Math CentralQuandaries & Queries


Dear Math Central,

I have been asked to tutor a 7th grader who is very good in math. He is taking the most advanced course that his school offers to 7th graders. This course will cover Algebra 1 over a period of two years, using McDougal Littell's Algebra, Structure and Method, Book 1, a book I like a lot.

I have been hired not to help him with his schoolwork, which is too easy for him, but to guide him through something in math beyond his schoolwork. This was his idea, an idea which surprised his parents, but one which they support.

I don't want to move him faster through the algebra he is doing in school, because this will set him up for even more boredom in the future.

One possibility would be for me to give him more challenging problems than he is getting in school, but problems that require only the algebra that he and his classmates are learning together. However, I have not been able to find a book that provides the type of problems I am thinking of.

Another possibility would be for me to take him through a course in number theory, combinatorics, discrete math, or something else that he would see very little of in school. However, I have not been able to find a textbook in number theory, combinatorics, or discrete math that would be appropriate for a 7th grader.

I have purchased for him Raymond Smullyan's The Riddle of Scheherazade and Other Amazing Puzzles. I think this will challenge and amuse him, but will not be nearly enough.

Do you have a suggestion for me? If so, I would be very grateful to hear from you. I think this could be a lot of fun for me and my new student, if I pick the right path.

Thanks and best regards,


We have three responses for you

Dear John ,

I'm not an expert in teaching children so the best I can do is offer an uneducated opinion based on my beliefs. My suggestion is to look for topics that build logic and problem solving skills. Discrete math and discrete probability are good choices for that. There is a beautiful old book by Ivan Niven called "How to count without counting" that is easy to read. Probably it isn't at the right level for a seventh grader, but you could look at it and introduce him to the material. Another suggestion is classical Euclidean geometry. There might even be some good software tools (or toys) that might help turn it into more of a process of discovery. Perhaps you could investigate Geometers Sketchpad? Finally, I would suggest using math to help also develop language skills. For that I suggest lots of exercises that require careful reading, followed by questioning and thinking, followed by a reasonably detailed written solution (more often than a computation leading to a number).

Best of luck.



I completely agree with your decision to go for breadth. We need our best mathematical minds to learn as much as possible, not to finish as young as possible.
Some time ago I made up a collection of links to interesting math resources.

A couple seem to be dead - I don't know what has happened to Vladimir Bulatov's page - and a few more may not be relevant. I do recommend the books on the book page. POV-Ray and Life seem to be perennial favorites among smart kids

One author I haven't (yet) included is Dennis Shasha, whose "Dr Ecco" books are challenging and well written, in the same genre as Smullyan.

Good Hunting!


Not sure how to adapt this - but here is something I did in the past with a high school student who had completed the current curriculum.
We took a translated Russian Geometry book, and Geometers Sketchpad, and explored problems for an hour or more a week.

The Russian (well almost any European) curriculum is years ahead of North American curriculum in geometry. It was challenging for both of us! I anticipate there would be comparable books for children his age.

Walter Whiteley

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