How do I start teaching my 1.5yo nephew math?

Language acquisition and physical activity are much more crucial at that age. A little counting is ok if it involves physical activities. Kids should be playing, especially with other kids through age 6. Reading and talking with them too. But by age 2 you need to be asking them open ended questions.

Just let him be a kid.

You want to focus on number theory, not math. Think about things like "this stack has more blocks than that stack" or "let's make stacks of the same size".

You could make 2 equal groups of blocks (e.g. 3 each), then move a block from A to B and show that B has more blocks now. Or create 2 unequal groups of blocks and have them add blocks to make them equal.

Or have containers with different quantities in them, or of different sizes, and have them arrange them in order.

That will be plenty of effort for just 1wk with a 18mo child. I have a child of the same age - they have amazing interest in things around them and very good memory, but teaching concepts takes focus and attention which they don't have as much of.

As others have said, at this age just playing and exploring (and love/attention) is the best thing you can do for them. Studies have shown that math can easily be picked up much later (age 4-5) without detriment.

Know what, brother? I tell you that studying the humanities in high school is more important than mathematics — mathematics is too sharp an instrument, no good for kids.

Stephan Banach quoted by Steinhaus in Through a reporter’s eyes, Roman Kaluza, 1995

I think 1.5yo is too young for maths. When they get a bit older - fun board games with maths mechanics (probabilities, dice rolls, etc.)

I have some positive experience with using this book [1] to older students, I hope you can use your smartphone to translate it from Russian. The book is very much about sets which are shown as bags. It is supposed exactly for math geniuses as I can judge. I do not think showing this book from the screen is a good idea not only because it is on foreign for you language but also because it requires student to write down in it. But you can print a few translated by you pages or maybe recreate the illustrations with a real-world examples (bricks with letters, toys of defined parameters such as color, shape, type of entity etc, arranged in clearly visible groups).

Also if you play music try to return to the very roots of our civilization and explain Math like Pythagoras did - using consonance/dissonance of two strings with defined relative thickness/length.

And please do not introduce him to smartphones! If the parents did that (which is highly likely nowadays) at least do not show the kid that you have it somewhere in your house or your effort will be wasted!

[1] https://file.11klasov.net/1733-matematika-1-klass-uchebnik-c...

PS. The first task requires you to see what are rows, what are columns and a way of visualizing 12345, I tell you this because it was hard to me when I first time opened the book.

Take a visit to an educational supply store... there are a lot of tangible math games for very young kids. One that works well at very young ages is a physical balancing game. You get a balance and a variety of tokens (some that look like blocks or small animals, etc.) and some that look like actual numerals. The numerals have the same weight as the same number of tokens. So kids can put the number 3 on one side of the balance and then learn that they have to stack 3 tokens on the other side to make the balance balance. You can also ask questions, e.g., you can place the number 3 on one side of the balance and then one token on the other side and ask them to predict how many tokens need to be added to that one token to add to the number on the other side. And you can make it progressively more complex, e.g., stack the number 3 and number 2 on one side of the balance and then let kids figure out how many individual tokens need to be stacked on the other side to amount to the sum of 3 and 2. The pivoting action of the balance tends to keep kids' attention (but be realistic about the attention spans of young kids... we're talking under 15 minutes a session).

Anecdotal, but I think my son's math skills owe at least as much to the Numberblocks videos [0] as they do to my math degree and insistence on showing my kids some related interesting thing whenever they have a math question.

[0] https://www.youtube.com/channel/UCPlwvN0w4qFSP1FllALB92w

I suggest watching the entirety of the Feynman Lectures on Physics together. It should be some very light content for a 1 year old!

How about reading him "Quantum Physics for Babies"? Or "General Relativity for Babies".

https://www.csferrie.com/book/baby-university-board-book-set

Even with a whole week I fear 1.5 is far too old to catch up.

It's too early for this but when he's old enough for videogames get him Kerbal and/or Factorio. Not math per se but technical thinking games (and if he gets obsessed enough with Kerbal he'll have to break out the math).

Why? He's a child. Apart from counting with integers, his tiny brain is too undeveloped to be worth your time and angst, just yet.

Heinlein - "Never try to teach a pig to sing. It only wastes your time and annoys the pig."

Not sure if Lego is appropriate for a 1.5 year old (I would guess not), but growing up I didn't have many toys but one thing I played with the most, was a pathetic looking lego set.

I'm not talking the fancy stuff you get nowadays with wheels/pullels or where you can build the Millennium Falcon (I was so envious), but about 50 4x2 different coloured bricks and maybe 5 6x1 long ones.

But man, the amount of creativity that sparked in my younger cell was amazing. The amount of crudely built spaceships I built kept me entertained for hours.

Constraints breeds creativity. A lesson I still try and apply to by daily life/work.

Assuming your goal of turning your 18-month-old nephew into a genius is tongue-in-cheek, and that you just want to lay some groundwork for numeracy, I'd say add in some number words in your play together. Make trades, make up puzzles and if they aren't fun don't sweat it, move on. Be a caring, attentive, curious, kind, and intellectually humble adult in this child's life.

Look up Maria Montessori—she pioneered a structured and tangible way for kids to learn math concepts.