# Strategies for Math Problem-Solving in 2018 – Something Old, Something New

Posted: December 15, 2017By: James Most of us learned our math facts in elementary school. We used those flash cards and memorized our addition and multiplication facts at least. Then we learned long multiplication and division. It all seems like such a waste now – that time sent on memorization when we have calculators that can do it all for us.

Teaching in mathematics has finally begun to get on board with technology. And priorities are being set. How much time should be spent on timed math fact worksheets versus time spent on strategies for solving word problems that require higher level thinking skills? If teachers are committing to common core objectives in math, then they understand that problem solving strategies for math are far more important than fact memorization, and this is where they will spend their time.

### Why Kids Struggle with Math Word Problems

Memorizing math facts is at the lowest level of Bloom’s taxonomy of learning. It requires only rote, low level brain activity. When priority is given to this, there is no movement into the higher levels of this taxonomy – application, analysis, etc. And that is what math problems that involve words are all about – reading the problem, analyzing what is being asked for, and then performing the operations that will arrive at an answer. It’s all about experiencing these types of math problems and learning a strategy or two (or three or four) to solve them.

When kids are not provided with enough experience in how to solve word math problems and do not develop problem solving strategies for math, they are at a disadvantage through the rest of their math schooling and in real life situations, where math facts are totally secondary to problem-solving.

We need to give kids strategies for solving word problems – strategies that they can experience, practice, and, ultimately, master.

### How to Solve Math Word Problems Strategies

There are several strategies that can be taught to kids. Not all will work for every student, because their learning styles are different, but all will find two or more that should work.

1. Look for Key Words or Phrases that Speak to the Right Operations

Addition = sum, more than, increased by, plus

Subtraction = difference, decreased by, minus, less than, how many more

Multiplication = product, twice (3, 4, 5 times or more), times, percent

Division = quotient, equal shares, divide

If key words are not clear, then try an operation that you think might work. If it doesn’t work, try another.

1. The Most Common Basic Procedure
• Read the problem very carefully and try to state in your own words what is being asked for. This will make the problem simpler.
• Then, go back and read the problem again. Note what information has been given up front. At this time, look for those key words that indicate which operation(s) should be used.
• Draw a picture or figure that will give you a visual depiction of the information and the question.
• Give it a try. Perform the operation.
• Check to see if the answer makes sense. If it doesn’t, try a different operation.

Here is a list of math problem-solving strategies in more detail.

1. Draw a Figure or a Diagram

For kids who are visual learners, this is a great strategy. And it usually clears away any irrelevant words. All relevant information can be labeled on the picture or diagram.

1. Using a Table for the Data

This is a good strategy for more complex problems that give more information. For example, if there are several competitors in a race and their rates are all listed, setting up a table with those rates will clear out the words that can be distractions.

1. Guess and Test

Some students like to work things out in their heads and can churn information better than others. These kids may prefer to make an “educated” guess at an answer and then test it using one of the other methods. This is not a good strategy for kids who simply want to hurry through without careful thought.

1. Make Up a Similar Problem that is Simpler

Here is an example of this strategy. Suppose students are asked to figure out how many one-foot square tiles will be needed to cover a floor that has two sections – one 10 X12 and one that is not even. Drawing a picture will help, but also will simplifying the problem by dividing the sections, especially the uneven one, into smaller sections. Then one small section can be applied to the larger sections.

1. Working Backward

The 5th strategy is exactly what is used when linear equations are solved, but it can be used for word problems too. This strategy works well for percentage problems especially. If, for example, the problem involves figuring out what percentage of \$35 is \$4.00, then working backwards will look like this:

\$4.00 is X% of \$35. “Of” mean multiply. And “is” means equal to. Set up a simple equation: \$4.00 = X% of \$35. To get the “X” by itself, get rid of the \$35 on that side of the equation, by dividing both sides by \$35. \$4.00 Divided by \$35.00 will give the answer.

1. Analysis of Dimensions

This is the perfect strategy for those pesky problems that must determine how far someone walks or travels, given the amount traveled per minute or hour. So, for example, if someone walks 29 kilometers in 30 minutes, what is the average traveled per hour. Plugging in the units in order will allow cancellations to get the right combination:

Km/min X min/km X min/hour = the answer.

1. Use Internet Tools

This is the “something new.” There are a number of websites that provide free math help. You can literally insert the word problem and receive an answer, along with an explanation of how the problem was solved. Not only do you get the right answer, but you also see how the problem was solved. It is a solid learning experience and will guarantee a good grade on your homework assignment.

### How to Present/Remember the List of math Problem Solving Strategies

Students need to have reminders of these strategies as they are presented with word problems. As they practice, they will ultimately remember them. But for now, having a poster for each strategy displayed in the classroom makes for easy reference.

And it is important the examples of each of these strategies area presented to students regularly. These can be crafted in advance as a PowerPoint presentation and displayed when a word problem is introduced. Students can then discuss how they would use each strategy to solve the problem.

### Don’t Make Assumptions

Just because students are presented with and practice these strategies in every elementary grade, do not assume that they have mastered them. Students in middle and high school math classes still need reinforcement for continued retention.

As a student, you should keep your own list of problem-solving strategies, identify those that work best for you, and refer to those when you are tasked with math word problems. Don’t assume that you can remember them in detail.

And remember this: Word problems in math do not have to create immediate anxiety. Stay calm, read the problem carefully; get rid of irrelevant words; look for cue words and phrases; and then use a strategy that works well for you.