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Practical Homeschooling® :

Math Counts

By Joyce McPherson
Printed in Practical Homeschooling #84, 2008.

What can our children gain by entering this famous math competition?
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Joyce McPherson

How Hard Is It?

The MathCounts materials teach problem-solving strategies to help students find solutions. The strategies include:

  • Compute or Simplify
  • Use a Formula
  • Make a Model or Diagram
  • Make a Table, Chart, or List
  • Guess, Check, & Revise
  • Consider a Simpler Case
  • Eliminate
  • Look for Patterns

These strategies are a great help, and students soon realize that they can solve complicated problems in creative ways. We often found that two students used completely different strategies to find the correct solution.

Here’s an example of some MathCounts problems from The Student Handbook 2007/2008, “Warm-up 2”:

Noah will mount a 5-inch by 5-inch photograph on an 8-inch by 10-inch mat board. How many square inches of mat board will be visible?

Pi plates cost $24 each. Shipping costs $10 for orders under $100 and $15 for orders of $100 or more. How much more does it cost to order and have delivered five Pi plates instead of four Pi plates?

A month ago the ratio of nurses to doctors on a hospital staff was 3:5. Since that time two additional nurses joined the staff, no nurses left and the number of doctors remained the same. The ratio of nurses to doctors on the hospital staff is now 4:5. How many nurses are now on the staff? (Hint: this problem could be a complex algebraic problem with two unknowns, or the student could “guess, check and revise” using sets of ratios and checking to see if the first numbers differ by two. For example: 3:5 and 4:5... 6:10 and 8:10...)

A word about calculators: Some students find that there is a competitive edge using scientific calculators such as the TI-30X. The viewer shows all the numbers entered, enabling students to catch careless errors in data entry. Regardless of the calculator of choice, it is important to train with the same calculator all year. Remember to install new batteries the morning of competition.

If you think about the difference between a good student and an excellent student, their mathematical abilities are often what distinguishes them. Yet for math, more than any other academic subject, there are tricks to the trade. A student who knows a few of these tricks looks like a superstar in a college math class.

My daughter experienced this first hand as a result of her participation in MathCounts. Now she is in college and coaches a MathCounts team of her own. Two of her little brothers are going through the same training that launched her on a path toward confidence in math.

I would like to share an insider’s view of what is involved in MathCounts and how anyone can become a “mathlete.”

Opportunities from MathCounts

MathCounts sponsors both math clubs and competitions for students in 6th through 8th grade. The organization wants to encourage math exploration in all its various forms, but there is an emphasis on problem-solving and upper-level skills such as statistics and probability. For most students in middle school the concepts are very advanced, but with a little coaching they can quickly build on their own math foundation.

A basic example is the use of the Pythagorean Theorem. Students think it is nifty to be able to calculate the third side of a right triangle with this theorem. In training we add to this formula the very useful Pythagorean triples. The first one is the 3-4-5 right triangle. MathCounts (and the SAT and ACT tests) love this little fact. If you know that two legs of a right triangle are 3 and 4 then you instantly know the hypotenuse is 5. This works for any proportion like 6-8-10, etc.) Once students solve a few problems using this concept they become hounds for finding 3-4-5 triples.

If this sounds like Greek to you, don’t worry. After a few work-outs, both coaches and students begin sounding like mathletes. It’s just a few tricks to the trade. . . .

Training is Part of Everyday School

The advantage to participating in MathCounts is that students are preparing for the competition every day when they do their math assignments. Our math team met for training once a month and used the intervals to practice MathCounts work-out sheets and memorize important math facts. The motivation they received to push themselves to work harder was the best reward from this program.

Starting Your Own Team

So what do you need to know to start your own team? First, you can register and learn a lot about MathCounts by visiting their site at www.mathcounts.org. Registration is due by the first week of December, but in order to train for competition, it’s good to form your team a month or two earlier. The competition takes place in February. MathCounts charges $80 to register a team of four students. If you don’t have enough students for a team, you may register an individual for $20. The site features volume I of the School Handbook so that you can start training right away. You can also sign up for the free “Club in a Box” without registering for the competition. The box comes with volume II of the School Handbook as well as a poster, pencils, a pin, and the Club Resource Guide. Clubs can move through various levels of achievement based on the number of students and how much they participate.


Once you are registered, it’s time to start training your team. Our first year we relied on the solid math skills of our students and only practiced with the MathCounts School Handbook. Subsequently we learned that there is a body of math facts that everyone needs to know. We trained using The MATHCOUNTS Bible According to Mr. Diaz which is subtitled: “What you must memorize, without excuses and for the rest of your lives (not just for MATHCOUNTS).” You can find this useful tool in various forms on the Internet. Basically it lists facts such as squares through 30 squared, cubes through 12 cubed, prime numbers through 109, powers of 2 through the 12th power, formulas for volume and area, Pythagorean triples, and equivalences for fractions, percents and decimals. This stuff gets really interesting.

One day my son asked me, “Why does all this work?” It makes you think about the One who made the universe in the first place.

The Practice Competition

After your group has trained, the next step is to meet for a practice competition which is provided by MathCounts. We like to have a “math camp” near the end of Christmas break, and spend a day with our students. We hold the competition before lunch, then have fun playing around with math in the afternoon.

The top four students from the practice competition represent our homeschool group, and the next four students may attend as alternates. We send a full alternate team so that our future mathletes have a practice year. It usually works out that the seventh and eighth graders make the team and the sixth graders are alternates.

The MathCounts Competition

The MathCounts competition is held on a Saturday in February. There are three rounds. The first “Sprint Round” contains 30 problems, and calculators are not permitted. This is where speed and accuracy with math facts come in handy. The next “Target Round” features 8 multi-step problems. Calculators are allowed for this round. The problem-solving skills developed in training will come to the fore in this part of the competition.

The next “Team Round” requires team members to work together. Calculators are permitted. It’s important to develop a team strategy during training to maximize the gifts of individual members. For example, one student may have a feel for how to solve problems while a second student has more accuracy in calculations. They can work together faster and better if they practice how to coordinate their skills. As in most things in life, the best way to learn the skill is to practice, practice, practice.

Most competitions provide lunch for the students. An optional Countdown Round after lunch showcases the math skills of the top-scoring students. This round is a one-on-one oral competition, and calculators are not allowed. Look for tricks like the 3-4-5 right triangle here. Parents and coaches are invited to watch this round.

The MathCounts competition concludes with awards for top teams and individuals. The top team will go on to represent the area at the state competition. The audience cheers for all the mathletes. It is an opportunity to recognize the rigorous training they have completed during the year.

The Deeper Goal

The morning that my sons left for the MathCounts competition, I knew that whether they won or not, we had achieved our goals for “math training.” They had learned over 200 useful facts and math “tricks,” and had worked harder than they knew they could. They had made good friends who shared their interests. They had also learned that a large part of mastering a subject is simple hard work. And that is a lesson you can use anywhere.

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