WORD PROBLEM SOLVING STRATEGIES


Solving word problems is a difficult, but important skill! There are four basic steps to solving a word problem:

Step 1:
Read the problem and find the question that is being asked.

Step 2:
Identify the important information in the problem. Circle it, underline it, highlight it, or do something to it! You will need this information to solve the problem!

Step 3:
Choose a problem solving strategy and solve the problem. There are a lot of strategies to choose from (see below). If your strategy doesn't work, don't worry, just choose another one and try again!

Step 4:
Look back on your work. Check to make sure that your answer makes sense and to make sure that you've answered the question being asked.


Here are some problem solving strategies to choose from...

Strategy

How to do it...

When to use it...

Compute and Simplify

Calculate and solve using arithmetic.

When doing a simple math arithmetic problem will solve the problem.

Draw a Picture

Sketch a diagram of the situation.

When you need to visualize something to solve a problem.

Make a Table or Chart

Organize the information into a table or chart so that you can see and use it.

When you need to work with different sets of numbers or the numbers are changing and you want to find a pattern.

Look for a Pattern

Look at the information to see if there is a pattern that is happening

When you are given a series of numbers that can be extended or generalized.

Make an Organized List

Organize your thinking by listing your work in a way that makes sense to you.

When you need to find combinations of things.

Work Backwards

Start with the end result and go through the problem backwards, looking for the start.

When you are given the end result and need to find the start

Guess and Check

Try a number. If it is not correct, figure out why and try a different number.

When there is no systematic way to solve the problem. Use as a last resort!

Use a Simpler Case

Solve a similar by easier problem to see how it works, then go back to the original problem and solve it.

When you have a complex problem and you want to break it into smaller steps, change large numbers into smaller numbers, or reduce the number of items given in the problem.




Compute and Simplify

Sometimes all you have to do to solve a word problem is a simple arithmetic problem.

Example
Jane has 10 kittens and was given 9 more. How many total kittens does she have?

To solve this, we simply have to add 10 + 9. This gets us 19, and that is our answer!


Draw a Picture

If no picture is given for a problem, you may find it helpful to draw your own. Drawing a picture or diagram to solve problems can help you understand and manipulate data. It is an especially useful strategy for problems that involve mapping, geometry, and graphing.

Example
Billy Bob always sits in the same pew at the church. The pew is second from the front and eighth from the back. There is a center aisle. Each pew seats 6 people. What is the seating capacity in Billy Bob’s church?

A picture would really help us get a good idea of what the seating looks like.
Now we can see that there are 9 pews in the row and there must be two rows, for a total of 18 pews. Each pew holds 6 people, so 18 x 6 = 108. The answer is 108 people.


Make a Table or Chart

Making a table or chart is a good way to organize data presented in a problem. This problem solving strategy allows you to see relationships and patterns among the data. This strategy also gives you a way to record your numbers and ideas.

Example
Mr. Ohashi raises a Green Plant that grow one foot a day and a Purple Plant that grow two feet a day. Today, the Green Plant is one foot high and the Purple Plant is seven feet high. In how many days will the Purple Plant be three times as high as the Green Plant?

If we make a table, we can keep track of all the height changes.

Plant
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7
Green
1
2
3
4
5
6
7
Purple
7
9
11
13
15
17
19

As we can see, on Day 5, the purple plant is 3 times bigger. So the answer is in five days!


Look for a Pattern

Looking for a pattern is one of the most important and most often used problem solving techniques. This strategy involves analyzing patterns in data, making predictions to generalize your analysis, then checking your generalization. By identifying the pattern, you can predict what will come next and what will happen again and again in the same way.

Example
Sally Jo used 6 blocks to build this staircase with 3 steps. How many blocks will Sally Jo need to make a 6-step staircase?


For a 1-step, we have to have 1 block. To make it a 2-step, we have to add 2 more blocks. To then make it a 3-step, we have to add 3 more blocks. See the pattern yet? Maybe this picture will help:
Now you can see the pattern - to make the staircase, you add one more block than you added the previous time! The answer must be: 1 + 2 + 3 + 4 + 5 + 6 = 21 blocks!


