and

*Math Olympiad Contest Problems for Elementary and Middle
Schools* by George Lenchner.

*Reviewed by Susan Richman*

These books by George Lenchner, founder of the *Math Olympiad for Elementary and Middle Schools*,
help your upper elmentary or junior high school students learn to solve tricky multi-step problems,
the kind of problems your kids will later encounter when they take the SAT's.

The *Creative Problem Solving* book systematically teaches a repertoire of
strategies to deal with math word problems. The *Math Olympiad* book gives you the actual problems
from previous years, PLUS full solutions. A must for the family with a budding
mathematician. Here's what Susan wrote in her reviews of each book.

by Susan Richman from Issue 27 (Spring 1989) of *PA Homeschoolers* newsletter.

George Lenchner, who began the *Math Olympiad* has written an excellent book, *Creative
Problem Solving in School Mathematics* published by Houghton Mifflin Co. This book is one of
the very best I've seen on problem solving, with clear format, specific examples all through,
and suggestions for further problems of similar types. My kids especially
appreciated the classifying of possible ways of going about solving problems--
trial and error, acting out a problem, using equations, making a diagram or chart,
looking for a novel twist, and more.

Work at home with this books is a *real* help-- there are sample Olympiad sets
from early years in the back, with solutions, and kids soon get to know the types
of questions that are likely to be asked-- "Oh, that's another 'cryptorithm' one... aha!
another painted cube problem... and there's one I could use that writing out an equation
idea with." The problems become old friends in new disguises rather than
frightening strangers.

Our own Math Olympiad group has just completed our last meet, and the children's scores have gone steadily up with each session...

by Susan Richman

Many readers of PA Homeschoolers are well aware that one of my favorite programs for helping kids become top-flight young mathematicians is the Math Olympiad for Elementary and Middle Schools program. I first found out about this challenging yet very friendly math competition way back when our oldest son Jesse was in sixth grade, and I believe our little group of 8 homeschoolers was the very first homeschoolers' team in the world to take part. What a window into the excitement of really tough multi-step problem solving, unique non-routine problems, and the fun of working together with other kids on mathematics. Math became suddenly a social activity, a reason to get together regularly with friends, something to talk and share about and have a great time with. It has always been exciting somehow to us to know that over 80,000 kids all over the world are taking part in doing these same problems just like we are-- we feel part of a much larger community of young mathematicians. We've been coaching a team of homeschooled kids in the Math Olympiad ever since that first year, and I continue to feel it is the very best possible preparation for a really strong math program that you can give your kids. It's been so exciting to see how so many other homeschoolers have also taken part-- there must now be over a dozen Math Olympiad team among homeschoolers just in PA, and there are more all across the country.

So I was delighted to see that Dr. George Lenchner, the
founder of the Math Olympiad, has just revised and expanded his excellent
book **Math Olympiad Contest Problems, **containing all of the Olympiad
problems from the last sixteen years. The book, aimed at students from
4th to 8th grades, also has many helps to problem solving, including a
wonderful section of "hints" on how to get going on each problem
in the book, followed by even more detailed solutions to all the problems--
and often several possible ways of going about a problem also. Parents
can photocopy the Olympiad problem sets for their children too, and is
nicely laid out for this purpose with the five problems from each set on
their own page. The problems are very similar to the problems many of you
have become familiar with through the excellent *Figure it Out* workbooks
that we also sell in our catalog-- just a bit harder in general. This book
is the real thing, the next step.

This is obviously an invaluable resource for a homeschool
parent who is coaching an official Olympiad team, as you can let your team
members practice with actual old problems sets. But the book would also
be a great supplement for any upper elementary or middle school math program
at home, and can be used over a number of years. I also wouldn't be at
all surprised to see some high school homeschoolers who could benefit from
these terrific problems-- they involve the same type of problem solving
skills often tested on the SAT, in fact. I think homeschool dads in particular
might really enjoy sitting down with several of the older children in an
evening and working through a few of the problems for fun-- and I guarantee
that Dad will find here many problems to really challenge *his* thinking
also!

I hear from some parents who lament that their child
just isn't "ready" for such tough problems, because basic computation
is what they still really need to work on. And so they ignore problem solving
altogether and only do drill, and drill, and drill, and more drill. And
often their kids never get very good at math, even at that basic computation
that they spend so much time on. I'd go for problem solving any day, myself,
and let the child develop both their number sense and their computation
skills while solving some intriguing real problems. Just today Hannah and
her friend Becky were working cooperatively on a Math Olympiad homework
set. In the course of their work they had to do long multiplication-- in
fact their task was to find a number that when multiplied by itself would
come closest to a given 4-digit number, so they actually had to do MANY
calculations to gradually get closer and closer to the correct answer.
They had to add up series of numbers, but in the context of seeing how
many combinations of certain coins they could make given certain problem
parameters. They had to multiply with fractions, use all basic operations,
know basic math terms, and much more-- quite a plateful for a 4th and 6th
grader, and they were also having a great time *together* to boot,
because these problems just aren't like other math problems you come across
in most textbooks.

So don't feel that computation practice will be missed
by spending more time with more challenging word problems-- students are
not allowed to use calculators on the Math Olympiad, and so need to continually
work hard to develop sound computational strategies. And more importantly
they develop their *number sense*. And in a given set of five problems
your child will be asked to use a much wider range of computational procedures
than in almost any math book.

It all reminds me of something I read once about a visitor
from Germany who was touring American schools and was surprised to find
so much emphasis on computation in isolation. He stated that in Germany
they *never* were given mere pages of computations to do, but were
always asked to work in the context of multi-step word problems, *using
*the new computational strategies they had been learning in varied ways.
Or it also reminds me of when I heard a person working for the math division
of the PA Department of Education stating that if, after 12 years of schooling
all a kid can do is basic computation, than we haven't helped the child
become anything more than a cheap $3.00 pocket calculator. But to help
a child *use* a growing range of math strategies and computational
skills to solve real and challenging problems-- that's something that no
calculator can do at all.

So I hope you try this book, and try the Math Olympiad.
With supportive help from you as you work along side your kids to solve
these problems, as you find yourself *talking *mathematics with your
kids instead of just *checking* their work, you'll find your kids
gaining a whole different feel for mathematics. This book can be an important
step in making that transition.