I was asked to give extra lessons to a 5 year old boy who loves math (he says he likes 3 sports: football, swimming and math). However, I have never tought at this age and I am unfamiliar with the best theoretical way to proceed.

Hence, I would like some references on teaching at this age, particularly to gifted children.

EDIT: as requested, I did take a time with him and tried to assess what he knows. He is fluent in:

  • counting
  • addition, subtraction
  • knows fractions (in a intuitive way, he knows nothing about the notation and relation to division)
  • he knows that negative numbers are ok in math but cannot account for a 'real' thing. In his words "there cannot be -2 me's".
  • he has great intuition: knowing there's not a largest number and that infinity isn't a number either.
  • he has trouble with problems which don't have a "precise" answer- such as: "if I toss a die many times, which number will appear the most?", to which he replied "one", but could not justify why.

That's about it; as mentioned, I am not even sure how to properly assess what he knows, so everything helps.

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    $\begingroup$ I just wanted to comment that your assessment is an incredibly impressive snapshot. :) $\endgroup$ – Chris Cunningham Apr 29 '15 at 18:41
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    $\begingroup$ How about teaching to make a "bank" (with some loose change) as a way to teaching him negative numbers? He can keep track of "deposits" and "loans". $\endgroup$ – Michael Joyce Apr 29 '15 at 22:31
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    $\begingroup$ May I recommend my math activities gallery? matheducators.stackexchange.com/questions/4448/… $\endgroup$ – Marius Kempe Jul 28 '15 at 12:00

I would recommend "math enrichment" instead of straightforward math acceleration.

(1) Here is one source from the US Florida school system: Math SuperStars (a.k.a. Sunshine Math). It covers grades K-5, and contains weekly problem worksheets. It is a bit too problem-based (rather than project-based) for my tastes, but at least it gives you a consistent set of problems at well-defined developmental levels.

Here is a snippet from 1st-grade, week 5:


(2) For a project, I might suggest building the Platonic solids with polydrons or their functional equivalents, and seeking & noticing patterns. Of course lurking beyond is $V-E+F=2$.


  • $\begingroup$ Yes, I totally agree with you. My intention is to mainly make him cultured in all aspects of math I can teach him. I am pretty sure that later he will be able to accelerate himself. $\endgroup$ – Lucas Virgili Apr 29 '15 at 21:23
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    $\begingroup$ +1 definately, also @LucasVirgili check out these question and answers for some interesting problems and ideas that i think would be appropriate to push this young mans mathematical mind :) matheducators.stackexchange.com/questions/7394/… and matheducators.stackexchange.com/questions/4448/… $\endgroup$ – celeriko Apr 29 '15 at 21:32
  • $\begingroup$ wow, I really want those polydron kits! but they are so expensive! @celeriko I'm using those already, thank you! $\endgroup$ – Lucas Virgili Apr 29 '15 at 23:56
  • $\begingroup$ @LucasVirgili: I have to purchase them from the UK, so the shipping (to the US in my case) adds to the expense. $\endgroup$ – Joseph O'Rourke Apr 30 '15 at 0:06
  • $\begingroup$ @JosephO'Rourke I live in Brazil :( Shipping here is so expensive... $\endgroup$ – Lucas Virgili Apr 30 '15 at 0:20

Three books you can read with your young student:

The Cat in Numberland. After reading it, you get to discuss orders of infinity.

The Man Who Counted, by Malba Tahan. (Do you and your student speak Portuguese together? This was originally in Portuguese; the author is Brazilian.) As you read each episode, try to predict what Beremiz will do to solve the dilemma.

The Number Devil. Lots of intriguing math concepts explored.

  • $\begingroup$ Yes, we do speak Portuguese. I believe now that I am going to read Tahan's book with him. It should be a nice way for him to practice his reading too! Thank you. $\endgroup$ – Lucas Virgili Apr 30 '15 at 11:48
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    $\begingroup$ De nada. Agora eu 'tou pensando em leer-lo em portugues, pra melhorar meu vocabulario. $\endgroup$ – Sue VanHattum May 1 '15 at 4:50
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    $\begingroup$ Also, my book, Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers might offer some inspiration, though it's not exactly what you're looking for. It's here: naturalmath.com/playingwithmath And some day I'd love to get it translated into Portuguese, to share with my Brazilian loved ones. $\endgroup$ – Sue VanHattum May 1 '15 at 4:51

I was impressed by some of the material used in the first and second grades of my son's elementary school in the USA, where I suspect the material comes from the recent Common Core standards. There were some basic enumeration problems ("How many ways can you attach three squares together on their sides, so that the whole side is shared by the squares?") that were open-ended. (I get five if the squares are rigid and I get to use three dimensions.) The best part though was to get them to explain why, and show their work. Ambitious for second grade even, but starting good habits sooner is usually a good thing.

I recommend puzzles and other things come from discrete math. He may not be ready for Fibonacci numbers and binomial coefficients, but some of the ideas leading up to them it seems he can handle.

I also recommend Adrian Paenza. I imagine he has some resources available that might interest your student.

Gerhard "Oh, To Be Five Again!" Paseman, 2015.04.29

  • $\begingroup$ Thank you! Will look Paenza. $\endgroup$ – Lucas Virgili Apr 30 '15 at 2:08
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    $\begingroup$ Of course, if you glue two faces together, you get more arrangements. Gerhard "I Think That's Cheating Though" Paseman, 2015.04.29 $\endgroup$ – Gerhard Paseman Apr 30 '15 at 2:08

Have you tried KenKen puzzles? For those unfamiliar with them, these puzzles require logic and arithmetic operations to solve. One of the best sites is here. You can choose puzzles of different levels of difficulty with different combinations of the four operations. I have had a lot of success using these puzzles with first through fifth graders.

This edit/addition is in response to a comment. In first grade I usually introduced addition only puzzles to my gifted class. I started with 3 numbers in each row. Students who caught on quickly were given a book and many of them enjoyed working on it independently. The book's puzzle increase in difficulty and the number in each row go from 3 numbers to 6 numbers. Some students needed guidance and weren't ready to work independently; even those children could figure out what was missing with well framed questions. All the children enjoyed it and those who earned a book by completing several puzzles were very proud.

  • $\begingroup$ Have you seen bright five year olds do such puzzles? I agree that they can be an item to inspire interest, but it would have to be a pretty special first grader for me to share such puzzles with them. Five years of age is a bit of a stretch. Can you say something about the first graders you saw doing them? Gerhard "Might Do It At Six" Paseman, 2015.07.24 $\endgroup$ – Gerhard Paseman Jul 24 '15 at 22:58
  • $\begingroup$ The easiest KenKen puzzles involve only addition of the digits 1, 2, and 3 on a 3x3 grid (aside from the condition that no digit is repeated on each row or on each column), so I think a 5-year old can do them. (I haven't tried it, though.) $\endgroup$ – Joel Reyes Noche Jul 25 '15 at 13:17

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