[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:
- Counting and Probability I by Keone Hon
- Counting and Probability by Jason Batterson
The Science of Counting
One of my favorite things about coaching MathCounts is that I learn as much as the kids. When I was in school, as far as the curriculum was concerned, discrete math didn’t exist. The first year I coached our math team, I struggled with this topic, but I’ve learned enough over the years to stay at least two steps ahead of my students.
I typed up a one-page summary of the basics for my students:
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.
For Further Study
In addition to Mr. Hon’s tutorial, we’ll be using several of these online resources from the amazing Art of Problem Solving website:
- Why Discrete Math Is Important
“Because discrete math does not figure prominently in most states’ middle or high school “high-stakes” progress exams, and because it also does not figure prominently on college-admissions exams such as the SAT, it is often overlooked. However, discrete math has become increasingly important in recent years, for a number of reasons…”
- Counting and Probability Videos
Explanations and worked problems that go with the AoPS Introduction to Counting & Probability textbook. The videos are grouped by the corresponding chapter of the textbook.
- Correcting for Overcounting
“Often in counting problems, the most convenient solution is to count too much, and then somehow correct for the overcounting…” From AoPS Introduction to Counting & Probability, chapter 3.
- Probability Using Areas
“Point C is chosen at random atop a 5 foot by 5 foot square table. A circular disk with a radius of 1 foot is placed on the table with its center directly on point C. What is the probability that the entire disk is on top of the table (i.e. that none of the disk hangs over an edge of the table)?…” From AoPS Introduction to Counting & Probability, chapter 10.
- Constructive Counting and 1-1 Correspondences
“The basic idea is that in order to count the number of a items in a certain set, we think about how we would construct an item belonging to that set. During the construction, we keep track of the number of choices that we have at each step…” From AoPS Intermediate Counting & Probability, chapter 4.
- Three Types of Probability
“If you think about it, labels are a big key to the way we organize ideas… In short, labels help us organize — and organization simplifies problem solving! This article seeks to demonstrate the power of intelligent classification using types of probability as an example…”
- Counting in the Twilight Zone
“In this chapter we will look at counting methods which go far beyond common sense, and thus allow the counting of far more interesting things…” From The Art of Problem Solving, Volume 2: and Beyond, chapter 17.
More Counting Links
Here are two more websites with links to tutorials and puzzles:
Alcumus Online Learning System
6 thoughts on “Math Club: Counting 101”
what a really great post! my girl is not quite 3, but i was never very good at math (or so i was led to believe) and i’m trying to get a few steps ahead of her. she already adds and subtracts her stuffed animals just for fun and i want to do whatever i can to make sure math continues to be fun for her.
i don’t usually comment, but i always enjoy your blog.
Wow! If this post is only a few steps ahead of your 3yo, I’m impressed. Have you explored the Hoagies site? Lots of great info and links there.
Congratulations, your post will be featured in the October 22nd edition of the Carnival of Education. You can view that carnival here when the link goes live on 10/22.
hi denise – i haven’t sean the hoagies site, but i’m for sure going there now. 🙂 thanks!
This may or may not be directly related to this blog article but a colleague of mine recently wrote an article on clickandclimb.com blogs about importance of math in different careers.
Parents and teachers are constantly bombarded with this question from students- Why is math important and when will we ever use it. This article highlights some of those points hoping that it will make sense to parents and students and teachers. You can find the article here