Word problem situations in elementary grades

I still want to continue on the topic of word problems - not because it's my 'soap box' subject but because I feel parents and students can use lots of help with them.

If you didn't catch the earlier post on how your typical math books subtily teach kids NOT to think carefully with word problems, read it here.

The easy 'routine' word problems in early grades usually require just one operation to solve. I would recommend studying a bunch of such word problems WITHOUT calculating the answers but only thinking and finding which operation is needed to solve each problem.

After you do that enough times, the student should start associating the types of situations with the appropriate operations:

  • Total is divided into so many parts/containers, each part having same amount.

    This is the multiplication/division situation:
    (number of parts) × (amount in each) = total

    • If you know how many parts and how much in each, MULTIPLY.
    • If you know the total and the number of parts, DIVIDE.
    • If you know the total and the amount in each, DIVIDE.

  • Total is divided into unequal groups.

    This is the addition/subtraction situation:
    (amount in group 1) + (amount in group 2) + (amount in group 3) + etc. = total.

    • If you know the amounts in groups but not the total, ADD.
    • If you know the total and the amounts in all but one group, SUBTRACT. This is the opposite of addition.

      Of 187 pictures, 45 were black-and-white. How many were color pictures?
      There were 57 pumpkins and 15 of them were ripe. How many were not ripe?

      Notice that NOTHING is 'going away' or being 'taken away'. They are typical "addition situations":

      color pictures + black-white pictures = total pictures
      ripe pumpkins + non-ripe pumpkins = all pumpkins

      They are solved by subtracting because the total is already known and in essence we're trying to find the missing addend.

Then there are some other subtraction situations:
  • You know what the total used to be, but part of it went away or got used - the easy, classic 'take away situation'.
    Jenny had $14.56 and she bought a doll for $2.55. How much money is left?

  • How many more (= difference)
    Joe has 24 stamps and Bill has 13. How many more does Joe have?
    Note nothing is 'taken away'.

I would also devote extra attention to problems involving time.

I'm not claiming this is a complete coverage of all the possible situations that are solved by single operation (let me know of others), but I wonder how much it would help the kids if these ideas were explicitly taught to them.

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