Rate × Time = Distance Problems

I love how Richard Rusczyk explains math problems. It’s a new school year, and that means it’s time for new MathCounts Mini videos. Woohoo!

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Sign Up for the MathCounts Club Program

The MathCounts Club Program provides enrichment activities and puzzles for 6th-8th grade math clubs within schools — and homeschool groups may join, too! Participants receive a free Club in a Box Resource Kit, which includes the Club Resource Guide, two game boards to accompany one of the meeting plans, 12 MathCounts pencils, and a MathCounts tote bag for the coach. (Apparently they had good intentions, but they didn’t follow through. My box had no tote.)

A school (or homeschool group) may choose to participate in the Club Program, the competition or both programs. Since these programs can complement each other, any school that registers for the MathCounts competition automatically gets the Club in a Box Resource Kit, too.

For more information, check out these links:

Don’t miss any of “Let’s Play Math!”:  Subscribe in a reader, or get updates by Email.

How to Translate Word Problems

Hooray! The MathCounts Mini videos are back. September’s edition is all about translating word problems into algebra:

Download activity sheets and answers.

Do your students like making videos? This year, MathCounts is challenging students in grades 6-8 to create a math problem video. Check out the details:

Don’t miss any of “Let’s Play Math!”:  Subscribe in a reader, or get updates by Email.

Planning a New Math Club

[Photo by Waponi.]

A few years ago, I had several (potentially) future engineers in our homeschool math club, and we enjoyed the challenge of MathCounts and AMC puzzles — but the current crop of local homeschool students is another story.

Last year’s contest-based club meetings dwindled to one student. Even before the recent MathCounts rule changes, I knew I needed a new plan. The final straw was Kitten, whose moaning complaint that she “hates math” has begun to drive me crazy.

So, what’s a homeschool math teacher to do?

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MathCounts: Grandfather Clause for Existing Homeschool Teams

Click here for the official update. Small schools are not mentioned, but it seems logical that their existing teams would also be grandfathered in. Maybe? and according to Mathmom’s comment below, small schools are left out in the cold.

… After taking all concerns into account, a compromise was crafted that would grandfather in homeschools and virtual schools that participated in the 2009-2010 program year to allow them to participate on teams in this year’s Competition Program. All new homeschool and virtual school participants must abide by the new eligibility rules that require those participants to register only as individuals. This compromise was brought to the MATHCOUNTS Board of Directors and approved unanimously.

Therefore, for the 2010-2011 school year, all homeschool and virtual school groups that registered for the MATHCOUNTS Competition Program either as teams OR individuals during the 2009-2010 program year will be allowed to register teams or as individuals for the upcoming 2010-2011 program year, following all of the 2009-2010 requirements for participation.

Don’t miss any of “Let’s Play Math!”:  Subscribe in a reader, or get updates by Email.

MathCounts: No More Homeschool Teams

MATHCOUNTSIf you’ve heard rumors about the new ruling, here is the official take.

I try to avoid ranting on this blog, but I’m deeply disappointed. My students always enjoyed the team aspect of working/suffering together. I don’t know if any of them will be willing to participate as individuals.

Don’t miss any of “Let’s Play Math!”:  Subscribe in a reader, or get updates by Email.

Free Online Math for Middle School and Up


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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MathCounts — Ready or Not, Here It Comes

[Feature photo above "You're a mean one, Mr. Grinch" from CheezBurger.com.]

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…

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Math Club: Counting 101

[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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Checking for Old, Rusty Links

Photo by Clearly Ambiguous.

If you blog about MathCounts, beware that they recently overhauled their website — which made almost everyone’s links to them obsolete. I ran a routine check for dead links and found quite a few on my blog. I hope that I’ve caught most of them, but if you stumble across one of those nasty “Page not found” messages when you click a link on my blog, I hope you will report it in the comments section.

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Substitute Teacher Experiments with Combinatorics

Photo by peigianlong.

Here is a puzzle from Just a Substitute Teacher:

Lesson plan entry: “Hand out worksheet packets and have students staple before starting. They know what to do.”

Sounds simple enough! Four numbered sheets, eight total pages, printed front and back. What could go wrong?

Do you know how many possible combinations four pieces of paper can be arranged for stapling?

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Happy Pi Day II

[Feature photo above by pauladamsmith.]

Now there is an ancient Greek letter,
And I think no other is better.
It isn’t too tall,
It might look very small,
But its digits, they go on forever.

— Scott
Mrs. Mitchell’s Virtual School

Time to Celebrate

Are your students doing anything special for \pi Day? After two months with no significant break, we are going stir crazy. We need a day off — and what better way could we spend it than to play math all afternoon?

If you need ideas, here are some great \pi pages:

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“Monday Math Madness” link

math puzzle
Photo by Behdad Esfahbod.

I have been busy with the end of Math Olympiad season and getting ready for the MathCounts state test this weekend, but I wanted to post this link before it’s too late. You have until Sunday evening to send in your answer to the first…

Monday Math Madness puzzle

Combinatorics is my weak area, but I gave it a try. How about you?

