Math Problem Solving Strategies (solutions, examples, videos)


problem solving strategies math

Problem Solving Strategy 9 (Find the Math, Remove the Context). Sometimes the problem has a lot of details in it that are unimportant, or at least unimportant for getting started. The goal is to find the underlying math problem, then come back to the original question and see if Author: Michelle Manes. Every year my students can be fantastic at math until they start to see math with words. For some reason, once math gets translated into reading, even my best readers start to panic. There is just something about word problems, or problem-solving, that causes children to think they don't know how to complete them. Every year in math, I start off by teaching my students problem-solving skills. On this page we discuss Problem Solving Strategies under three headings. What Are Problem Solving Strategies? Strategies are things that Pólya would have us choose in his second stage of problem solving and use in his third stage (What is Problem Solving?In actual fact he called them Pólya they were things to try that he couldn’t guarantee would solve the problem but, of.

Problem Solving Strategies | NZ Maths

Think back to the first problem in this chapter, the ABC Problem. What did you do to solve it? Even if you did not figure it out completely by yourself, you probably worked towards a solution and figured out some things that did not work. Unlike exercises, there is never a simple recipe for solving a problem. You can get better and better at solving problems, both by building up your background problem solving strategies math and by simply practicing.

As you solve more problems and learn how other people solved themyou learn strategies and techniques that can be useful. But no single strategy works every time. He was born in Hungary inreceived his Ph. This is all well and good, but how do you actually do these steps?!?!

Steps 1. Much has been written since to explain these steps in more detail, but the truth is that they are more art than science. This is where math becomes a creative endeavor and where it becomes so much fun.

We will articulate some useful problem solving strategies, but no such list will ever be complete. This is really just a start to help you on your way. The best way to become a skilled problem solver is to learn the background material well, problem solving strategies math, and then to solve a lot of problems! You need to be sure to go back to the original problem at the end, but wishful thinking can be a powerful strategy for getting started, problem solving strategies math.

Problem Solving Strategy 2 Try Something! If you are really trying to solve a problem, problem solving strategies math, the whole point is that you do not know what to do right out of the starting gate.

You need to just try something! Put pencil to paper or stylus problem solving strategies math screen or chalk to board or whatever! This is often an important step in understanding the problem; just mess around with it a bit to understand problem solving strategies math situation and figure out what is going on.

And equally important: If what you tried first does not work, try something else! Play around with the problem until you have a feel for what is going on. Last week, Alex borrowed money from several of his friends. He finally got paid at work, so he brought cash to school to pay back his debts.

Who got the most money from Alex? After you have worked on the problem on your own for a while, problem solving strategies math, talk through your ideas with a partner even if you have not solved it. What did you try?

What did you figure out about the problem? This problem lends itself to two particular strategies. Did you try either of these as you worked on the problem? If not, read about the strategy and then try it out before watching the solution. Problem Solving Strategy 3 Draw a Picture. Some problem solving strategies math are obviously about a geometric situation, and it is clear you want to draw a picture and mark down all of the given information before you try to solve it.

But even for a problem that is not geometric, problem solving strategies math, like this one, thinking visually can help! Can you represent something in the situation by a picture? How can the picture help you problem solving strategies math the problem? Part of what makes this problem difficult is that it is about money, but there are no numbers given.

That means the numbers must not be important. So just make them up! Then figure out how much he gives to each person. Now, work backwards and figure out how much each person got. So after you work everything out, be sure to re-read the problem and answer what problem solving strategies math asked! If you are not sure problem solving strategies math is being asked, or why the answer is not just 64, be sure to ask someone!

What did you figure out about the problem, even if you have not solved it completely? It is clear that you want to draw a picture for this problem, but even with the picture it can be hard to know if you have found the correct answer. The numbers get big, and it can be hard to keep track of your work. Your goal at the end is to be absolutely positive that you found the right answer.

Could you imagine a more accessible related problem? Can you solve the problem for smaller boards? Of course the ultimate goal is to solve the original problem. Problem Solving Strategy 6 Work Systematically. If you are working on simpler problems, it is useful to keep track of what you have figured out and what changes as the problem gets more complicated.

You could keep track of the information in a table:. Sometimes even drawing a picture may not be enough to help you investigate a problem. Having actual materials that you move around can sometimes help a lot! For example, in this problem it can be difficult to keep track of which squares you have already counted.

You can actually move the smaller squares across the chess board in a systematic way, making sure that you count everything once and do not count anything twice. Sometimes the numbers in a problem are so big, there is no way you will actually count everything up by hand. We will come back to this question soon. So if you are not sure right now how to explain and justify the patterns you found, that is OK.

This clock has been broken into three pieces. If you add the numbers in each piece, the sums are consecutive numbers. Consecutive numbers are whole numbers that appear one after the other, such as 1, 2, 3, 4 or 13, problem solving strategies math, 14, Can you break another clock into a different number of pieces so that the sums are consecutive numbers? Assume that problem solving strategies math piece has at least two numbers and that no number is damaged e. Remember that your first step is to understand the problem.

Work out what is going on here. What are the sums of the numbers on each piece? Are they consecutive? What progress have you made? Sometimes the problem has a lot of details in it that are unimportant, or at least unimportant for getting started. The goal is to find the underlying math problem, then come back to the original question and see if you can solve it using the math.

In this case, worrying about the clock and exactly how the pieces break is less important than worrying about finding consecutive numbers that sum to the correct total. Ask yourself:. Of course, solving the question about consecutive numbers is not the same as solving the original problem.

You have to go back and see if the clock can actually break apart so that each piece gives you one of those consecutive numbers. Maybe you can solve the math problem, but it does not translate into solving the clock problem. When solving problems, it is easy to limit your thinking by adding extra assumptions that are not in the problem.

Be sure you ask yourself: Am I constraining my thinking too much? In the clock problem, because the first solution has the clock broken radially all three pieces meet at the center, so it looks like slicing a piemany people assume that is how the clock must break, problem solving strategies math. But the problem does not require the clock to break radially. It might break into pieces like this:.

Were you assuming the clock would break in a specific way? Try to solve the problem now, if you have not already, problem solving strategies math. Skip to content Increase Font Size. Problem Solving. Problem 2 Payback Last week, Alex borrowed money from several of his friends.

Then: Describe all of the patterns you see in the table. Can you explain and justify any of the patterns you see? How can you be sure they will continue? Problem 4 Broken Clock This clock has been broken into three pieces. Previous: Problem or Exercise? Next: Beware of Patterns!


Math Problem Solving Strategies - Maneuvering the Middle


problem solving strategies math


Math problem solving strategies Some math problem solving strategies will be considered here. Study them carefully so you know how to use them to solve other math biggest challenge when solving math problems is not understanding the problem. Problem Solving Strategy 9 (Find the Math, Remove the Context). Sometimes the problem has a lot of details in it that are unimportant, or at least unimportant for getting started. The goal is to find the underlying math problem, then come back to the original question and see if Author: Michelle Manes. Problem Solving Strategies - Examples and Worked Solutions of Math Problem Solving Strategies, Verbal Model (or Logical Reasoning), Algebraic Model, Block Model (or Singapore Math), Guess and Check Model and Find a Pattern Model, examples with step by step solutions.