. A stop for breakfast takes

about 30 minutes. It will take about 15 minutes to park and

get to the terminal. At what time should you leave home?

Move the hands of the clock to find the time you should leave home.

Write the starting time for each event.

Reasoning Strategy: Work BackwardLESSON 5-6

Additional Examples

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(continued)

You should leave home at 5:45 A.M.

Reasoning Strategy: Work BackwardLESSON 5-6

Additional Examples

PRE-ALGEBRA

Solve by working backward.

1. Jason has a total of 212 sheep. Last spring, 52 lambs were born, but 9 died. How many sheep did he have before the lambs were born?

2. The bus picks up Tom every morning at 7:20 A.M. Tom walks his dog every morning before school for 36 minutes. It takes him 25 minutes to get ready for school and 7 minutes to walk to the bus stop. At what time does Tom need to wake up in order to get to the bus stop on time?

169 sheep

6:12 A.M.

Lesson Quiz

Reasoning Strategy: Work BackwardLESSON 5-6