Most of our math contest preparation consists of working lots and lots of old test problems. Occasionally, however, I put together a tip sheet summarizing a topic that my students have trouble remembering.
Here are a couple of tip sheets I will be adding to my Handouts page:
Things to know about triangles (pdf 64KB)
We started with some basic observations about the relationship between angles and sides in a triangle, then moved to equilateral triangles and the 30-60-90. Unfortunately, I didn’t have much space for the Pythagorean Theorem — I really need to make a new tip sheet on that! Page 2 covers some basics about hexagons, especially as they appear in MathCounts problems.Counting and Probability Basics (pdf 57KB)
Permutations, combinations, probability, odds — what’s the difference? This tip sheet gives you just the facts, with an absolute minimum of factorial notation. Mix with plenty of problems to solve, stir well, and discuss.
And here is one more source of practice problems, from my Resources page:
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. Fun!
Denise Gaskins' Let's Play Math 
Denise, thanks so much for sharing your MATHCOUNTS tips!
You’re welcome. This is only my second year doing math contests, so I haven’t collected very many tips yet, but I expect I will continue to tweak these and create others. Whether or not the students use them to study — and usually, I think they forget them immediately after class! — at least the tip sheets help me get my mind around a topic.
I didn’t look at all three, but the rhombus problem on the triangle sheet bothers me a bit. I know what they want, but there are ways to do it with more rhombuses, and worse, I cannot easily convince myself that there is only 1 basic dissection.
That’s true — depending on the rhombus or trapezoid or whatever that the student uses, there are many ways these questions could be answered. The worksheet is expecting students to imagine Pattern Block shapes, but that doesn’t really matter.
The main goal is for students to realize that they can tessellate the hexagon with shapes and then use the relationship between the shapes and the hexagon to solve other problems. For example, one of their MathCounts problems [which also showed up on the AMC8] had a hexagram, and they were to compare the area of the six outer triangles to the area of the inner hexagon.
Denise, I emailed you a tip sheet that another coach shared with me.
Thank you! It is always interesting to see what other math teams are doing.
My son has created a very helpful math contest website:
http://www.homeschoolmathcontests.com
It has over 25 contests open to individual students ages 5-19, organized in a chart with ages, due dates, prizes, and descriptions, to make it easy to figure out which are the best fit. In addition, he has listed over 100 regional meets by state for those who would enjoy the excitement of participating in large, local math competitions.
The site also includes math curriculum reviews and helpful articles about how to integrate contests with the rest of a student’s learning.
We hope this website is a help to other families seeking to enhance their children’s enthusiasm for math.
Elizabeth Fox
Great site! I am impressed with your son’s work in putting together a very helpful resource for his fellow homeschoolers.