My 5 year old son knows a lot of math for his age. He seems very interested in exploring it further (e.g. making up his own math problem, asking questions, etc.) We gave him a few Kumon books, but they are quite repetitive (and I don't want to associate math with boring in his mind.) I'm trying to spend time with him and show him interesting things (e.g. geometry, negative numbers, fractions, roman numerals, playing board games, etc.) but I can't be with him 100% of the time. Do you know any good, interesting math books / workbooks for young children, that encourage problem solving, thinking, and the love of math? Ideas for home-made activities are welcome too.<p>Thank you!
Cuisennaire blocks / rods are useful to show fractions etc. available in wood or plastic. Here's one cheap set but many others are available. <a href="http://www.woodentotsmk.co.uk/Library/0330%20cuisinaire%20rods.htm?gclid=CMuL9eeB77ECFSsntAodB0QA7w#" rel="nofollow">http://www.woodentotsmk.co.uk/Library/0330%20cuisinaire%20ro...</a><p>Pound o dice: you can buy a pound (weight) of dice with diiferent numbers of sides from amazon and ebay etc. these are usually Chessex (a quality brand). They are bright and shiny and fun. Don't eat them. You can work out your own dice games and problems. Button men is a simple quick game to play <a href="http://en.m.wikipedia.org/wiki/Button_Men" rel="nofollow">http://en.m.wikipedia.org/wiki/Button_Men</a><p>Use estimation in everysay life - how many bricks in that wall, how many leaves on that tree, how many cookies in the packet?<p>Rules and tape measures are fun and lead to simple arithmetic. How many cm taller is A than B?<p>Math teaching techniques might be different now than when you were taught. Heres a good book
<a href="http://www.amazon.co.uk/gp/aw/d/0224086359" rel="nofollow">http://www.amazon.co.uk/gp/aw/d/0224086359</a>
Dreambox is a good online option for self-directed math exploration. Otherwise the best results will come from interaction... be prepared to answer lots of questions, and ask lots of interesting questions.<p>There are plenty of fun games you can introduce, one of my favorites is graph-paper racing: <a href="https://en.wikipedia.org/wiki/Racetrack_(game)" rel="nofollow">https://en.wikipedia.org/wiki/Racetrack_(game)</a> Also Monopoly or any money-based game where you can learn to make change. Set and Quirkle are good logic-based games. I'm experimenting with some tabletop gaming with my 7yo, starting with Battletech quick-start rules. It's a hit so far. Not very challenging math-wise, but a lot more fun than Monopoly. :)
Life of Fred is pretty entertaining. Though you may need to read the stories to your son. Teaching Textbooks, my older daughter's favorite, has video tutoring. Singapore Math is good, too. There are programs you can look for that have lots of manipulatives. Don't recall the company names.<p>Learning how to use an abacus was something the kids enjoyed and helped with ways of thinking about numbers quite a bit.<p>You may find researching what home schoolers are doing for math programs helpful.
The Miquon Math materials<p><a href="http://miquonmath.com/" rel="nofollow">http://miquonmath.com/</a><p>have a playful spirit of exploration and go well with the Cuisennaire rods already recommended by DanBC, a recommendation I heartily agree with. My children all began their initial math instruction with the Miquon Math materials, and my oldest son, grown up and working as a hacker, definitely benefited from playing around with mathematics a lot as he grew up.
Our 5yo and 8yo have been playing DragonBox a lot to learn algebra: <a href="http://www.dragonboxapp.com/" rel="nofollow">http://www.dragonboxapp.com/</a> and it has been a great way to teach complex concepts to younger kids. We always try to find some fun apps and online games that has a dual purpose plus we always have a whiteboard at the ready to explain what they find perplexing.
Art of Problem Solving is a good web site for math enthusiasts, and their "Beast Academy" books may interest your son. A math curriculum I like is Singapore Math.<p>I suggest searching the Davidson Gifted Forum <a href="http://giftedissues.davidsongifted.org/BB/" rel="nofollow">http://giftedissues.davidsongifted.org/BB/</a> for posts about math resources and posting there.
You do not need to be by his side. Math requires a lot of personal, intimate, lonely thinking.<p>Many problems can be formulated in just a few words. You apparently have some mathematical culture yourself, so just give him a handful interesting problems, at the edge of his intellectual reach, and let him wonder for some time.<p>When he was a child, Gauss discovered by himself the formula for the sum of integers from 1 to n, because his teacher asked him about it for n=100.