Okay, kids, I know you’re on break, but Mr. Grinch would tell you that’s no excuse to laze around playing games and eating cookies. There is only a month until our school MathCounts competition, which doesn’t give you much time to prepare. I’ve collected several resources to build up your mental muscle-power before the test…
Step 1: Check Off the Basics
Begin by taking inventory. Have you mastered the basic math facts? I don’t mean your multiplication tables — although those are important, too. Do you know the square numbers and primes? How about the area and volume formulas for basic geometric shapes?
Print out one (or both!) of the following review lists. Go through each page, checking off all the things you know. Then try to learn at least one new math fact per week between now and test time.
- The MathCounts Bible According to Mr. Diaz
“What you must memorize, without excuses and for the rest of your lives (not just for MathCounts).”
- MathCounts Toolbox
This is a 9-page summary of the basic facts of elementary arithmetic and geometry.
[See my comment below for more links about basic math.]
Step 2: Master Simple Probability
If you have been practicing our math club worksheets, you know that MathCounts loves to ask probability questions. Unfortunately, you may not have studied probability in your regular school work — but fortunately, it isn’t hard to learn. So take advantage of your vacation from textbooks and master the topic now. Check out these websites:
- Introduction to Probability
A short tutorial with interactive questions from Mrs. Glosser’s Math Goodies. See also: Rolling a Pair of Dice, Conditional Probability, and the Challenge Exercises.
- Math Club: Counting 101
In order to master probability, you must learn to count. There is more to it than simply 1, 2, 3! Check out as many of these links as you have time for, and you will be well prepared for the test.
- From Counting to Probability
When more than one thing is happening in a probability problem, how do you know whether to add the probabilities or multiply them? And what happens if the events are not mutually exclusive?
- Puzzle: Random Blocks
If you are brave, test yourself with the puzzles in this post. Don’t read the comments until you have tried to answer the questions — but then, be sure to read them and be encouraged. We math teachers don’t always get the correct answer right away, either!
Step 3: Try Your Hand at Triangular Numbers
It’s amazing how many puzzles involve the triangular numbers pattern. For instance, have you heard of the handshake problem? If you learn to recognize these numbers, you will have a head start on many MathCounts questions.
- Triangle Numbers
A short introduction to these number patterns. Also, check out Alexander Bogomolny‘s explanation of the important formula for the nth triangular number, .
- Puzzle: Figuring Out Figurate Numbers
Join Alexandria Jones in exploring the triangular numbers and related formulas.
- Triangular Numbers are Everywhere!
[The IMSA Math Journal is offline, as of my 2011 edit of this post, but the Internet Archive Wayback Machine comes to our rescue!] This worksheet from the IMSA Math Journal examines several examples of triangular numbers in mathematical problems. Can you figure out the patterns?
Step 4: Practice, Practice, Practice
The best way to prepare for any math test is to work lots and lots of problems.
- Preparation Drills for MathCounts
You can choose the type of problem (such as geometry, counting, or probability), whether you want multiple-choice or fill-in-the-blank questions, and anywhere from 5-30 problems on a page. Enjoy!
- Last Year’s School, Chapter and State Competitions
And the Wayback Machine provides us with plenty of prior-year problems. Print out and practice to your heart’s content. Solutions are provided for Chapter and State levels.
- Yet More Practice
[Thanks again to the Wayback Machine!] MathCounts-style problems (not from official competitions), with solutions.
Step 5: Take Time Out for a Laugh
If the video doesn’t display properly, you can find it at this link:
This post is featured in the Carnival of Homeschooling~The Teal Edition.