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Way To Go, Boys!

Math competition
Photo by ccarlstead.

Congratulations, math team! All your hard work paid off, and I hope you enjoyed yourselves thoroughly. Of course, as C. S. Lewis wrote:

…if you do one good deed, your reward usually is to be set to do another and harder and better one.

C. S. Lewis
The Horse and His Boy

Now it’s time to practice for the state level in March. You can find practice problems online at:

Preparation Drills for MATHCOUNTS
The “Go Figure!” math challenge
[ACK! MathCounts has re-written their website. The old link is no longer any good, but I haven't yet found the new location for this game.]

And give the new interactive Countdown Round game a try:

AoPS For The Win!

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How to Read a Fraction

Fraction notation and operations may be the most abstract math monsters our students meet until they get to algebra. Before we can explain those frustrating fractions, we teachers need to go back to the basics for ourselves. First, let’s get rid of two common misconceptions:

  • A fraction is not two numbers.
    Every fraction is a single number. A fraction can be added to other numbers (or subtracted, multiplied, etc.), and it has to obey the Distributive Law and all the other standard rules for numbers. It takes two digits (plus a bar) to write a fraction, just as it takes two digits to write the number 18 — but, like 18, the fraction is a single number that names a certain amount of whatever we are counting or measuring.
  • A fraction is not something to do.
    A fraction is a number, not a recipe for action. The fraction 3/4 does not mean, “Cut your pizza into 4 pieces, and then keep 3 of them.” The fraction 3/4 simply names a certain amount of stuff, more than a half but not as much as a whole thing. When our students are learning fractions, we do cut up models to help them understand, but the fractions themselves are simply numbers.

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Reading to Learn Math

[Photo by Betsssssy.]

Do you ever take your kids’ math tests? It helps me remember what it is like to be a student. I push myself to work quickly, trying to finish in about 1/3 the allotted time, to mimic the pressure students feel. And whenever I do this, I find myself prone to the same stupid mistakes that students make.

Even teachers are human.

In this case, it was a multi-step word problem, a barrage of information to stumble through. In the middle of it all sat this statement:

…and there were 3/4 as many dragons as gryphons…

My eyes saw the words, but my mind heard it this way:

…and 3/4 of them were dragons…

What do you think — did I get the answer right? Of course not! Every little word in a math problem is important, and misreading even the smallest word can lead a student astray. My mental glitch encompassed several words, and my final tally of mythological creatures was correspondingly screwy.

But here is the more important question: Can you explain the difference between these two statements?

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Puzzle: Random Blocks

Red block puzzle

In the first section of George Lechner’s Creative Problem Solving in School Mathematics, right after his obligatory obeisance to George Polya (see the third quote here), Lechner poses this problem. If you have seen it before, be patient — his point was much more than simply counting blocks.

A wooden cube that measures 3 cm along each edge is painted red. The painted cube is then cut into 1-cm cubes as shown above. How many of the 1-cm cubes do not have red paint on any face?

And then he challenges us as teachers:

Do you have any ideas for extending the problem?
If so, then jot them down.

This is strategically placed at the end of a right-hand page, and I was able to resist turning to read on. I came up with a list of 15 other questions that could have been asked — some of which will be used in future Alexandria Jones stories. Lechner wrote only seven elementary-level problems, and yet his list had at least two questions that I had not considered. How many can you come up with?

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How To Start a Homeschool Math Club

From a recent e-mail:

Hello! I am on the board of a homeschool co-op. We have had requests for a math club and wondered if you have any tips for starting one. We service children from K-10th and would need to try to meet the needs of as many ages as possible.

There are several ways you might organize a homeschool math club, depending on the students you have and on your goals. I think you would have to split the students by age groups — it is very hard to keep that wide of a range of students interested. Then decide whether you want an activity-oriented club or a more academic focus.

When I started my first math club, I raided the math shelves in the children’s section at my library (510-519) for anything that interested me. I figured that if an activity didn’t interest me, I couldn’t make it fun for the kids. Over the years we have done a variety of games, puzzles, craft projects, and more — always looking for something that was NOT like whatever the kids would be doing in their textbooks at home.

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Skit: The Handshake Problem

[Feature photo above by Tobias Wolter (CC-BY-SA-3.0) via Wikimedia Commons.]

If seven people meet at a party, and each person shakes the hand of everyone else exactly once, how many handshakes are there in all?

In general, if n people meet and shake hands all around, how many handshakes will there be?

Our homeschool co-op held an end-of-semester assembly. Each class was supposed to demonstrate something they had learned. I threatened to hand out a ten question pop quiz on integer arithmetic, but instead my pre-algebra students presented this skit. You may adjust the script to fit the available number of players.

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Confession: I Am Not Good at Math

I want to tell you a story. Everyone likes a story, right? But at the heart of my story lies a confession that I am afraid will shock many readers. People assume that because I teach math, blog about math, give advice about math on internet forums, and present workshops about teaching math — because I do all this, I must be good at math.

Apply logic to that statement. The conclusion simply isn’t valid.

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