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[quote=Anonymous]He sounds so much like my daughter (now grown).  Around the time of her fourth birthday, she started shocking me with the math she'd come up with.  We were driving in the car when she announced, "Mommy, I have a new way to count", and started listing the odd numbers.  A few blocks later she decided to count by the wven numbers (she didn't know the concepts of even/odd).  Over the next few days she came up with several new ways to count (skip counting by 3's, 4's, etc.).  I soon realized that to her numbers were basically another kind of "toy" to play with.

I think you're great for encouraging your son's interest in math, but would discourage you from getting him a calculator.  A calculator is a black box that's less about math and more about pushing buttons.  Until my daughter got past Algebra, she wasn't allowed to use one for homework unless she got my permission for her specific assignment

Does your son know all the numbers (names and symbols) to 100?  With my daughter, we'd done occasional counting around the house, and she'd watched Sesame Street, but that hadn't gone anywhere near 100.  I printed out a 10x10 grid of the numbers 1-100 and explained the patterns to her.  For the sake of clarity, I slightly modified the names I taught her so that we called thirteen "threeteen", fifteen "fiveteen", twenty "twoty", thirty "threety", fifty "fivety".  While it appalled my teacher mother-in-law, it made it very easy for my daughter to understand and remember the names.  They were similar enough to the conventional names that over time as she heard the conventional names, she adopted them and within a couple of years she'd forgotten we had used modified terms.

We got a Bingo set and used Froot Loops as tokens, that she was allowed to eat afterwards.  Since we didn't normally eat sugary cereals, she loved this game and we'd play it for years (long after she learned her numbers).

Once he can count to 100, teach him how to count money.  For my daughter I printed a 10 by 10 grid with squares large enough to hold a quarter.  I shaded each block of 25 with a contrasting color.  I changed the text color for multiples of five to red. Then she could lay the money on the grid to count it out.  You can buy play money for kids, or let them use your spare change.  Once my daughter could count money, we started giving her a weekly allowance of $1.00 in random change that she had to count out.  I think playing with money (whether or not they keep it as an allowance) is great for math.  It deals with counting, place value, addition, subtraction, and provides an introduction to multiplication.

Get him an analog watch.  They make teaching models:
https://www.amazon.com/teaching-time-watches/s?k=teaching+time+watches

Initially, I thought teaching time would be easier than teaching money.  I got workbooks that I thought would help.  My daughter hated the workbooks, so they got dropped.  She was mu h more interested in learning money than time, so we did money first and then time was pretty easy for her.

Play games with him.  Prerty much every game has some math component (counting moves, keeping score, etc.)  My daughter loved strategic games like Connect 4, Checkers, Chinese Checkers, etc.  Some games have more direct connections to math.  When your child is ready for basic addition, Sleeping Queens is excellent (despite the name, I don't think it's excessively girly).

Give him a tape measure so he can measure things around the house.

Cook with him.  Cooing/baking is an outstanding introduction to fractions.  You can also double or halve recipes.

Buzz is a verbal math game where you count and replace the numbers in a chosen pattern with the word buzz. For example, if you select the rule to be numbers with a 3 in them then when you reach numbers like 3, 13, 23, 30, 31, 32, . . . You say the word buzz. This game is flexible because you can change the rules to match whatever the child is learning (even/odd, multiples, primes, squares, Fibonacci numbers, etc.) You can also mix and match rules (all numbers with a 7 and multiples of 5).

The National Library of Virtual Manipulatives allows kids to play around with different math concepts:

http://nlvm.usu.edu/

Hoagies has links that offer enrichment for all subjects. Here's the math page (for all ages, some links he won't be ready for yet) and the page for young kids (different subjects, not just math)

https://www.hoagiesgifted.org/math.htm

https://www.hoagiesgifted.org/young_kids.htm

Things that your son might not be quite ready for yet, but to keep in mind:

Cyberchase on PBS is a fantastic animated show exploring math concepts.

Zoombinis is a computer game that involves a lot of logic puzzles, looking for patterns, etc. (Things related to mathematical thinking,  if not necessarily arithmetic).

Sir Cumference books by Cindy Neuschwander introduce geometry concepts in the framework of a story.
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