How old are your kids?

Try to find math problems everywhere. Let's say you are making a cake (a real one, nor an imaginary one) if you must put 5 eggs in the cake and you already put 3, how many more must you add?

My old daughter used to play 6x6 sudoku. It's the closest thing to math in mainstream. Note that the strategies to play 6x6 are the same than in 9x9, but the best order to apply them is different. It's a nice game because you must make a lot of inferences and keep very clear what you really know and what you wish were true.

There are a few books with math problems for kids, but don't know any translated to English. One book that has some math stories is https://en.wikipedia.org/wiki/The_Man_Who_Counted It's doesn't have too many problems for the kid, but it has a few problems that the protagonist solves. The numbers that appear in the problems are extremely well selected to create coincidences that the protagonist must solve.

Kid is 5.5. He gets money for doing chores and saves up to buy games and toys. We look at prices online, compare, figure out what he still needs to earn. If he’s short a few dollars I’ll loan him and then it’s dealing with negative numbers. Sometimes a job will have a “bonus multiplier” and then we have multiplication.

I'd like to hear more of your stories. :)

My favorite simple math problems are found in cabinet making. It's all simple arithmetic but there is a lot of it to get a cabinet right.

One example: If you're working with 16.5mm boards and want a 600mm wide cabinet then what width is your top and bottom panel. It's a simple 600 - 2 x 16.5.

I don't know why but it's very satisfying to sit down and work out the size of each panel and the location of each dowel hole. Then to see it all become a cabinet.

Obviously this might be a bit too much as you'd be teaching wood working as well but it is a lot of fun.

I would encourage you to see math as larger than computation. But rather math as a way to model the world with numbers. That way math is everywhere and has a more casual approach.

Everything that has a rate is mathematical. Water flow, mph, # of chocolate chips per cookie, etc.

Then statistics and estimation is everywhere too. About how many? What do you estimate ____ is? Is there a way we could get more accurate with the guess?

Cooking, Buildings, Traveling, eating, nature, social media has math everywhere.

I've built things with my child, mostly carpentry; ranging from doll beds to chicken pen and furniture and some other things. Whenever possible we draw out plans and have her calculate angles and distances and work up "bill of material" lists. Practical math. Pythagorean theorem is far easier to remember when you have a real use for it (how long do we cut this brace board?).

Yeah, and programmers don’t practice logic. Got any other zingers for us?

Math, euclidean geometry specifically, is a core part of carpentry.

Core part of carpentry is functional hands, core part of math is functional brains. If doing carpentry is considered doing math, then playing some silly games also may be considered doing math. I do not recommend going that shady way of redefining definitions.

By that definition a physicist is also not doing math. Just because it's encapsulated in something else doesn't make it not math.

Not agreed. Most of mathematical universities are phys-maths or mech-math.

For kids, it's easier to make activities with applied math. So my abstract advice is to offload some of the mathly part of the activity to the kid in spite it may be obvious for the adult. It can be applied to carpentry, or cooking, or whatever is your (kid) favorite activity.

Math in cooking? It's like how many cookies will be if we add 2 cookies and 3 cookies?

The recipe says 1 cup of flour and .75 cup of sugar for 24 cookies; but we're making 18, so how much of each do we need now?

Math is everywhere. All you need to do is show it and show how it makes getting things done easier. Show the reason we have "math" to someone and they'll want to learn it on their own.

Yes! My 5 yo daughter can count up to 12 or 19, perhaps 29 with some help. But she only groks up to 5. For example she understand that 5-2=3, but she does not understand that 6-2=4. (In a story, like "There are 5 apples on a table, and I eat 2, how many are left?") She is improving, but it's slowly than what imagined before having kids.

As the sibling comment explains, for older kids proportions is a natural and important topic, but it's too much for my daughter yet. (I recommend to start doubling or halving the recipes, and later more advanced stuff like 18/24.)

I guess it's not possible to advance too much after that with kids, but there are a few nice initial activities.

