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Graphic Organizers in Math

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The use of a graphic organizer can start as early as first or second grade and can continue to be useful for some learners all the way through high school. In subjects such as math, that grow increasingly complex as students get older, these tools can be especially helpful in maintaining organized work habits and enhancing problem-solving skills. If used correctly and consistently as students develop, the concepts of strategic thinking graphic organizers instill will likely have reached the point that many learners no longer need them by the time they reach high school.

How To Use Graphic Organizers in Math

Using graphic organizers has been a proven effective problem-solving strategy for helping young learners think and process information more efficiently by allowing them to both visualize and organize the information they need to solve problems. Creativity and careful attention to detail can be greatly enhanced via the use of visual maps—which is exactly what a graphic organizer is. A graphic organizer aids in organizing thought processes as well as creating a framework to collect and compare the information that's being gathered. That's why, in addition to structuring information, organizers can be used to improve students' abilities to comprehend and process that information by seeing it separated it into categories of what is more important and what less important. 

​Over time, graphic organizers help learners become strategic problem solvers. Provided they're used effectively and consistently as an integral part of the  problem-solving  process, graphic organizers can also improve test scores. 

How Graphic Organizers Work for Math

A typical graphic organizer has the problem printed on it. The paper is divided into four quadrants with the problem appearing at the top, although sometimes, it can be found in the middle of the page. 

The first quadrant is used for the student to determine what the problem is actually trying to solve for. The second quadrant is used to determine what strategies are needed to solve the problem. The third quadrant is used to show the steps involved in order to solve the problem. The fourth quadrant is used to answer the question that is initially being asked and to indicate why the answer the reasoning behind how the answer was arrived at, and why the answer is correct. 

Graphic Organizers: The Takeaway

Graphic organizers can be a parent or teacher's go-to problem-solving tool of choice for many reasons but the bottom line is, the better a student can visualize and organize the strategy that goes into arriving at their answers, the more likely young learners are not only to come up with the appropriate solutions but also, to understand how they arrived at those solutions and what makes their answers correct.

Ultimately, the learner:

• determines what's being asked
• considers and tries out strategies
• determines and shows answer
• looks back to ensure that all parts of the question have been answered
• provides a final answer to the question

Some of the graphic organizers used for problem-solving in math are referred to as 4-Block , 4 Corners, 4 Square or the Frayer Model. Regardless of which template you choose, you'll find that when it's used effectively and consistently, enhanced problem solving will be the result.

• The Frayer Model for Math
• Using Graphic Organizers for Special Education
• Examples of Problem Solving with 4 Block
• Problem Solving in Mathematics
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• Algebra Age-Related Word Problem Worksheets
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The Reframing Matrix

Using creative perspectives to solve problems.

By the Mind Tools Content Team

When you're stuck on a problem, it often helps to look at it from another perspective. A "fresh pair of eyes" can be all that you need to come up with a great solution.

But sometimes it's difficult to think about what this new perspective might be. You may be so used to dealing with a situation in the same way that you simply can't see any alternative. And, as a result, you may miss out on a better, more efficient, or longer-term answer to your problem.

This is when the Reframing Matrix can help. In this article and in the video, below, we'll look at how you can use this simple tool to look at problems from different points of view.

Click here to view a transcript of this video.

About the Matrix

The Reframing Matrix tool helps you to look at business problems from various perspectives. You can use these perspectives to generate more creative solutions.

The technique was created by Michael Morgan, and published in his 1993 book, "Creating Workforce Innovation." Morgan identified that different people with different experiences will likely approach problems in different ways. The matrix helps you to put yourself into the minds of these people, to imagine the ways that they would face the problem, and to explore the possible solutions that they might suggest. [1]

How to Use the Reframing Matrix

The Reframing Matrix is very easy to use. Here's how to apply the tool in three steps:

Step 1: Draw the Grid

Start by drawing a simple four-square grid, but leave a space in the middle of the grid. Then, in the space, write down the problem that you want to explore.

Figure 1 – Reframing Matrix Step 1

Sometimes, you know there is a business problem that you need to solve, but you're not sure what's causing it. If this applies to you, tools like the Simplex Process and Root Cause Analysis can help you to define your problem clearly.

Step 2: Decide on Perspectives

Now, decide on four different perspectives to use in your matrix. Two useful approaches for doing this are the 4Ps Approach and the Professions Approach .

The 4Ps Approach (not to be confused with the 4Ps of Marketing ) helps you to look at problems from the following perspectives:

• Product Perspective: Is there something wrong with the product or service? Is it priced correctly? How well does it serve the market? Is it reliable?
• Planning Perspective: Are our business plans, marketing plans, or strategy at fault? Could we improve them?
• Potential Perspective: How can we increase sales, or productivity? If we were to seriously increase our targets, or our production volumes, what effect would it have on the problem?
• People Perspective: What are the people impacts and people implications of the problem? What do people involved with the problem think? Why are potential customers not using or buying the product?

These examples are just some of the questions that you can ask as you look at your problem using these four perspectives.

The Professions Approach helps you to look at the problem from the viewpoints of different specialists, or stakeholders . For instance, the way a doctor looks at a problem would be different from the approach that a civil engineer or a lawyer would use. Or, the way a CEO views a problem may be different from the way an HR manager sees it.

This approach can be especially useful when you're trying to solve a problem that involves many different types of people, or if you need to step away from your usual way of thinking so that you can be more innovative .

Step 3: Brainstorm Factors

The final step is to brainstorm factors related to your problem from each perspective, and to enter your findings in the appropriate quadrant of the matrix.

