Problem Solving: Simplify the Problem

When a problem is too complex to solve in one step, it often helps to divide it into simpler problems and solve each one separately.
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  1. Check Your Answer

    Students should read the problem again to be sure the question was answered.

    Yes, I found the miles per hour.

    Then, they should check the math to be sure it is correct.

    1 3/4 + 12 1/2 + 3/4 = 15 miles
    2:45 to 4:15 is 1 hour and 30 minutes
    15 divided by 1 1/2 = 10 miles per hour

    Students should determine if they chose the best strategy for this problem or if there was a better way to solve it.

    Simplifying this problem was a good strategy.
  2. Explain

    Students should explain their answer and the process they went through to reach it. Because this strategy involves logic, it is important for students to talk or write about their thinking.

    On your way to visit a friend, you leave your house at 2:45 P.M. and travel 1 3/4 miles to the train, 12 1/2 miles on the train, and 3/4 mile to your friend's house from the train station. If you get there at 4:15 P.M., how many miles per hour did you travel?

    This was a confusing problem, so I simplified the numbers and solved the simpler problem to figure out the steps. The simpler numbers I used were:

    You left the house 1:00, traveled 12 miles, and arrived at 4:00. How many miles per hour did you travel?

    Then I figured out the answer. I traveled 12 miles, and it took 3 hours. To find my miles per hour, I divided 12 by 3 to get 4 miles per hour.

    I wrote down the steps to solving the problem:

    • Find the distance traveled.

    • Find the time spent.

    • Divide to find the miles per hour.

    Then I used the real numbers from the actual problem to find the solution.

    • Find the distance traveled.
      1 3/4 + 12 1/2 + 3/4 = 15 miles

    • Find the time spent.
      From 2:45 to 4:15 is 1 hour and 30 minutes, or
      1 1/2 hours.

    • Divide to find the miles per hour.
      15 divided by 1 1/2 = 10 miles per hour

    I checked my calculations, and my answer is 10 miles per hour.

  3. Guided Practice

    Have students try solving one of the following problems by simplifying it.

    • A new movie theater sells 6,783 tickets in the first year, 5,697 tickets in the second year, and in its third year, sells 634 fewer tickets than in its second year. How many tickets are sold in 3 years?

    • or

    • A tiger eats 730.29 pounds of meat in 10 weeks and 4 1/2 cans of meat in a month. How much food does he eat in a year?

    Have students work in pairs, in groups, or individually to solve this problem. They should be able to tell or write about how they found the answer and justify their reasoning.

How Can You Stretch Students' Thinking?

Math problems can be simplified in a variety of ways. Modeling and working through many different problems will help students become flexible and creative in their problem-solving strategies. Students should work through problems by simplifying the numbers, rewording the problem, or by using a more familiar scenario. Have students find other ways to simplify problems. Record these strategies on a chart in the classroom, adding new strategies as students find them.

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