I remember when I was a kid, Kangaroo math puzzles were incredibly fun. I don't know if you can get your hands on some materials, but they were such a blast. https://mathkangaroo.org/mks/

I recommend getting some math olympiad books; at that level they're just like puzzles so should be fun.

https://artofproblemsolving.com/wiki/index.php/Olympiad_book...

Go for general problem books (non-topic-specific), and start with the easiest problems that they find fun.

I remember the following two books were interesting (though might be somewhat harder). You might find them on the internet archive or pdf's online.

Challenging Mathematical Problems With Elementary Solutions (Volume I, Combinatorial Analysis and Probability Theory) - A. M. Yaglom, I. M. Yaglom.

Challenging Mathematical Problems With Elementary Solutions (Volume II, Problem From Various Branches of Mathematics) - A. M. Yaglom, I. M. Yaglom.

Additionally, look into various olympiads:

American AMC 8 and AMC 10 from various years should be easiest:

https://artofproblemsolving.com/wiki/index.php/AMC_Problems_...

And when they feel adventurous, take a look at contests. Some countries (e.g. Romania, Russia) have contests for lower grades, though they are still quite difficult.

https://artofproblemsolving.com/community/c3754998_aops_year...

Video games often present some nice math lessons. Trying to understand why the Grief runeword in Diablo 2 did so much more damage than other items that had way bigger numbers was a great exercise in math, lol (and I didn't fully grasp it until my 20's).

Another example is card games, like Hearthstone or Pokémon TCG. For younger kids you can focus on the more basic "how much damage do you need to kill this?" or "given these coin flips, how much damage can you expect on average?", while for the older kids you can present bigger challenges like "how likely are you to start with this card in hand?" or "how likely are you to find it in the first 10 turns?", "how likely is it that this crucial card to your gameplan is going to be hidden in the prize card list?" etc. But perhaps the adult here needs to be good in card games in order to be able to grasp the math behind the game and properly teach kids.

Anyway, math is often hidden behind interesting things, which is way better than boring plain exercises.

The series of books published by Haese Mathematics used in the International Baccalaureate (IB) programs are quite good. Lots of worked out examples, practice sets and detailed answers to problems available. You can Google for free pdfs online and print the sections you need:

https://www.haesemathematics.com/international-baccalaureate...

This might work if your kid is a self-starter and really driven to improve himself/herself. Otherwise I highly recommend an extracurricular math program; there are many different ones depending on which area you are in. I know of Kumon and Mathnasium, there's probably bunch of other ones too.

They maintain their own curriculum, often somewhat in sync with school program, but ahead of it. They also help kids participate in various math competitions, including Math Kangaroo, AMC 8/10, etc.

Just make sure to carefully evaluate the program in advance, talk to the teachers and the parents. They are typically NOT cheap, but if you want your kids to get good at "maths" (R) it'll be worth it.

As a teenager who has went to one of these in the past, I can vouch. It definetly gave me a stronger foundation that other kids which has helped me a lot with physics and other interests!

Could solve Project Euler problems in Lua - aka, the easiest programming language to learn

https://projecteuler.net/

Alternatively, you could get a homeschool math textbook. They're written differently because the assumption is that the kid is going to have to teach themselves, and as such they are significantly more thorough and easy to understand. I highly recommend them. Don't get the kind that are "workbooks", those are usually trash. Find a good textbook that the kid can write in their own notebook for and sell after they're done with it. They'll learn how Ebay works, and algebra!

Many communities offer a "math circle" which also builds some mathematical community. Some can be found on https://mathcircles.org/

That is a pretty big range. A 10 year old is a year into division. A 17 year old is starting Pre-Calc or Stats.

17 was AP Calc 2. Division can be taught as early as 7, probably earlier if you’re doing enrichment at home.

Yeah, meant only as a sample. I mainly mean leaving the really introductory stuff behind. My emphasis now is ~middleschool.

Good question :) We've a similar challenge to you, kids a few years younger, despite some efforts in school by teachers, they still don't get fed enough of the cool hard stuff they're hungry for, and youngest in particular finishes schoolwork early including extensions and gets bored. So I've done some searching possibly similar to you. found this : https://ukmt.org.uk. which has some good resources. Also just purchased off eBay this weekend, the Murderous Maths series by Kjartan Poskitt. Remains to be seen how good that'll be, might be a bit young for yours, although he did write some other books possibly for older kids. Some schools here in UK use this : https://sparxmaths.com. Maybe you can use that as an individual? Main thing is make sure to keep it fun, right? Playing card games is good too I think. Ones our family played include - "Oh hell". - like a simpler Bridge, you declare how many tricks you'll make and after a round you score 1 point for each trick plus an extra 10 if you made exactly what you said you would no more no less - quite tactical especially if you plan to make 0 tricks. "Black Lady" - sometimes called "Hearts" - each Heart is 1 bad point, Queen of Spades 13 bad point, King of Spades 10 and Ace 7, aim of the game is to not win tricks containing the bad cards. Seems to me those card games teach the brain to work in such a way that helps when doing various unrelated maths problems later on.

