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
- 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
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,
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