Hacker News Books

I can second this, with a minor caveat. My daughter (third grade) loves these books, and we get a lot of good problem-solving into the curriculum as a result. The caveat, in my opinion, is that they don't provide enough cyclic review in their default configuration.

Each chapter includes 80-100 problems, divided in to usually between 4-8 sections. The problems are great, but once a section is complete they're weak on later refreshes. I've been working around this by doing even-numbered problems the first time through a section, then half of the odds a few days later when we're a couple of sections downstream, then selecting randomly from all of the unfinished problems in the entire curriculum for just a couple of extra "old stuff" problems each day throughout the year. We also supplement with a number of other great resources, if you're looking to implement a more problem- and exploration-oriented math curriculum:

1. Kitchen Table Math is great for selecting concepts to lead number talks with (for building number sense - this is the first part of our day)

2. Saxon has excellent spaced-repetition exercises for shoring up the calculation side of things, and giving the student some easy wins for confidence building (we typically use Saxon's material as a warmup before Beast Academy)

3. Thinking Mathematically (the one by J. Mason and L. Burton) has a unique and useful mental process for attacking hard problems when you're not handed a nice formula to plug things into. Once a week, we work through a hard problem using the method in this book.

4. I haven't worked it in yet, but Arthur Benjamin's "Secrets of Mental Math" has a lot of stuff in it that will solidly connect arithmetic and algebraic thinking later.

Assuming a uniform distribution, the probability is 1/365 for any person#. Those probabilities add up linearly if the people are guaranteed to have different birthdays (union/OR). Otherwise the probability of NOT having someone with the same birthday goes down exponentially as a an exponential power of the fraction 364/365 (intersection of complement/AND NOT)

It’s exactly what you would expect from classical combinatorics with cards with or without replacement. Your term “confident” is vague.

I produced a series called Thinking Mathematically on youtube that makes all of this and other related topics clear for anyone... I recommend checking it out!

https://m.youtube.com/channel/UCuge8p-oYsKSU0rDMy7jJlA

And here are the notes for it

http://magarshak.com/math/numbers.pdf

http://magarshak.com/math/sets.pdf

http://magarshak.com/math/logic.pdf

# if we exclude all people born leap years

A few years ago, I was teaching a class and decided to record a short series on the fundamentals of mathematics, for complete "beginners" - whether they be kids or adults.

This is the first video in the series Thinking Mathematically (after the introductory video, "Why think Mathematically?") which I put on YouTube under a channel of the same name. It proceeds through the sets of numbers, N -> Z -> Q -> R -> C and yes it's for beginners. Would love some feedback:

https://www.youtube.com/watch?v=Wd1lzqR3xW0

The other videos you'll find on that channel are:

  1. Why think mathematically?
  2. Numbers and Algebra
  3. Sets and Infinity 
  4. Logic and Probability

Here is the channel with all the videos. They might be useful to share with people who you want to understand these concepts from the ground up:

https://www.youtube.com/channel/UCuge8p-oYsKSU0rDMy7jJlA

(PS: I am generalizing this approach in our upcoming app, https://teaching.app)