Khan Academy is great, but for anything you’re going to need to sit down there with them. I’d start with the grade level test to see what they are missing then you can hone in on that. Or if they are missing some core concepts you can go back as many grades as you need. With an hour per day of _your_ time as well as theirs they can plow through multiple years of material in months.

I have 10 and 9 year-old kids. We don't have school homework either (by design!) so do a little math enrichment at home. Here are a few options we liked:

- MOEMS contests and practices were great for problem solving. You can buy books of previous tests, and try them. Honestly, these are fun math puzzles to solve as an adult, too. This definitely helps them learn important strategies like organizing your work, bootstrapping from simpler problems, looking for patterns, etc.

- Khan academy is fun and gamified. It also helps with computer literacy a bit. The most useful feature for me is that it can quickly identify holes in their understanding.

- Sometimes we watch Numberphile or Stand-up Maths on Youtube if the content is interesting and age-appropriate. This is mostly to cultivate curiosity.

I agree with other posters that ideally there is a "math circle" to work on these items together. Although, sometimes a "family math circle" works, too...

Hope that helps!

While this is online, the work on paper is pretty much required for harder topics. https://mathacademy.com/ starts at where your kids currently are and then they can work as fast or as slow as they need through practical exercises.

Here is a good book for some of the school-level math - https://archive.org/details/skanavii/mode/2up - in Russian.

I used Brilliant (https://brilliant.org/) with my kids and it was helpful, if only because they did try to explain some of the theory around the work in different ways. Considering your comment around videos and artwork, it might not be what you are after, but you can check out some of their free courses to get an idea of how they work.

The biggest issue for me was that it is concept based rather than curriculum based, so it wasn't perfect for trying to teach them on a regular basis, but it was helpful if we encountered a topic they didn't understand.

For a younger age group (13-15 maybe), George F. Simmons’ “Precalculus Mathematics in a Nutshell” (https://www.amazon.com/Precalculus-Mathematics-Nutshell-Geom...) is quite good though might require a bit of help to grasp. It features lots of exercises and a quite decent explanations for the age range.

Better to let them live as they would like and learn math only if they would like.

If your kids were really gifted or really inclined to learn it, you wouldn't need to research it yourself.

Around that age 10-12 they generally can use the internet and already have their own interests, and are smart enough to Google it and build stuff by themselves.

If you keep getting that much involved in their lives they will have development issues. You only get involved if they are really slow and get a professional to help.

> You only get involved if they are really slow

Was a reasonable approach in the previous century. Not clear that it will be enough these days...

The math Olympiad problems were quite fun from what I remember, even though I never got past the regional round. I bet the previous years will be available online.

Alcumus

https://artofproblemsolving.com/alcumus/problem

Probably one of the best if not the best out there. Worth every penny.

I'm just browsing the site now. Did you purchase their books, courses, other?

Yes, I have purchased their elementary level (under Beast Academy brand) as well we later books.

Have also subscribed to their online classes. Alcumus is free. I like AoPS and can recommend them.

Came here to make sure that Art of problem-solving and beast Academy are mentioned. They are fantastic. My son is deep into art of problem-solving after having finished beast Academy.

Another recommendation for Art of Problem Solving. The books even have complete solutions manuals so they're perfect for self-teaching.

https://artofproblemsolving.com/store

Try to see if they'd be using spaced repetition software like Anki to schedule review of problems they've understood how to solve.

Geometry could be fun, or elementary number theory.

Apart from brilliant.org, someone posted this website https://www.synthesis.com/tutor before, the courses are very good for kids, interesting, but the price I think is a bit pricy.

They might like https://SineRider.com which was built by a bunch of teenagers at Hack Club, a nonprofit I work for.

It’s been played thousands of times and is a super cool way of building intuition around function composition.

What kind of math homework? Word problems or just arithmetic? By 17, I think I was taught algebra, geometry, and calculus.

It would be pretty simple to create a web app that produces printable random arithmetic problems (with optional answer keys) with levers for difficulty.

Other types of problems would be harder.

Quite the variety of problems, really. I'm seeing them work on word problems, graphing, geometry, etc. The best resource I've found is https://www.math-aids.com . It's pretty close to the mark, actually, but some of the domains are just a bit rigid in their configuration so I'm scoping out anything else.

What about the PSAT and SAT prep books? They are tests only (with answers at the end of the chapter) and don't teach the techniques, but I found that my math skills got better just by doing more of it.

Suggestion: Anything that says math "problem", turn it into a math puzzle instead. A much more interesting way to look at math.

I like the IXL workbooks. They seem good enough.

+1 for the IXL ios app. My 6 y.o. son’s school doesn’t give homework and its math pace seem lagging with the standards so I supplement his math learning with the IXL app.

I like that they offer several different ways of explaining / visualizing concepts plus exercises that reinforce.

For example, my sons is starting to learn multiplication and finally clicked with the app’s visualization of how multiplication is just repeatedly adding the same number over and over again.

Mathacademy.com will curate an adaptive course for 4th grade math thru college

send them to europe

Why ?