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going shopping is a great hands-on experience in using multiplication (and division) skills with a good retention rate. i.e if i buy 3 of these that are £4 each, how much will it cost? or i've got £20 to spend on art materials, how many packs of £5 pencils can i buy? and you can amp it up a little buy putting a time-limit on it too.

Or counting sushi items?

First time commenter here.

It's not a game, but The Number Devil by Hands Magnus Enzensberger would be a great book to read with him. My seven and eight year old loved it. I've also heard good things about the Murderous Maths series, yet haven't seen them yet.

And as for patterns in music, Mysterious Thelonious by Chris Raschka is a beautiful book.

The Number Devil:
https://www.amazon.co.uk/Number-Devil-Mathematical-Adventure/dp/0805057706

Mysterious Thelonious:
https://www.amazon.co.uk/Mysterious-Thelonious-Chris-Raschka/dp/0531300579

One really fun way to get into math is through programming. It may not teach the reflex knowledge so much, but it's splendid for the more intuitive and interesting stuff like probability, patterns, and growth and decay.

When I was 9 I got really into MicroWorlds, which was great but didn't connect to anything physical or shareable. Just this week I've been introduced to the Arduino USB board and am back to my 9-year-old programming self, this time with speakers, LEDs and motors.

How much math goes into the Mindstorm legos?

MicroWorlds:
https://www.microworlds.com/solutions/index.html

Arduino:
https://www.arduino.cc/

Adding numbers on car plates, but I think that's already old.

my 8 year old has just started playing with Moshi Monsters. It's a Club Penguin-esque virtual world. You create a monster and earn credits by playing daily puzzles. He's loving it so far - I'm not sure of the educational value but it's fun and the more he plays the better the puzzles are attuned to his abilities. It's in Beta at the mo but I've got a spare code if you're interested.

As far as the beuaty of numbers go it's probably preferable to avoid anything too worthy and look for things that have concepts woven into the narrative. I liked the look of the book co-written by Stephen Hawking and his daughter:
https://icanhaz.com/hawking-kids-book

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