6th Grade Math Textbook, Fundamentals

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Problem 2:You want to cook a hamburger for exactly 7 minutes.
You have only a 4-minute timer and a 5-minute timer.
(These are like hourglass sand timers. They empty in 4 or 5 minutes,
but they cannot be used for marking other times.)
How can you use these timers to time exactly 7 minutes?

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Lesson 11-12 for exercise sets.

Read to understand what is being asked.

List the facts and restate the question.

Facts: You have only a 4-minute timer and a 5-minute timer.

Question:How can you use these timers to time 7 minutes?

Select a strategy.

You can try to work backward.

Start with the 7-minute time frame and try to find a way to represent

it in terms of 4 and 5 minutes.

Apply the strategy.

You know that (3 • 4)  5 7. This suggests that you can run

the 4-minute timer three consecutive times and “take away”

the 5-minute timer once.

The diagram below shows how this can be done.

So here’s the plan:

• Begin both timers at the same time.


• When the 4-minute timer finishes, restart it.


• When the 5-minute timer finishes, begin cooking the burger.
  (The 4-minute timer has 3 minutes left on it.)


• When the 4-minute timer ends (at which time the burger
  has been cooking for 3 minutes), restart it.


• Stop cooking when the 4-minute timer ends again.
  (The 4 additional minutes give a total of 7 minutes of cooking time.)

4 minutes

5 minutes

7 minutes

begin cooking

start timer stop cooking

start timer

4 minutes 4 minutes

Check to make sure your answer makes sense.

You can verify this in 12 minutes by acting out the action while two

of your classmates use their watches as 4- and 5-minute timers.