What happens when you don’t involve math in carpentry?

Math is something more than Pythagoras theorem and arithmetic.

One way of saying you're not a good carpenter.

How old are your kids? Educational games have been basically dead as a genre since shovelware flooded the market in the 90s but some of the classics from companies that actually put effort into the curriculum are still the gold standard in terms of educational content to this day.

Treasure math storm[0] ages 5-9 is great if your kids can get past the graphics (in my experience most can, particularly if you make make it the only game they're allowed to play for a particular hour of the day)

I'm really sad no one's figured out a way to properly signal that their educational game took the curriculum seriously because IMO they can be one of the best ways to get kids to practice. It's a shame good educational games for kids aren't being made today :/

[0] https://www.classicgames.me/treasure-mathstorm.html

A few years back I saw an HNer recommend a "function box" game that's fun for kids. The kid tells you an input, and you tell the output. After a few iterations, the kid then guesses at what the function is that transforms the input into the output. You start with just addition/subtraction, then bring in multiplication, powers, etc., and mix-and-match.

Eventually you can swap roles, and the kid can proudly give you function boxes (usually there are some mistakes at first, but it's all part of the learning process). One interesting discovery that becomes apparent is that there are infinitely many function boxes that will yield the same result. Sometimes I would guess that my daughter's function was 2x + 3, and she would tell me that no it was "times four, divided by two, then add one then add two". We worked through how these functions are identical, even though they look very different.

Bigger picture, we try to connect learning math to being able to do things. Our older kid is very skilled at math and I have encouraged her to keep learning until she reaches her limit. But I've also made clear that the benefit of accelerating her math understanding now is not so she can become some amazing mathematician as an adult, which is very unlikely. Rather, it's so she can learn physics, economics, and all sorts of other things at a relatively young age, after having learned the math that is used in introductions to those subjects.

Lastly, we've also used Khan Academy (not KA Kids) quite a bit. The one downside to it is that it introduces a skill and then gives a quiz. This can lead to the false impression that practice is not required to master a skill. Eventually we decided that our kid had to do the quiz three times at 100% in order to move on — otherwise she'd get 100% in just one or two tries (it's mostly multiple choice), and think she'd mastered something she hadn't. This was frustrating for her, but it helped her to understand that practice is a necessary part of learning.

Beast Academy. The books, not just the practice website. Most kids love stories and characters and corny jokes and detailed Waldo-esque cartoons and cultural references. For some, that makes the “productive struggle” of learning problem solving more palatable. My elementary school kid thinks a lot about whether he wants to be like Grogg, Winnie, Alex, or Lizzie in the future.

The 1st and 2nd grade books may be too hard for many kids to read on their own (math has big words and long sentences - even curricular materials like EurekaMath seem to be written above grade level for K-2) so it becomes family reading time as well.

I had more energy with my first. On the walk to kindergarten, we would practice skip counting which she was not entirely fond of. She had memorized and internalized up to her 12s before first grade. This let us talk about groups of numbers and early division and fractions. By 2nd grade (with some problem scaffolding), she could add and subtract fractions. She never got bit by the math bug and liked boys better than calculus in high school. But she is very comfortable with basic numeracy, so I'll take it.

My favorite math memory was when in 7th grade, I thought I'd show some fancy algebra to prove that 0.999... is 1. I first asked her how it could be. A couple of seconds later, she said 1/9 is 0.111... so 9/9 is 0.999... and also 1. Waaaaay better than my method. Good job kiddo.

Another favorite 1st or 2nd grade: look at the thermometer outside. Can it get colder than zero? What does that mean? And her eyes grew big, "there are numbers below zero?!?!"

The valuable part is abstract math, thinking in symbols, not counting 2+3. A good old way to teach is to invoke a surprise, as it grabs attention, and then explain. So you'll need easy problems, but with surprising solutions. One that comes to my mind is the old story where a simple man asked a king a simple favor: put one grain on the first square of a chessboard, put twice that much on the next square, twice more on the next square and so on until the board is filled. A categorically different understanding of math happens when you learn what a proof is, but I'm not sure how to make this problem interesting.