If you find yourself slipping into habitual modes of thinking, you could involve other team members in the process, too. Divide them into groups and ask each group to think about the problem from one of the four different perspectives. Or, try collaborating with co-workers from other areas of your organization – their knowledge may help to generate fresh insights.

Once you've completed the matrix, you'll have a better understanding of your problem, and you'll be able to generate more solutions.

The Perceptual Positions and Six Thinking Hats techniques can also be useful when you want to see things from other people's viewpoints.

Our article on CATWOE offers a similar approach. This asks you to look at a problem from the perspectives of Customers, Actors, the Transformation process, the World view, the Owner, and Environmental constraints.

Example Reframing Matrix

In the example in figure 2, below, a manager has used the 4Ps approach to explore why a new product is not selling well.

Figure 2 – Example Reframing Matrix

Example Reframing Matrix adapted from Morgan, M. (1993), 'Creating Workforce Innovation,' West Chatswood, Australia: Business & Professional Publishing, p75, by permission of Allen & Unwin .

The Reframing Matrix tool was created by Michael Morgan, and published in his book, "Creating Workforce Innovation." It helps you to look at a problem from different perspectives.

Use the tool by drawing a simple four-square grid and writing your problem or issue in the middle of the grid.

Then, choose four different perspectives that you will use to look at your problem, and brainstorm factors related to your problem from each of those perspectives.

[1] Morgan, M. (1993). 'Creating Workforce Innovation,' West Chatswood, NSW, Australia: Business & Professional Publishing. p75.

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Home > ETD > 157

Theses and Dissertations

Using the four square strategy to enhance math problem-solving.

Andrea Gerrard

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This study examined whether the use of the Four Square problem-solving strategy would improve the math problem-solving performance of students who receive supplemental services for language arts literacy and mathematics from a basic skills teacher or a special education teacher. The Four Square strategy was used in conjunction with the enVision math series. It was also used during all problem-solving lessons. Students' growth in math problem-solving was measured using the enVision problem-solving pre- and post-test and the Measure of Academic Progress Test (MAP). Students showed growth on the enVision test. The students showed work when solving problems instead of just selecting one of the available answer choices and were able to increase the number of questions correct on the assessment. Students did show growth on the MAP test. They were able to close the gap between other students in the sixth grade who receive supplemental services for language arts literacy and mathematics from a basic skills teacher. The results indicate that the Four Square strategy can be a useful way to enhance students' problem-solving skills. The Four Square strategy allowed students to take ownership of their problem-solving skills and to improve these skills throughout the study.

Recommended Citation

Gerrard, Andrea, "Using the Four Square strategy to enhance math problem-solving" (2013). Theses and Dissertations . 157. https://rdw.rowan.edu/etd/157

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Examples of Problem Solving with 4 Block

Using 4 Block (4 Corners) Template in Math Print the 4 Block Math Template in PDF In this article I explain how to use this graphic organizer in math which is sometimes referred to as: 4 corners, 4 block or 4 square. This template works well for solving problems in math that require more than one step or with problems that could be solved by using different strategies. For younger learners, it would work well as a visual which provides a framework for thinking through the problem and showing the steps. We often hear “use pictures, numbers and words to solve problems”. This graphic organizer lends itself to support problem solving in math.

Using 4 Block for a Math Term or Concept Here is an example of using 4 block to help with the understanding of a term or concept in math. For this template, the term Prime Numbers is used. A blank template is provided next.

Blank 4 Block Template Print this blank 4 block template in PDF. This type of template can be used with terms in math. (Definition, Characteristics, Examples and non Examples.) Use terms like Prime Numbers, Rectangles, Right Triangle, Polygons, Odd Numbers, Even Numbers, Perpendicular Lines, Quadratic Equations, Hexagon, Coefficient to name a few. However, it can also be used to solve problems like a typical 4 block problem. See the Handshake Problem example next.

4 Block using Handshake Problem Here is an example of the handshake problem being solve by a 10 year old. The problem was: If 25 people shake hands, how many handshakes will there be? Without a framework to solve the problem, students often miss steps or don’t answer the problem correctly. When the 4 block template is used regularly, learners improve in their ability to solve problems as it forces a way of thinking that works for solving problems.

Author: Arya Math

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Get Ready to Negotiate: the Four Quadrants (tool #1)

It is often said that a good negotiator is the one who is capable of turning a win-lose situation into a win-win situation. The only way to do so is generating fresh ideas and options which could at least partially satisfy the interests of the parties. However, reaching this goal is extremely difficult, for negotiations are usually characterized by objective (e.g., time constraints, difficult procedures) and subjective (e.g., strong feelings and emotions, misperceptions) obstacles. In order to overcome these obstacles, it is of the utmost importance to get ready for the negotiation. In this post, and in another one that will be online next week/tomorrow, two tools are introduced. They are taken from a great book, Beyond Machiavelli , written by Roger Fisher (founder of the Harvard Negotiation Project and co-author of Getting to Yes ), Elizabeth Kopelman, and Andrea Kupfer Schneider. Check it out on Amazon to have more information on the negotiation tools, on how to use them, and on many other interesting ideas they put forth.

The first tool is the Four Quadrants. Before sitting at the negotiating table, try and think analytically and go through with the four categories shown in the chart below. According to the authors of Beyond Machiavelli , “a Four-Quadrant Analysis encourages systematic yet creative problem-solving.”

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Machiavelli Negotiation win-win

09/05/2013 at 7:59 am

A good negotiation has no winners and no loosers. The negotiatior has to well know is own goals and even better the goals of te counterpart. This should be the starting point of a good negotiation.

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