math recommendations for a 3 year old

I was recently asked for suggestions by a parent of a 3 year old.

There are a lot of different resources I could suggest, but they really depend on the child and the parents. The main question for customization is about the parents: what are their starting assumptions about math/math learning and how much do they want to engage on selecting/planning activities?

For example, if a parent doesn't really get the growth mindset, I would advise a heavy dose of Jo Boaler. If the parent wants open explorations and can build their own specific tasks, maybe the Vi Hart videos are good inspiration.

That aside, there are a few resources/products good enough that I’m willing to give blanket recommendations:

1. Lots of tools for measuring. Playing with measuring has so many benefits, I can’t list them all, but some of the highlights are (a) seeing math and numbers all around us, (b) tactile engagement, (c) inherent process of comparison, and (d) natural connection with language as the kids and parents talk about what they are measuring/why. The links I've provided just show examples, I am not necessarily recommending them over other versions.
1. Set of plastic measuring cups (imperial units and fractions)
2. Tape measure (we just used standard adult tape measures, but as a recommendation, you need to be careful about tape measures that have fast return springs for cutting or catching small fingers)
3. Balance scale and set of standard weights (this math balance is a good option and one we bought)
4. Timer (we liked this one)
5. For older kids, a step counter, GPS wrist-watch showing speed, thermometer, pH meter, electricity meter are all interesting additional measuring devices.
2. Talking Math with your Kids:
1. E-book
2. Blog. I recommend reading all the posts, I think they are a superset of the material in the e-book, so this is a better resource unless you want the “curated” highlights. This link goes directly to posts tagged 3 years old.
3. Tiling toys and shapes book in the TMWYK store. I particularly like Which on doesn’t belong? A better shapes book.
3. Denise Gaskin’s Playful Math books: these talk about general habits and methods in an intro section, then specific activities (mostly games) in the rest of the book.
4. I got a lot out of these storybooks (free to print) with my kids: CSMP Math Storybooks.
5. Standard gambling tools: playing cards and dice (I like pound-o-dice for the assorted colors, sizes, shapes)

There are some computer games/systems, a lot of board games, and mechanical puzzles, but the stuff above is where I think parents should start for young children.

What do you think of my recommendations? Any additions you think are worth adding to make a top 10?