# A Unique Way to Challenge Your Advanced Math Learners

## Ed Zaccaro's materials are ideal for challenging your high level math kids!

By Barry Nitikman

If you’re a fourth to ninth grade math teacher, you know how difficult it can be to make sure that all of your kids are challenged. There are a lot of options for helping your struggling students, but it's not always easy to find avenues for those who need the extra challenge.

In the never-ending search for interesting, creative (work) for your gifted pupils, Ed Zaccaro can be your best friend. He has written a variety of books that are chock-full of terrific material that will engage and challenge the more advanced members of your class. Here are the specific advantages his books offer:

- They are very easy to put into place as a regular part of your practice, because the various activities and explorations are put together as full units.

- They are set up so that the kids can work mostly independently.

- The way he presents the material is engaging and fun (sometimes a little silly, but most kids like silly.) What’s more, it’s very complete and well thought out.

- These are not just books of problems; Zaccaro provides thorough instruction and explanation in step-by-step fashion, which makes independent work really feasible. After the instruction, comes the practice in applying the concepts learned.

- The units are always arranged progressively, so that the challenge becomes greater as they go along. There are multiple levels your learners can work through, from "Level I" all the way through "Einstein" or "Super Einstein" level. Kids can go as far as they are able.

- There are complete, well-arranged answer pages, that are a huge boon to you, the teacher, who is juggling multiple levels of kids at the same time. These pages usually give not only the answer itself, but a detailed explanation of the process of solving the problem.

- If you make a few copies of a given unit (anywhere from five to fifteen pages), you’re set. I’ve been using these for years, and I can assure you that not only are they great for providing extensions to your regular curriculum, but kids really enjoy working with them.

- There are many complete units that apply almost directly to fifth and sixth grade topics.

- All are readily available (even used) on Amazon.com.

- Many units are applicable to grade level standards, but there are also many units that are independent of standards; they cover fascinating mathematical topics (see the examples below from the various books.) This has the tremendous advantage of providing you with material that you can use at any time of the year, and that will occupy your high-level kids with worthwhile activities.

### Two Books in Particular

As a longtime fifth grade teacher, I have gravitated toward two specific books: *Challenge Math*, and *Becoming a Problem Solving Genius*. Both of these books are comprised of a whole gamut of really interesting and stimulating activities. A high percentage of these activities apply directly to the fifth grade curriculum. They are ideal for fifth and sixth grade teachers.

There are several other Zaccaro books that would be excellent to use for advanced kids in fifth through eighth grades. Some of these are considerably beyond the fifth to sixth grade level, and I would venture to say that they would also be stimulating as extra enrichment for jr. high and/or high school kids. However, I don’t know enough about high school math to say for sure whether they’d be challenging enough for gifted high schoolers. I can say with certainty that they very interesting and engaging.

I’m going to provide a brief overview of a few of Zaccaro’s books, though I’ll focus mostly on the two that I’m most familiar with. I’ll give examples of units available from each that will give you an idea of their focus and scope, and hopefully show you just how valuable they can be for your teaching. At the end of this article, I’ve also provided a few links to examples of pages from some of the books. Please make sure to check out these examples!

*Becoming a Problem Solving Genius *

After attending a seminar by Mr. Zaccaro, this was the first Zaccaro book I bought. Here are some of the complete units (there are 16 units in all):

- Draw a Picture (problem solving strategy)
- Venn Diagrams
- Solving Equations
- Logic
- The Power of Rations
- Permutations
- Language of Algebra

At the fifth grade level, I’ve used Language of Algebra, Solving Equations, Function Machines, Venn Diagrams, and Draw a Picture; the latter two as part of the kids’ training in problem solving strategies. All are excellent.

*Challenge Math for Elementary and Middle Schoolers *is my favorite math extension book, hands down. If you’re a fifth or sixth grade teacher, get this book NOW*. *There are 19 units, plus a complete set of highly challenging math contests. Many are perfect extensions to fifth grade standards. Here are just a few to show you what I mean:

- Astronomy (decimals)
- Decimals (place value plus all four operations)
- Fractions
- Areas
- Perimeter and Circumference
- Volumes
- Percent
- Ration and Proportion

I have used almost all of these enthusiastically over the years. Again, make sure to check out the examples from a few of these units at the end of the article. Great stuff!

*Real World Algebra*

While this book is accessible to a high-performing fifth grader, I believe it is most suited to sixth to seventh graders—possibly as high as eighth grade. Obviously, for the higher grades, the challenge for an advanced student would be progressively less; but by the same token, they might be very appropriate for a regular eighth grader. Look at the examples to get an idea for yourself.

There are 22 chapters, too many to list. It covers a huge range of algebra-related areas. Here are a few chapter topics:

- The Language of Algebra
- Using Algebra to Solve Problems
- Distributive Property
- Algebra and Proportions
- Geometry and Algebra
- Distance = Rate x Time
- Simultaneous Equations
- Order of Operations
- Pythagorean Theorem

Once again, all are complete units filled with amusing and well-thought-out instruction, followed by a variety of problems at progressively higher levels. Ideal for independent and extension work!

*The 10 Things All Future Mathematicians and Scientists Must Know (But are Rarely Taught)*

This book is a goldmine of fascinating topics, full of strange-but-true stories that all have a mathematical connection. These are guaranteed to appeal especially to middle school kids, but older kids like them too.

Look at some of the titles of the chapters:

- Occam’s Razor: Covers some great historical events, such as Clever Hans, the horse who could seemingly use simple arithmetic; the saga of cold fusion; Bigfoot; and Crop Circles.
- Mistake and Frustration are a Part of Life
- How Nature Deals with Mistakes
- The Simple Mistake That Destroyed the Mars Climate Orbiter
- Apollo 13: Triumph from Tragedy
- The Three Mile Island Accident
- Math and Science Will Tell You the Truth: This includes sections on the Challenger Disaster, how a famous doctor used math to end a cholera epidemic, and how mathematicians made sure a trial was fair.
- It Is Important to Maintain a Healthy Skepticism: Includes topics, such as psychic surgery, facilitated communication, and lie detector tests.

There are several other chapters that are equally interesting and engaging. All contain the usual Zaccaro-type leveled challenge problems so that the kids can practice what they’ve learned from the unit.

*25 Real Life Math Investigations that will Astound Teachers and Students*

While a very gifted fifth grader could tackle this book, I see it as most appropriate for middle and high school kids. The units are, as with *The 10 Things*....., all fascinating topics that are guaranteed to be engaging to kids who like math. Check out some of these intriguing topics:

- Media Math Mistakes
- The Strange Medical Test
- Pilots Make Mistakes
- Help the Rats Escape
- The True Story of Teenage Drivers

When you acquire your first Zaccaro book, and especially when you start using it with your kids, you will be excited and gratified with the results, and with how much engagement you see in your advanced math kids.

### Examples from Various Zaccaro Books:

*Becoming a Problem Solving Genius*

*Challenge Math for Elementary and Middle School Students*