PROBLEM SOLVING Work Backward

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PROBLEM SOLVINGWork Backward

• Glinda Kerans
• Grandview Middle School

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(Teacher Notes)

• To move this presentation along more quickly.
  Click the mouse on the page as soon as you have
  seen one clip.

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Math Objectives

• Solve problems involving elapsed time as applied
  to real world situations.
• MA 4 3.5, 4.1

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Sometimes a problem may tell you what happened at
the end of a series of steps.

• And ask you to find what happened at the
  beginning or in the middle..

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When that occurs, you can start with
what you know and work backward.When you are
finished always check your problem to see if you
have a reasonable answer and then write a
concluding statement.

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Try this problem.

• Ed is trying to decide what time he needs to get
  up in the morning. He needs 45 minutes to get
  ready for school, the bus ride is 25 minutes, and
  he needs 20 minutes for a research project in the
  library. School starts at 830 a.m. and he
  cannot be late.

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This is a good time to stop and write what you
know about Eds schedule.

• 1st you know that he will need the following
  amounts of time before school starts.
• 45 minutes to get ready
• 25 minutes on the bus
• 20 minutes for research

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That is a total of how many minutes?

• 45 25 20 90 minutes
• Have you learned how to convert minutes to hours?
  It is not necessary for this problem, but a good
  skill to know. So lets work on it a minute ok?

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Minutes to Hours

• Since there are 60 minutes in an hour..
• We can divide the 90 minutes Ed needs by the 60
  minutes in every hour and learn that 90 minutes
  is the same as 1 hour and 30 minutes.

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So now we know that Ed needs to get up at least 1
hour and 30 minutes earlier than what time?

• Reread the problem if necessary

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Yes, you are right if you said ..

• 830 a.m.

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So now if we are going to work backwards from
830 a.m.

• The last thing Ed was going to do was research.
• We can start by figuring out what time he needs
  to start the research project that will take 20
  minutes.
• Remember school starts at 830 a.m., so 20
  minutes earlier than that is what time?

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Research time begins

• 810 a.m.
• Right?
• So now we have worked backward to 810 a.m. What
  was the next to last thing Ed was going to do?
• Right he had to ride the bus how long?

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Bus Ride

• a.m Thats right.. The bus ride was 25 minutes.
  So 25 minutes
• earlier than 810 a.m. is what time?
• Lets do this the easy way. Remember we need to
  work backward 25 minutes. So 10 minutes earlier
  than 810 would be 800 a.m.
• Can you count backward now and find 15 minutes
  earlier than 800. ?

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Sure you can..

• 15 minutes earlier than 800 is 745 a.m. or 15
  minutes until 800 a.m.
• So now we know that Ed must get up by 745 a.m.
  to ride the bus and do his research, but what
  else do we need to know?

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We need to know the amount of time Ed is going to
spend getting ready for school.

• He must be looking good if he spends 45 minutes
  getting ready, dont you think?
• Our job now is to figure 45 minutes earlier than
  745 a.m.
• You try it and then I will tell you how I did it

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What time to get up?

• Remember I like to do things the easy way, so Im
  going to say from 745 a.m. backwards 30 minutes
  will be 715 a.m.
• But I needed to go back 45 minutes, so I still
  have 15 more minutes to go back. So if I am at
  715 a.m. and I take off another 15 minutes, I
  will see that Ed must get up at 700 a.m.

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Did you get the same answer?Did you work the
problem the same way as I did?

• You didnt have to work it the same way.. You
  just need to make certain you have worked
  backward for 90 minutes from 830 a.m. when
  school started?

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Minutes to Hours

• Remember when I had you change minutes to hours?
• If you want to double check your answer to make
  sure it is reasonable, you can do so very easily
  now by just subtracting 1 hour and 30 minutes
  from 830 a.m.

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Is the answer reasonable?

• 830 a.m.
• -130
• ____
• 700 am.

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Sure it is

• And you have learned to work backward and check
  to be sure you have a reasonable answer.

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Can you write a concluding statement for this
problem?

• Try it and then check the next slide to see if
  you agree with me.
• Remember our concluding statements do not have to
  be exactly the same they do need to contain the
  same information and be written as a complete
  sentence.

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Concluding statement

• Ed must get up by 700 a.m. in order to get ready
  for school, ride the bus, do research, and get to
  class by 830 a.m.

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Thats all for now.

• Have a great day