This is a typical grade 4 competition Math problem

23% of 45 is what percent of 69?

The conventional solution is to simply do the arithmetic

23% of 45 = 0.23 x 45 = 10.35 (By long multiplication)
10.35/69 = 0.15 = 15% (by long division)

This is actually algebra, but instead of asking the student for the value of x  we asked “what percent of.”  But that is another story.  🙂

An imaginative MATH-Inic student will have an alternative solution using logic.

Notice that 23 is 1/3 of 69 and remember that 45 is 3 * 15.  Mentally, our MATH-Inic student will think:

• 23% of 45 = 23/3 % of 3*15
• which is the same as 69% of 15
• which is the same as 15% of 69
• which means 15% is our answer

Effectively, he gave the answer from logic instead of from long multiplication and long division!

by Ike Prudente

There are parents who are allergic to Math and  who say MATH is an acronym for

Mental Abuse THumans

They conclude that just because they are allergic to math and are certified math-haters, they cannot teach math to their children.  And I’d tell them the first and most important MATH lesson you can teach your child is “Mathitude.”

Mathitude is the term I use to refer to the attitude to use in approaching Math (and many everyday) problems. Among the more important things that I taught my children are:

• Most problems can be solved.
Complex problems can usually be broken down into simpler parts which are more easily solved.
• Problems can have different solutions.
Obvious solutions may not be the best.
• You can develop shortcuts in problem solving, but do not take shortcut in education.
One must not only learn, but also master, the basic concepts. Each succeeding math course builds upon the previous courses. If they find the current lesson hard to understand, then they must review the previous lessons.
• The cliché “practice makes perfect” is especially true in Math.
Math is learned not just by reading but by also doing. I ask my children to solve every available exercise or problem about the current lesson.
• Teaching helps learning.
I ask them to teach their classmates or younger kids. You cannot teach what you don’t know.
• Try to solve problems first before asking for help.
Study lessons before they are discussed in class. This helps the children develop self-reliance. But don’t be afraid to ask questions if needed.
• Understand and not just memorize.
Math is best learned by understanding the basic concepts and not just memorizing the math facts and solution steps.

Ike Prudente is a Math Advocate, creator of the Math-Inic system, and the best-selling author of the book
“25 Math Short Cuts.”

Subscribe to the free “There’s a Math Teacher in the House” newsletter at http://events.math-inic.org/TMaTH/