Make an Oragnized List

Sometimes you will be asked to find different combinations of things. To solve these types of problems, it may be helpful to make an organized list. This strategy will help you to organize your thinking, make it easier to review what you have done, and show you what steps still need to be finished. This strategy also gives you a way to record your numbers and ideas.

Example
An ice cream shop currently has three different flavors of ice cream: strawberry, vanilla, and chocolate. The shop also has three different toppings: chocolate syrup, sprinkles, and cookie crumbs. How many one-flavor, one-topping combinations are possible?

An organized list will help us keep track of the combinations we have:

Strawberry & chocolate syrup
Strawberry & sprinkles
Strawberry & cookie crumbs
Vanilla, & chocolate syrup
Vanilla, & sprinkles
Vanilla, & cookie crumbs
Chocolate & chocolate syrup
Chocolate & sprinkles
Chocolate & cookie crumbs

There are a total of 9 combinations!


Work Backwards

Some problems give you the end results and ask you to find the conditions at the beginning of the problem. To solve this type of problem, it may be helpful to reverse the action and work backwards.

Example
Joey's uncle said, "If you add 10 to my age and then double the sum, the result is 90." How old is Joey's uncle?

Start with 90 and work backwards.
To undo doubling, we divide by two. 90 divided by 2 is 45.
To undo adding 10, we subtract 10. 45 - 10 = 35.

We should check our answer. Add 10 to 35, and you get 45. Double 45 and you get 90. It works!

The correct answer is 35!


Guess and Check

Sometimes you can solve a problem by guessing the answer, checking the guess, revising the guess, then checking it again. Don't give up if your first guess isn't correct! Examine the result - was your guess too high or too low? Remember, errors give you information that will help you solve the problem!

Example
The sum of two numbers is 74.
The difference of the same two numbers is 16.
Find the two numbers.

Since we haven't talked about solving these types of problems with equations yet, let's try guess and check.

I'll start with a guess of 20 and 54, since they add to get 74. Their difference is 54 - 20 = 34. That's too far apart! I need to try numbers that are closer together!

I'll try 30 and 44, since they add to get 74 and they are closer together. Their difference is 44 - 30 = 14. I almost got it, they are just a little too close!

I'll try 29 and 45, since they add to get 74 and they are a little farther apart. Their difference is 45 - 29 = 16. That is it!

The answer is 29 and 45.


Use a Simpler Case

Using a simpler case is one way of simplifying the problem solving process. This problem solving strategy can be helpful in different situations:
  • Sometimes the problem given to you is more complicated than it needs to be. Look for a pattern to find a simpler problem that will give you the correct answer.
  • Sometimes a complex problem is too hard to do in one step. Divide the problem up into easier cases and solve each one separately.
  • Sometimes the numbers in a problem make it confusing to know what to do. Substitute less complicated numbers to figure out how to solve the problem. Once it makes sense, solve it with the original numbers.

    Example
    The NBA is hosting a basketball tournament for 32 non-professional basketball teams. Each team gets eliminated after they lose. How many games need to be played to determine a winner for the tournament?

    Let's try simpler problems to see if we can figure out a pattern...

    If there were only 2 teams, they would only need one game to determine a champion (Team 1 vs. Team 2).

    If there were 3 teams, they would need 2 games to determine a champion (Team 1 vs. Team 2, then the winner vs. Team 3).

    If there were 4 teams, they would need 3 games (Team 1 vs. Team 2, Team 3 vs. Team 4, then the winners would play each other)

    If there were 5 teams, they would need 4 games (Team 1 vs. Team 2, Team 3 vs. Team 4, then the winners would play each other, then the winner of that game would play Team 5)

    I see a pattern now! It always takes one less game than the number of teams. Since our original problem had 32 teams, we would need 31 games!



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    Copyright © 2004 Ricky Ohashi