Stardew valley: how many sprinklers do you need for this area? How many gold bars do you need for the sprinklers? How many days do you need to be in the mines for those gold bars?

And so on. You'll have them doing algebra by grade 3.

My son is 7 and plays Prodigy Maths (there is also an English version ) with account provided by school. He's so competitive with it with other kids in school and it's like an RPG with math battles and levelling up which he loves. He doesn't really play much other games so I let him play it when he wants (he also likes minecraft and I have a SNES mini). His sister (8) also has an account and is not really interested at all. They both read quite a lot.

I suggest an abacus. It's a fun way to concretize mathematic operations. You can learn to represent up to ten digit numbers on the abacus, then do addition, then multiplication and division. Once you're multiplying numbers you can start to learn shortcuts to make using the abacus faster.

I think the abacus is a fun addition. We keep one on the counter where we eat breakfast. It's fun to just pick two three digit numbers and multiply them out.

Children have much to learn about how the world works. There are many practical applications (ergo, relevant math problems) which build/strengthen basic math skills while teaching what children need to know. (Some of the books in the lie-bury will probably point in the right direction.)

Ideally the chosen practice will feature subjects individual children are enthusiastic about, and are age-appropriate.

We are big fans of Bedtime Math: https://bedtimemath.org/

When I was a kid, my dad just said flash cards with me. Everything up through division. When we'd be out in public doing errands and such, he'd quiz me while we were out. Really simple to do, and I think it worked pretty well.

Whenever I see parents doing that with their kids in public, I get a smile.

Strategy/tactical board games have a lot of math, which is the main reason I can't play them with my 3 years old

Recreational mathematics - games, puzzles and toys are what you are looking for.

Check out the Life of Fred series, those were helpful for me as a kid.

My kids are 13/11/9/7/3/1 and we homeschool. I took over math in September after the new baby came. I taught the four oldest from the Life of Fred series. The youngest was tearing through the books too fast, so at Christmas I gave her a cribbage board and we played that all spring. Her addition quickly surpassed the 9-year-old, and when we played 3-player together she would tell her sister how to work out things like 16+7.

For multiplication, King Domino is great.

I like that neither game requires reading. Century Spice Road is another one like that we enjoy.

Agricola is bigger and has arithmetic more in the background, but it has a lot of affinity with math. My oldest is decent at it. My youngest aren't competitive at all but they love just collecting big flocks of sheep. You can play without cards (the only reading), but personally I like to deal them a hand and let them ignore them if they like.

Another beautiful no-reading game with less arithmetic but plenty of affinity is Carcassonne.

My kids also get super excited about Robo Rally. It's kind of a programming/planning game. It's way more fun than that turtles game. It starts to bog down past four players though.

So I think one answer to "casual math" is playing games. You're giving them a chance to exercise their brain while having fun (and spending time with you!). No need to mention that it's for the sake of math.

Besides board games there are also puzzles. Just Saturday I brought home some books of brain teasers from Costco. These:

https://www.amazon.com/Mindworks-Brain-Training-Right-Brain-...

https://www.amazon.com/Mindworks-Training-puzzles-Bind-up-Pa...

They are much higher-quality than a lot of the math puzzle books out there. So far they seem to be really enjoying them.

For older kids, maybe read a Smullyan book together.

You can also just talk about math a lot, and if you love it you will infect them. One bedtime I explained the Bridges of Königsberg to a then-5-year-old, drawing pictures and letting her try to find a path. Even she could understand a casual proof that only the start & end locations could have an odd number of bridges.

If you tell them about negative/complex numbers a bit too early they feel like you've let them in on a big secret. The fact that high schoolers spend a year studying nothing but triangles blows their mind. I'm sort of notorious for fetching a pencil & paper in the middle of dinner to draw pictures about a thing from geometry/trig/calc/whatever. . . .