There are many different ways to solve a math problem, and equipping kids with problem-solving strategies is just as important as teaching computation and algorithms. Problem-solving strategies help students visualize the problem or present the given information in a way that can lead them to the solution.
Problem-solving strategies
1. Create a diagram.
2. Guess and check.
3. Make a table or a list.
4. Logical reasoning.
5. Find a pattern
6. Work backward
1. Create a Diagram
Creating a diagram helps students visualize the problem and reach the solution. A diagram can be a picture with labels, or a representation of the problem with objects that can be manipulated. Role-playing and acting out the problem like a story can help get to the solution.
Example
Problem
Noah ate 1/5 of the pizza. How much of the pizza is left?
This is a diagram to represent the pizza. The red part shows how much pizza Noah ate. The yellow part represents the amount of pizza that is left.
2. Guess and check
With this strategy, students solve problems by making a reasonable guess depending on the information given. Then they check to see if the answer is correct and they improve it accordingly. By repeating this process, a student can arrive at a correct answer that has been checked. It is recommended that the students keep a record of their guesses by making a chart, a table or a list. This is a flexible strategy that works for many types of problems. When students are stuck, guessing and checking helps them start and explore the problem. However, there is a trap. Exactly because it is such a simple strategy to use, some children find it difficult to consider other strategies. As problems get more complicated, other strategies become more important and more effective.
Example
Find two numbers that have sum 11 and product 24.
Try/guess 5 and 6 product 30 too high
adjust 4 and 7 product 28 still high
adjust 3 and 8 product 24
3. Make a table or a list
Carefully organize the information on a table or list according to the problem information. It might be a table of numbers, a table with ticks and crosses to solve a logic problem or a list of possible answers. Seeing the given information sorted out on a table or a list will help find patterns and lead to the correct solution.
To make sure you are listing all the information correctly read the problem carefully.
Example
Find the common factors of 24, 30 and 18
4. Logical reasoning.
Logical reasoning is the process of using logical, systemic steps to arrive at a conclusion based on given facts and mathematic principles. Read and understand the problem. Then find the information that helps you start solving the problem. Continue with each piece of information and write possible answers.
Example
Thomas, Helen, Bill, and Mary have cats that are black, brown, white, or gray. The cats’ names are Buddy, Lucky, Fifi, and Moo. Buddy is brown. Thoma’s cat, Lucky, is not gray. Helen’s cat is white but is not named Moo. The gray cat belongs to Bill. Which cat belongs to each student, and what is its color?
A table or list is useful in solving logic problems.
student | Cat name | color |
Thomas | Lucky | Not gray, the cat is black |
Helen | Not Moo, not Buddy, not Lucky so Fifi | White |
Bill | Moo | Gray |
Mary | Buddy | Brown |
Since Lucky is not gray it can be black or brown. However, Buddy is brown so Lucky has to be black.
Buddy is brown so it cannot be Helen’s cat. Helen’s cat cannot be Moo, Buddy or Lucky, so it is Fifi.
Therefore, Moo is Bill’s cat and Buddy is Mary’s cat.
5. Find a pattern.
Finding a pattern is a strategy in which students look for patterns in the given information in order to solve the problem. When the problem consists of data like numbers or events that are repeated then it can be solved using the “find a pattern” problem-solving strategy. Data can be organized in a table or a list to reveal the pattern and help discover the “rule” of the pattern.
The “rule” can then be used to find the answer to the question and complete the table/list.
Shannon ‘s Pizzeria made 5 pizzas on Sunday, 10 pizzas on Monday, 20 pizzas on Tuesday, and 40 pizzas on Wednesday. If this pattern continues, how many pizzas will the pizzeria make on Saturday?
Sunday | 5 |
Monday | 10 |
Tuesday | 20 |
Wednesday | 40 |
Thursday | |
Friday | |
Saturday |
6. Working backward
Problems that can be solved with this strategy are the ones that list a series of events or a sequence of steps.
In this strategy, the students must start with the solution and work back to the beginning. Each operation must be reversed to get back to the beginning. So if working forwards requires addition, when students work backward they will need to subtract. And if they multiply working forwards, they must divide when working backward.
Example:
Mom bought a box of candy. Mary took 5 of them, Nick took 4 of them and 31 were given out on Halloween night. The next morning they found 8 pieces of candy in the box. How many candy pieces were in the box when mom bought it.
For this problem, we know that the final number of candy was 8, so if we work backward to “put back” the candy that was taken from the box we can reach the number of candy pieces that were in the box, to begin with.
The candy was taken away so we will normally subtract hem. However, to get back to the original number of candy we need to work backward and do the opposite, which is to add them.
8 candy pieces were left + the 31 given out + plus the ones Mary took + the ones Nick took
8+31+5+4= 48 Answer: The box came with 48 pieces of candy.
Selecting the best strategy for a problem comes with practice. However, some problems will require the use of more than one strategies.
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Great article! Clear, concise and of course right on track!