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

Math Around the Clock Problem Solving

Posted by David Wetzel

Math Around the Clock Activity

Problem solving in math is the best way for students to demonstrate their understanding of math concepts. Being able to develop a strategy for solving math problems is critical for truly understanding math beyond rote memorization of procedures and worksheets.

“It is impossible to overstate the importance of problems in mathematics. It is by means of problems that mathematics develops and actually lifts itself by its own bootstraps… Every new discovery in mathematics, results from an attempt to solve some problem.” Howard Eves - Mathematician (1911 - 2004).

Providing students a problem solving situation as a lesson culmination activity allows students to internalize their learning and depending of the problem solving activity students may be able to visualize and artistically internalize a math concept.

Problem Solving Activity - Math Around the Clock

Students are tasked to develop an “8’s” clock similar to the “9’s Clock” pictured.

All clock numbers must be the product, addend, remainder, or dividend of a math problem that all uses the number.

Students must follow PEMDAS, along with having the ability to use any mathematics function.

Additional Math Problem Solving Resources

Math Function Generator Game

Math and Problem Solving Skills

An Algebra Problem That Demystifies Math

Posted by David Wetzel

Algebra Problem Solving

Every algebra teacher is bombarded with the same question every year — “What will I ever use this algebra stuff for?”

Well here is a sample algebra problem that you can use to respond to these insidious questions, along with proving to your students that there is no magic or mystery when algebra is used.

The Problem

Step 1 - Write down the year you were born. [P}

Step 2 - Write down a year when a memorable event took place in your life. [Q]

Step 3 - Write down your age as the last day of this year. [Y-P]

Step 4 - Write down the number of years since the memorable event (Step 2) took place. [Y-Q]

Step 5 - Add the 4 numbers obtained in Steps 1 through 4. [P + Q + (Y - P) + (Y - Q) = 2Y]

Every student will have the answer 2Y = 4018 or Y = 2009 (or what ever the current year is when calculating)

How does this work?

P +Q + (Y - P) + ( Y - Q) = P + Q + Y - P + Y - Q  (parentheses removed)

= P- P + Q - Q + Y + Y (rearranging the terms)

= 2Y ( P’s and Q’s cancel each other out)

= 4018 (when Y = 2009)

In other words, the number in Step 1 combined with that in Step 3, deleted the number in Step 1, giving the current year, 2009; similarly, the number in Step 2 combined with that in Step 4, deleted the number in Step 2, giving, once again, the current year, 2009.

Therefore, adding all the 4 numbers from Step 1 through Step 4 effectively deleted every number other than twice the current year, 2009, giving the result of 2 x 2009 = 4018!

(Note that most number puzzles undo what has been done, so as to “force” a certain result, as can be easily proved by using deductive logic or by using algebra.)

Resources

Tips for Solving Math Word Problems

Math Problem Solving