Problem Solving in Math is Personal

Posted by David Wetzel

Math Problem Solving

Problem solving in math is a mental process and is part of the larger process that includes identifying what problem must be solved.

The main reason for learning math is to become better problem solvers in all aspects of life.

Many problems are multistep processes and require some type of systematic approach.

Problem Solving is Personal

The ability to solve problems is the foundation of mathematics. For a student in any grade in school, the road to understanding math is through the problem solving gateway. This is not to be confused with completing worksheets; these are real world personal problems which require logical thinking and reasoning skills to solve.

For example:

• How many songs can be downloaded from iTunes with $7.75?
• How much to charge a neighbor for cutting their grass?
• How many cars do I need to wash to buy a new video game, when charging $5.00 each car wash?

To develop the ability to solve problems, children need to make a personal connection as they visualize, touch, and see the problem. In grades K – 7, children cannot think in the abstract like adults. Most children, but not all, begin to develop abstract thinking in the 8th grade.

Math Problems

When developing math problems, the topics must be appropriate for the grade level and cultural environment of the child.

For example:

• Rural farming communities should use examples which are farm related.
• Suburban schools should use examples related to the community and the child’s life.
• Urban settings need to use examples related to the child’s environment.

Regardless of the setting, math problems are everywhere; making it personal and meaningful is critical for stimulating problem solving.

Additional problem solving exercises include:

• How many marbles will fit inside a jar? They determine the volume in the jar. Next determine a reasonable estimate of the number of marbles by using similar materials.
• Cooking – using fractions for baking.

Resources

12 Tips for Solving Word Problems: Teaching Children How to Solve Math Problems

Math Problems: Order of Operations

Geometry of Triangles: Interactive Problem Solving

Posted by David Wetzel

Geometry of Triangles

These resources offer online opportunities to explore the geometry of triangles.

From ideas of congruence to reflections to relationships among the triangle’s angles and sides.

Interactive Geometry Websites

Congruence - Using virtual manipulatives, students can arrange sides and angles to construct congruent triangles using Congruence of Triangles.

Angles - This interactive problem solving exploration of triangles begins at the beginning—with angles and their classification. Students can practice their understanding and then move on to construct triangles and consider the sum of the angles of any triangle. Finally, they explore the special relationship among the sides of a right triangle—the Pythagorean theorem, demonstrated here through a Java slide show using Geometry of Angles.

Equilateral - Students learn the theorems of triangle congruence using a challenging problem solving application. Here students are presented with an intricate figure showing two overlapping equilateral triangles. Because this resource is an applet, students can rotate the figure and easily see that two triangles in the figure are congruent. The challenge is to prove the triangles are congruent using Two Equilateral Triangles.

Transformation and Reflection - Students can manipulate one of six geometric figures on one side of a line of symmetry and observe the effect on its image on the other side. A triangle may be selected and then translated and rotated. The line of symmetry can be moved as well, even rotated, giving more hands-on experience with reflection as students observe the effect on the image of the triangle using Transformations and Reflection.