How to Solve Math Problems

Posted on by Denise Gaskins

[Photo by Aaron Escobar. This post is a revision and update of How to Solve Math Problems from October, 2007.]

HowToSolveIt2

What can you do when you are stumped by a math problem? Not just any old homework exercise, but one of those tricky word problems that can so easily confuse anyone?

The difference between an “exercise” and a “problem” will vary from one person to another, even within a single class. Even so, this easy to remember, 4-step approach can help students at any grade level. In my math classes, I give each child a copy to keep handy:

[Note: Page 1 is the best for quick reference, especially with elementary to middle school children. Page 2 lists the steps in more detail, for the teacher or for older students.]

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Free: Calculus Student’s Best Friend

Posted on by Denise Gaskins

calculus-made-easy

Considering how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks… Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can.

— Silvanus P. Thompson

For years, I have recommended Calculus Made Easy as summer reading (and future reference) for high school or college students headed into a calculus course — and for the parents of those students, who may have studied calculus in ages past and now need to dredge out the dust bunnies of memory so they can help with homework.

The original book (second edition) is now out of copyright and available for free online:

[Hat tip to Sam and Michael for finding the Scribd version, which set me off searching for a clearer copy.]

Puzzle: Factoring Trinomials

Posted on by Denise Gaskins

Factoring Puzzle

My high school class ended the year with a review of multiplying and factoring simple polynomials. We played this matching game, and then I gave them a puzzle worksheet. I liked this idea, but I didn’t like the decoded answer. In my opinion, puzzles should give the student a “reward” for solving them — maybe a joke or riddle or something — but that answer seemed almost like nagging.

So I changed things around to make my own version:

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Math Game: Logarithm War

Posted on by Denise Gaskins

[Graph created at Draw Function Graphs.]

Kate at f(t) took my popular Math War game to a new level by making a set of Logarithm War cards. Cool! Download a deck for yourself:

Update

Logs and Trig War—Jim Pai extended Kate’s logarithm war to include trig functions. Double the cards, double the fun! Download from Jim’s blog: War: what is it good for?

Happy Square Root Day!

Posted on by Denise Gaskins

square-roots-by-arsheffield
[Photo by arsheffield.]

Check it out:

And coming soon: Pi Day.

Edited to add: Jonathan‘s class enjoyed extending the concept to include other products. Using the m/d/yy format (not the 4-digit year), how many times in your life has it been true that month \times day = year ?

MathNotations Contest for Middle-High School

Posted on by Denise Gaskins

math-team-edit
[Photo by ccarlstead.]

Can you can put together a team of 2-6 middle or high school students for an afternoon of mathematical play? If so, then Dave at MathNotations is running a math competition you just have to check out.

Teachers register by email on or before Thursday, January 29, and will receive the six thought-provoking contest problems and official answer form by return email. Hold the contest at your convenience on Tuesday, February 3, allowing your team up to 90 minutes to complete and electronically submit their answers.

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Free Online Math for Middle School and Up

Posted on by Denise Gaskins

alcumus

The Art of Problem Solving people recently announced their new Alcumus program, which provides online lessons on assorted math topics, including probability and combinatorics, which most math textbooks do not cover well, if at all.

Update October 2011:

Alcumus currently complements our Introduction to Algebra, Introduction to Counting & Probability, Introduction to Number Theory, and Prealgebra textbooks, as well as our Algebra 1, Algebra 2, Introduction to Counting & Probability, Introduction to Number Theory, and Prealgebra 1 online courses. We expect to continue to expand topics in Alcumus.

— AoPS Alcumus information page

I am signing up all my MathCounts students. If you’re a homeschooler, we would love to have you join us!

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2009 Mathematics Game

Posted on by Denise Gaskins

new-year
[Photo by Amanda M Hatfield.]

Have you made a resolution to exercise your mental muscles this year? Then please join us for the 2009 Mathematics Game. Here are the rules:

Use the digits in the year 2009 and the operations +, -, x, ÷, sqrt (square root), ^ (raise to a power), and ! (factorial) — along with parentheses, brackets, or other grouping symbols — to write expressions for the counting numbers 1 through 100.

  • All four digits must be used in each expression.
  • Only the digits 2, 0, 0, 9 may be used.
  • The decimal point may be used, as in .9, .02, etc.
  • Multi-digit numbers such as 29 or 902 may be used, but preference is given to solutions that avoid them.

By definition: 0! = 1 .
[See Dr. Math’s Why does 0 factorial equal 1?]

For this game we will accept: {0}^{0} = 1 .
[See the Dr. Math FAQ 0 to the 0 power.]

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Math Club: Counting 101

Posted on by Denise Gaskins

[Fature photo above by ThunderChild tm.]

The last couple of weeks, in Math Club, we’ve been learning to count. My new set of MathCounts students have never heard of combinatorics, so we started at the very beginning:

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