Also, this may not be relevant to many of the parents on here, but I tutor (math) in HS, and it's easy to see which kids had elementary school teachers who didn't like, or weren't really comfortable teaching math. I'd be concerned about having parents who are not themselves reasonably comfortable and fluent in math teaching it to their kids -- there are a lot of places where math education breaks down, but around 3rd/4th grade where we want kids to have a reasonably fluent understanding of basic arithmetic is a really importing point.

This means, for instance, that we'd expect a (5th grade) kid to be able to use several tactics to complete an arithmetic problem.

26*24 without paper is a good one to think about: you can re-group into

(25*4)*6 + 24, for instance, or

(26*20) + (20*4) + (6*4), or

possibly count by 26s, or

tons of other ways that I'm not thinking of. Or you can always resort to pencil and paper and use the algorithm we learned a million years ago, multiplying column by column...

Or my kid could just take out her phone and type 26*24 into the calculator app and immediately know the correct answer. :)

You're right, though. It's good for children to learn multiple strategies to enable them to think on their feet and at least come up with approximate answers without having to always resort to paper and pencil or a calculator.

Every day, I talk with my 9 year old daughter about short cuts she can use to figure things like that out. For example, we're constantly having to convert currencies in our heads. Every time we move to a different country, which uses different money, we have to come up with short cuts to help us approximate how much things cost without always having to get out a calculator to figure it out exactly.

We're also constantly having to calculate times in different parts of the world. Our nine year old often asks me to help her figure out things like, "If it's 5pm now in Malaysia and we're thirteen hours ahead of Memphis time, will my friend Alana be awake yet to play Minecraft? Okay, if Alana's still sleeping, what about Ruby in Melbourne? Melbourne is three hours ahead of Malaysia time, and Ruby has to go to bed by 10pm. If Alana wakes up at 7am Memphis time and Ruby has to go to bed at 10pm Melbourne time, how many hours will the three of us be able to play Minecraft before Ruby has to go to bed?"...

TBH, though, many times it's just easier to pull out my phone and look at the world clock app than it is to try to remember, "Okay, Auckland is five hours ahead of Kuala Lumpur and Melbourne is two hours ahead of Auckland, and I think Miami is thirteen hours behind KL, so how many hours is Auckland ahead of Miami?" WTF? I'll just look at the app. :)