Using Visuals to Solve a Math Problem

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  • 0:03 Visualization
  • 0:44 Sketches
  • 1:41 Manipulatives
  • 2:30 Mental Imagery
  • 3:13 Lesson Summary
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Lesson Transcript
Instructor: Clio Stearns

Clio has taught education courses at the college level and has a Ph.D. in curriculum and instruction.

Teaching students to problem solve is one of the most important things you can do for them as a math teacher. This lesson focuses on the significance of visuals in reasoning through mathematical problems.


Some students can solve math problems without doing much mental work at all, but these students are in the minority. For most students, one of the most important aspects of mathematics is learning how to solve problems. This means learning how your own mind works so that you can understand what strategies will help you most when you are faced with a difficult problem.

One important strategy that helps so many students is visualization. When students can visualize, or picture a math problem or scenario in their minds, they are often better able to understand what steps they need to take to solve a problem. Visualization can be helpful at all levels of math, and learning to do it early will equip students well for future success. In this lesson, we'll discuss some ways students might use visuals to solve math problems.


One of the first ways you can teach students to use visuals in their math work is by helping them make sketches. For example, imagine that a first grader is dealing with the following problem: Jenny has 3 apples. Susan gives her 2 more apples. How many apples does Jenny have now? This problem can seem totally insurmountable as an abstract concept relayed using only numbers and words. However, a sketch can help students make sense of a word problem.

For instance, ask the first grader to draw a quick sketch of Jenny and the apples she is holding, followed by Susan handing her two apples. Finally, ask the student to count how many apples there are altogether and write the figure down in numeral form.

While sketching may be time consuming at first, students will soon be able to symbolize, or sketch quick stand-ins for concrete objects in a problem, and work with other forms of visualization. For instance, once your students have a bit of experience, they can draw tally marks instead of actual apples to solve the problem we just discussed.


Math manipulatives are objects that students can work with using their hands, and these, too, can be extremely helpful in visualization. For example, imagine a third-grader working on this problem: Carlos' mom gives him 4 bags of soft pretzels to take to school. Each bag has 6 pretzels in it, and there are exactly enough for all the students in Carlos' class. How many students are in Carlos' class?

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