I should have been clearer. a|b + c| != |ab + ac|. It’s not always true.

So if you have |-2x+4|, you’d have to factor out the -2 within the absolute value |-2(x-2)| and then that becomes 2|x-2| which, if you distribute it back over is |2x-4|. But -2|x-2| wouldn’t yield that result. So I’d rather teach them how to factor out a common term from a function but not distribute it, since the there are only a few times it kind of works, like if the term is positive and the function is absolute value.

]]>Yep! But |3x+15| = 3|x+5| is true.

]]>Integrating math has always, but always, failed in America. Not just in popularity, but also as demonstrated by learning and test scores. We don’t stop teaching kids math in high school, while Europe tracks.

]]>Glad you enjoy it. I would never mark down a kid for distributing over a function, but it’s *incredibly* important kids understand they can’t distribute over a function. Just because somehting might be true doesn’t mean it’s not false. that is, 3|x + 5| = 3x + 15 is, I believe, a false statement, right? (I hate formal logic.)

]]>In general, they seem to know math very well, at a level above even other American math teachers. This is anecdotal, of course.

However, I do wonder if the Swedish guy was right in claiming that integrating math early on can help with a broader degree of understanding of algebra? Because the Soviet curriculum integrated math, including algebra, at a much slower pace at much earlier grades, which might make it a lot more accessible to a lot more people than dumping all that abstraction on kids in grade 9. ]]>

3|x+5| is in fact equivalent to |3x + 15| but this wouldn’t be the case with -3. So while you shouldn’t necessarily point this out to students proactively so as not to confuse them, it wouldn’t be proper to mark down a kid who distributed in that particular instance (or any always positive number/expression instead of 3). (You can see this because |a|*|b| =|ab| for any real a,b.)

]]>The power laws are far beyond repeated multiplication, so while everyone does think of it that way, it’s not helpful in moving to the more complex laws.

]]>Uh, sure. But either way, it’s the same basic process; I’m sure you’d agree that 3^2 is (3)(3) and (x+2)^2 is (x+2)(x+2). My point is that it’s helpful to think of it in that way, at least on a basic level, to understand what’s actually going on (and thus why you can’t distribute coefficients or treat exponents like coefficients). At least, I think it’s helpful.

]]>When we refer to exponents, we’re usually referring to pure multiplication. Squaring x+2 is referred to as binomial multiplication.

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